Spatial count data, such as remotely sensed vegetation wildfire counts, exhibit strong spatial spillover effects, yet conventional non-spatial Poisson models cannot account for such spatial dependence, yielding inconsistent and inefficient parameter estimates. Existing spatial transfer learning methods employ auxiliary source datasets to mitigate the ”small-n” problem in target domains; however, most of these methods typically assume error-free response measurements, and thus overlook ubiquitous systematic measurement errors caused by sensor limitations or reporting inaccuracies. This study develops the Selective Transfer with Measurement Error Correction (ST-MEC) framework to address contaminated count responses in spatial autoregressive Poisson (SAR-Poisson) models. We first derive a corrected log-likelihood function to rectify the estimation bias induced by these errors. To reliably combine knowledge from informative domains, we then propose a two-step penalized estimation procedure coupled with a spatial parametric bootstrap source detection mechanism. Furthermore, we incorporate a model averaging strategy to mitigate the model uncertainty inherent in high-dimensional variable selection. Extensive simulations and an empirical application to Chinese vegetation wildfire datasets demonstrate that the proposed method consistently recovers spatial effects and regression coefficients with higher accuracy than conventional approaches. By jointly addressing response measurement error and model uncertainty in small-sample, spatially dependent datasets, this framework provides a robust analytical tool for complex geospatial research.

In high-dimensional, small-sample settings, traditional principal covariate regression often suffers from overfitting and limited interpretability. To address these issues, we propose Transfer Learning for Sparse Multivariate Principal Covariates Regression (Trans-SMPCovR), which integrates transfer learning with sparse variable selection, and develop two variants: an idealized Oracle Trans-SMPCovR for settings with known informative auxiliary domains and a practical Trans-SMPCovR with relevance-aware screening for settings in which auxiliary-domain informativeness is unknown. Under the representative high-dimensional, small-sample simulation settings considered here, both transfer-learning-based methods improve predictive performance and structural recovery relative to the no-transfer baseline, with substantial gains in prediction accuracy and marked improvement in Tucker congruence; paired comparisons and bootstrap confidence intervals further support these improvements. Additional heterogeneity-gradient experiments show that Oracle Trans-SMPCovR performs best when auxiliary domains are highly similar to the target domain, whereas Trans-SMPCovR is more robust as cross-domain heterogeneity increases. In the Pittsburgh Common Cold Study, Trans-SMPCovR outperforms the no-transfer baseline, while the Oracle version is more sensitive to domain mismatch. These results suggest that Trans-SMPCovR provides a practical and robust framework for high-dimensional, small-sample, multi-source data analysis.

In the high-dimensional modeling problem of proportional response variables, how to achieve effective prediction and stable estimation with a limited number of target samples has always been an important topic in statistical modeling and transfer learning research. Based on the Beta regression model framework, this paper presents a two-parameter transfer modeling method that integrates Lasso regularization and multi-source transfer learning ideas. In response to the problem that source-task heterogeneity may cause negative transfer, this paper designs a likelihood transferable source detection algorithm, evaluates the transfer effect through threefold cross-validation, selects the source tasks that are beneficial to the target task, and jointly constructs the transfer model. In the simulation experiment, this paper assesses the performance of the proposed method under different transfer intensities and compares it with multiple benchmark methods to verify its robustness and effectiveness. This paper conducts an empirical study based on OECD regional well-being data, focusing on verifying the effectiveness and superiority of the proposed transferable source detection mechanism in migration modeling. The results show that the method proposed in this paper has strong transfer ability under small sample conditions, can effectively avoid negative transfer risks, and maintain high interpretability and stability while improving model performance.

Deep learning is known for its exceptional ability to tackle complex problems and handle large-scale data. Its primary strengths include automatic learning of intricate data representations without the need for manual feature extraction, as well as managing nonlinear relationships and vast datasets. To utilize the advantages of deep learning in capturing complex structural features in feature space, we investigated the variable selection issue in a likelihood-based nonparametric spatial autoregressive Tobit model and introduced the NSTVSNet algorithm. This algorithm combines the sparsity of lasso with the nonlinear approximation capability of neural networks, integrating lasso penalties into residual networks with spatial effects for feature selection. By introducing a set of auxiliary variables, the variable selection problem is transformed into a parameter optimization challenge. Simulation experiments and real-data analyses demonstrated the effectiveness of our approach.

Spatial autoregressive (SAR) models become difficult to use when the response is non-Gaussian, the target sample is limited, and the fitting procedure is required to include privacy-oriented randomization. This paper proposes the TranSAR_BC_DP framework, which combines joint Bayesian Box–Cox–SAR estimation, source-aware transfer learning, and a final Gaussian-perturbed fine-tuning stage with explicit Rényi differential privacy (RDP) accounting. The transformation parameter, spatial autoregressive coefficient, regression coefficients, and innovation variance are estimated jointly under positivity, full-rank, stability, and non-collinearity conditions. A practical local-identifiability condition is stated in terms of the rank of the joint sensitivity matrix for (λ,ρ,β), and representative fits are evaluated using the numerical rank and scaled smallest singular value of its column-normalized form. The use of proper priors yields a well-defined finite-sample posterior under the stated assumptions. Candidate source domains are screened by residual-bootstrap comparisons. The empirical support count is converted to a one-sided binomial sign-test p-value, and the Benjamini–Yekutieli step-up rule is used to control the false discovery rate under arbitrary dependence among candidate-source tests. Retained sources are weighted by the Spatial Autocorrelation Congruence Index (SACI), a bounded score that combines normalized spatial autoregressive strength with fixed-dimensional bounded descriptors of the spatial weight matrices. The final noisy-gradient kernel uses Poisson subsampling, per-record clipping, Gaussian perturbation, and explicit RDP composition. Its formal (ϵ,δ)-DP guarantee requires the transformation, feature-standardization constants, source-selection quantities, transfer summaries, spatial contextual inputs, and initialization either to be fixed independently of the protected records or to have been produced by separately privatized mechanisms whose privacy costs are composed. In the reported benchmark pipeline, several upstream quantities are estimated from the same target data; consequently, the reported ϵ̄ values quantify the accountant-calibrated final-stage perturbation and are not presented as an end-to-end DP guarantee for the complete implemented pipeline. Experiments on synthetic data and county-level COVID-19 mortality data illustrate the statistical and final-stage perturbation–utility behavior of the stage-wise procedure. In a representative ablation comparison, TranSAR_BC_DP reduces RMSE by 70.4% and residual Moran’s I by 78.6% relative to Standard SAR. In the California application, the finite-perturbation fit indexed by the nominal final-stage accountant level ϵ̄=0.5 attains a model-specific utility preservation rate of 95.3% relative to the matched non-perturbed version of the same architecture. These empirical values describe the evaluated benchmark configurations and are not interpreted as universal performance or legal-compliance claims.

This paper proposes a spatial autoregressive hybrid quantile–expectile regression (SARHQER) framework for modeling conditional distributional features in the presence of spatial dependence and distributional heterogeneity. The proposed method combines the quantile and expectile losses through a hybrid quantile–expectile loss, and uses a tuning parameter γ∈[0,1] to control their relative weights. It therefore provides an adjustable compromise between quantile-type robustness and expectile-type smoothness. To address the endogeneity of the spatial lag term WY, this paper adopts a two-stage estimation procedure based on instrumental-variable projection and a control-function correction, and uses SARHQER-CF as the primary implementation. Theoretically, identification, consistency, asymptotic normality, and local convergence of the Newton-type algorithm are studied under a fixed (τ,γ) framework. When γ(τ) is selected from a finite candidate set, the corresponding inference is interpreted conditionally on the selected value of γ. Monte Carlo simulations show that the relative performance of the competing methods varies with the error structure, the strength of spatial dependence, and the evaluation metric, and that SARHQER-CF provides a compromise in several moderately heavy-tailed settings. An empirical analysis of California housing data shows that SARHQER-CF has standardized out-of-sample prediction performance close to that of SQAR-CF and yields lower errors than SAER-CF at several quantile levels; meanwhile, the results do not support a uniform predictive advantage over IVQR-style. Overall, SARHQER-CF provides a more flexible and interpretable hybrid quantile–expectile modeling tool for spatial data with spatial dependence and distributional heterogeneity.

Spatial autoregressive (SAR) models are widely used in economics, environmental science, and epidemiology to capture spatial spillovers, while transfer learning has become an essential tool for improving estimation with limited or high-dimensional data. Existing SAR transfer learning methods are typically developed under Gaussian-type modeling assumptions and do not explicitly incorporate transformation mechanisms. While such models perform well under symmetric response distributions, their flexibility may be limited when the response exhibits substantial skewness. We propose a novel Box–Cox SAR transfer learning framework that jointly estimates transformation and regression parameters and incorporates a bootstrap-based detection procedure to adaptively screen transferable sources. This framework unifies distributional adjustment, spatial dependence, and selective transfer within a single scheme. Simulation studies and an empirical analysis of California Housing data confirm its robustness and predictive improvements over conventional SAR and naive pooling, establishing a principled direction for applying transfer learning to complex and heterogeneous spatial systems.

In the era of big data, spatial data has become pivotal for exploring geographic phenomena due to its spatial correlation and heterogeneity. Traditional spatial autoregressive models are constrained by linear assumptions and parameter estimation limitations, making them ill-suited for handling non-stationary data and extreme risk analysis. While quantile regression overcomes limitations in error distribution, existing spatial quantile models still fail to capture nonlinear spatial spillover effects of the dependent variable due to the assumption of linear endogenous effects. To address this, this paper proposes a robust estimation method for spatial quantile autoregressive models under nonparametric endogenous effects, innovatively incorporating deep neural networks to handle nonlinear relationships. To address quantile overlap issues, two models are constructed: one fits customized models for each quantile, while the other employs a multi-task model to simultaneously estimate multiple quantile functions, thereby avoiding overlap. Dedicated neural network frameworks and algorithms are designed for both approaches. Numerical simulations demonstrate both neural network approaches exhibit superior predictive performance and interpretability. Validation using U.S. San Diego housing rent data further confirms their practical utility and forecasting advantages.

In the era of data-driven decision-making, stochastic frontier models (SFMs) have become a powerful tool for analyzing production efficiency across various domains. While model averaging is an effective strategy to mitigate model misspecification and enhance prediction accuracy, existing approaches often overlook the risks of individual privacy leakage during the model weighting process. To address this challenge, we propose a novel differentially private model averaging framework for stochastic frontier models. We develop two variants of differentially private Frank-Wolfe algorithms tailored to low-to-moderate and high-dimensional candidate model spaces, respectively, achieving a favorable trade-off between privacy protection and estimation accuracy. Our method integrates differential privacy guarantees into the weight optimization procedure via perturbation mechanisms and privacy-aware algorithms,such as a private variant of the Frank-Wolfe algorithm. We further analyze both theoretical utility bounds and empirical performance under various privacy budgets. Simulation studies demonstrate that our approach achieves a favorable balance between prediction accuracy and privacy protection, outperforming baseline regularization methods in scenarios with high model uncertainty.

Transfer learning has shown great promise for improving estimation and prediction in small-sample, high-dimensional settings. However, most existing methods assume that the response variable follows a symmetric or Gaussian distribution, limiting their applicability in real-world scenarios where skewness and heterogeneity are common-particularly in gene expression, clinical biomarkers, and economic indicators. To address this gap, we propose a transformation-aware transfer learning framework that jointly estimates two sets of parameters: the Box-Cox transformation parameter, which normalizes skewed responses, and high-dimensional regression coefficients. This dual-parameter estimation contrasts with conventional approaches that typically model only covariate effects. We further introduce a profile-likelihood-based method to automatically identify transferable source domains. Together, these components support both known and unknown source settings. Extensive simulation studies and real-data analysis based on GTEx v8 transcriptomic data demonstrate the robustness and effectiveness of the proposed framework under multi-source distributional heterogeneity. In the JAM2 prediction task for Brain-Cerebellum, A-trans-BCT achieved the best predictive performance among all competing methods, reducing the RMSE from 1.4815 to 1.4204 and increasing the coefficient of determination from 0.8159 to 0.8327 relative to the Target-only baseline.

This paper develops and evaluates HQER-SFA, a likelihood-based stochastic frontier specification that embeds a hybrid quantile-expectile error layer into the bilateral noise component while preserving the standard one-sided inefficiency structure. The model nests Quantile-SFA when γ=0 and extends it by normalizing the hybrid loss into a proper bilateral error density, so that likelihood inference, residual decomposition, and technical-efficiency recovery remain in a unified stochastic-frontier framework. We compare HQER-SFA with Traditional-SFA and Quantile-SFA using three processed production modules, Monte Carlo parameter-inversion experiments, an expanded R=300 robustness design, γ sensitivity and ablation checks, convergence diagnostics, and a source-assisted small-sample extension. The results demonstrate clear gains for technical-efficiency recovery: in the R=300 design, HQER-SFA attains win rates of 0.5646 for technical-efficiency RMSE and 0.5578 for technical-efficiency rank correlation, and the agricultural module shows the strongest real-data improvement under the flexible bilateral error layer. The source-assisted analysis further shows that same-domain initialization improves small-sample validation RMSE by about 2.43%, while excessive source-centered penalties should be controlled. Overall, HQER-SFA provides an interpretable and computationally feasible extension for technical-efficiency recovery, especially when bilateral noise is asymmetric, tail-sensitive, or heterogeneous across production modules.

Transfer learning has been successfully applied across multiple domains, aiming to uncover intrinsic relationships between data or models and transfer knowledge gained from source domain training to target domains. As a core method for evaluating technical efficiency, stochastic frontier models have consistently attracted significant attention. This paper innovatively combines the two approaches, proposing the Spatial Durbin Stochastic Frontier Model with an integrated transfer learning framework (Trans-SDF-STE). This model retains the Spatial Durbin model’s ability to capture “spatial correlation effects between an entity and its neighboring units” while extending the Stochastic Frontier Analysis’s advantage in quantifying heterogeneity in technical efficiency. Simultaneously, it overcomes modeling limitations in target domains with small samples through transfer learning mechanisms. We employ spatial residual bootstrapping to select source domains exhibiting “spatial structural consistency and efficiency mechanism similarity.” By integrating 2SLS estimation to construct instrumental variables addressing endogeneity, followed by a two-stage transfer learning approach (“transfer + bias removal”), we migrate the source domain to the target domain. This enhances the accuracy of model parameter estimation and technical efficiency measurement. Through simulation experiments and real-world data applications, we validate the effectiveness and practicality of the proposed method.

Spatial expected shortfall regression (SESR) characterizes spatial dependence and tail losses at a given quantile level. However, high-dimensional small-sample data easily lead to parameter redundancy and estimation distortion. Although existing transfer learning can alleviate the small-sample problem, it relies on raw data sharing and source domain screening, incurring privacy leakage risks and high computational costs. To address these issues, this paper proposes model averaging transfer learning at the spatial quantile regression (SQR) stage. Different from traditional mean regression frameworks, the proposed method first fuses multi-source information to improve SQR estimation accuracy, and then constructs SESR based on the optimized SQR results, without raw data sharing or source domain screening, thereby achieving SESR parameter estimation under high-dimensional small-sample conditions. Numerical simulations, robustness tests, and empirical analysis on the London property prices dataset demonstrate that the proposed method outperforms conventional approaches, providing a reliable analytical framework for spatial tail risk measurement under high-dimensional small-sample settings with privacy constraints.

To address the issues of unstable parameter estimation and variable selection under limited target-domain observations in spatial point processes (SPPs), this paper proposes an algorithmic framework based on transfer learning. Unlike conventional target-only variable selection methods for SPPs, the proposed framework aims to leverage transferable information from source domains to improve target-domain intensity estimation and sparse variable selection. In scenarios where transferable sources are known, we develop a two-stage transfer algorithm by optimizing a Poisson quasi-likelihood objective model combined with an adaptive ℓ _0 -sparse penalty, employing Iterative Hard Thresholding (IHT) and a Warm-Start strategy to improve computational efficiency. Furthermore, when transferable sources cannot be determined, we design a data-driven source detection algorithm based on spatial block cross-validation. This approach screens candidate domains by comparing empirical loss differences, thereby reducing the risk of negative transfer. Numerical simulations conducted under Poisson and Thomas point process settings demonstrate that the proposed method can improve estimation accuracy and variable selection stability, while exhibiting robustness against clustering effects among spatial points. Finally, we apply this algorithm to analyze vehicle crime data in Nottingham, UK, which further illustrates the practical utility of the proposed method.

The spatial Durbin model has been widely applied in regional economics, real estate, and environmental policy studies for its ability to capture both direct and indirect effects. However, when the target domain suffers from limited sample size or distributional discrepancies with available source domains, conventional single-domain estimation often encounters sample representativeness limitations and external estimation bias. To address this challenge, this paper introduces the concept of transfer learning into the spatial econometric framework and proposes a transfer learning method for spatial Durbin model, which enables knowledge transfer across multiple domains under spatial dependence. Furthermore, under the scenario where transferable sources are unknown, we develop a transferable source detection mechanism that combines instrumental variable transformation and cross-validation to automatically identify source domains most similar to the target domain. Both simulation and empirical analysis demonstrate that our methods outperform the baseline methods.

This paper investigates the problem of variable selection in joint mean and variance models under high-dimensional settings within the transfer learning framework. The primary goal is to enhance parameter estimation and prediction accuracy for the target dataset by leveraging source datasets that share similarities with the target. First, a two-step transfer learning method based on the Lasso penalty is proposed for scenarios where the transferable source datasets are known. Second, for situations where transferable sources are unknown, an algorithm-independent, data-driven source selection method is introduced. This approach effectively distinguishes between transferable and nontransferable sources and improves prediction performance on the target dataset by utilizing the identified transferable sources. Extensive simulation studies demonstrate the superior performance of the proposed methods. Furthermore, experiments on real-world datasets highlight their practical applicability and effectiveness.

Transfer learning is a machine learning approach that enhances target domain performance by leveraging knowledge from source domains. Although this method has been widely applied in regression problems, research remains limited for scenarios involving partially missing response data in the target domain. This study addresses the dual challenges of missing responses and small sample sizes in spatially dependent regression problems by proposing an EM algorithm-based transfer learning framework. The framework first employs the EM algorithm to handle missing responses in spatial autoregressive models, then develops a two-step transfer learning method for known source domains, along with a cross-validation-based detection algorithm for unknown transferable sources. Numerical simulations demonstrate that the proposed methods exhibit superior performance in both parameter estimation accuracy and model robustness.

The spatial stochastic frontier model approaches to evaluate firm-level productivity and maximum potential output, while accounting for the influence of neighbouring geographical areas or economies. Existing studies, however, overlook small-sample scenarios. We propose integrating machine learning with traditional statistical methods to address this gap. Specifically, transfer learning which leverages knowledge from related tasks is introduced to enhance estimation under limited data. Novel algorithms are developed for cases with known or unknown source datasets, aiming to improve parameter estimation efficiency by addressing spatial correlation and endogeneity in small samples.

Tobit models are widely used to explore the relationship between response variables and covariates when the response variable is censored. Since the traditional Tobit model cannot capture complex nonlinear relationships, it may not be applicable to the analysis of many datasets. To overcome this problem, we replace the linear component of the Tobit model with a nonparametric component, thus expanding the traditional Tobit model into a new nonparametric model. Combined with the advantages of deep neural networks in capturing the feature space of complex structures, we propose a likelihood-based variable selection method for Tobit models that combines variable selection with deep learning. To evaluate the effectiveness of the method, we conducted simulation experiments and example data experiments to demonstrate the good results of the method.

Transfer learning, as a forefront direction in the field of statistical machine learning, aims to transfer knowledge from one domain to another to enhance model performance and address the scarcity of knowledge in the target domain. However, real-world data is often affected by missing values, posing additional challenges to transfer learning. To overcome this issue, we propose an innovative approach utilizing optimal transport for transfer learning (OT-TL) with missing data. Through simulation experiments, we validate the discernibility of transferable sources by OT-TL under various scenarios involving different source domain quantities and types of missing data. Additionally, our method adapts dynamically to allocate importance weights for different source domains, achieving favorable transfer effects. Comparative studies with different missing data imputation methods demonstrate the excellence of our proposed approach. In empirical evaluations, our method exhibits strong performance in both regression and classification tasks, as evidenced by studies on datasets related to fat content measurement and UCI Arrhythmia classification. Exploring the application of optimal transport theory in transfer learning addresses the crucial issue of achieving knowledge transfer in the presence of data missing challenges. This research provides a novel avenue for tackling transfer learning in practical problem-solving and opens up additional possibilities for real-world applications of cross-domain knowledge transfer.