Repeated sample splitting, cross-fitting, conformal ensembling, and related randomized workflows often produce multiple dependent valid p-value functions for the same target. Existing p-merging theory guarantees pointwise validity under arbitrary dependence, but turning the merged output into a confidence region typically requires repeated evaluation on a grid over the parameter space. This inversion step can be computationally costly, approximation-dependent, and increasingly difficult to scale. We study when confidence regions can instead be computed exactly from split-wise regions without gridding the parameter space. Our main structural result shows that mergers induced by step calibrators form a broad exactly executable class at the region level, and a partial converse within the calibrator-induced family indicates that exact executability is closely tied to step structure. Within this class, we develop exact voting algorithms, including an adaptive multi-quantile contour aggregator that avoids pre-specifying a single order-statistic threshold while preserving finite-sample validity under arbitrary dependence. Simulation studies on repeated-split regression and conformal prediction, together with real-data regression examples, show that the proposed methods provide stable, robustness-oriented exact inference with substantial runtime gains over grid-inversion comparators. A grid-resolution benchmark shows that fixed-k voting and adaptive multi-quantile voting are essentially insensitive to inversion-grid refinement, while a multidimensional single-threshold stress test illustrates the dimensional blow-up faced by grid-inversion baselines in a simple box-geometry setting. Taken together, the results show that arbitrary-dependence contour merging can be turned into an exactly executable region-computation framework rather than merely a pointwise validity device.
In this paper, we propose a moment method for inferring the parameters of random effects in a stochastic differential equation driven by fractional Brownian motion, where the likelihood function is generally difficult to formulate explicitly. We obtain moment estimators for the random effects, and we study their consistency and asymptotic normality. We then derive parameter estimates for specific random effects distributions. The theoretical results are supported by numerical simulations and illustrated through an empirical study on Asian financial data.
This study tackles estimation and hypothesis testing in a multiplicative distortion model with an unobserved Beta-distributed variable distorted by an observable confounder. We propose three calibrated estimators for model parameters: maximum likelihood, moment-based by utilizing expectation-variance and symmetric moment ratios, and log-moments estimators, and analyse their theoretical properties and asymptotic efficiency. We then investigate two hypothesis tests: one for parameter equality for symmetry and another for Beta distribution goodness-of-fit. For symmetry testing, three test statistics are introduced and their asymptotic properties under the null hypothesis are explored; for goodness-of-fit, a novel symmetric covariance measure and test statistic are proposed. Monte Carlo simulations compare our methods with existing approaches, and a real-world dataset analysis illustrates their practical utility.
In this paper we have developed two correlated stationary processes X-n and Y-n, where P(X-n=Xn+1)>0 and P(Yn=Yn+1)>0 . The model has been developed based on two real life data sets. Efficient inference procedures and goodness of fit test have been developed. The motivation of this work came when we were trying to analyse the gold price data {X-n} of the Indian market and the exchange rate data {Y-n} between Indian Rupees and US dollars during the same time period. Although, both of them are stationary processes, it is observed that there is a significant amount of time X-n=Xn+1 or Y-n=Yn+1 , and they cannot be ignored. Moreover, Xn and Yn are dependent, and if we want to analyse the data during the same period, they should be analysed together. In this paper first we have proposed a new stationary process based on Marshall-Olkin bivariate exponential distribution type construction combining with frailty, so that P(X-n=Xn+1)>0 . Different properties of the proposed bivariate stationary process have been established. The maximum likelihood estimators of the unknown parameters have been obtained. Goodness of fit test of the proposed model has been proposed. We have performed the analysis of gold price data and the exchange rate data using the proposed model and the results are quite satisfactory. Then we have extended the process to the bivariate case where P(X-n=Xn+1)>0 , P(Y-n=Yn+1)>0 and X-n , Y-n are dependent. We have demonstrated how it can be used in practice.
Assuming exponential lifetimes, exact expressions of the Pitman closeness (PC) probabilities were derived for comparing two maximum likelihood estimators (MLEs) of theta under different termination times from a Type-II hybrid censoring scheme (HCS). Assuming that the lifetime data follow an exponential distribution with scale parameter theta, prior work had computed the Pitman closeness (PC) probabilities for estimators based on Type-I right-censoring, Type-II right-censoring and Type-I hybrid censoring schemes (HCS). However, the derivation of the PC under a Type-II HCS has not yet been addressed in the literature. This paper examines two comparisons of MLEs for theta, the scale parameter, for exponentially distributed lifetimes arising from the Type-II HCS: (1) between estimators corresponding to different numbers of observed failures and (2) between estimators with different censoring times. Closed-form expressions for the PC probabilities are derived, and numerical results are reported for various sample sizes, censoring times and study durations. The results show that increasing the pre-fixed termination time or the number of failures led to an estimator that was Pitman closer to the true parameter, which confirm the intuition that increasing the termination time or the number of observed failures will lead to an estimator that is Pitman closer. However, the PC probability also accounts for the cases where the estimators are equal. Conditional on the estimators being different, there were a surprising couple of instances where there is a higher probability that the estimator based on a shorter termination time is closer to theta compared to the estimator based on the longer termination time.
Count data characterized by overdispersion, underdispersion, and an excess of zero observations present persistent challenges for regression frameworks. The Zero-Inflated Conway-Maxwell Poisson regression model (ZICMPRM) has emerged as a flexible alternative capable of accommodating this full spectrum of dispersion patterns. However, a well-recognized limitation of the maximum likelihood estimator (MLE) is its sensitivity to multicollinearity among covariates, which can substantially inflate variance and compromise inferential reliability. To address this issue, we propose a new Liu-type within the ZICMPRM framework. Theoretical comparison demonstrates that the proposed estimator outperforms the existing estimators in the presence of multicollinearity. The finite-sample performance of the proposed estimator is assessed through an extensive Monte Carlo simulation study, with results consistently demonstrating their superiority over MLE, ridge, and Liu in terms of MSE across varying levels of dispersion and multicollinearity. The practical utility of the estimator is further illustrated through application to real-world count data, where the proposed estimator yields notably more stable and efficient parameter estimates. These findings emphasize the necessity of adopting biased estimation procedures when fitting ZICMPRM to multicollinear data structures.
{Classical and Bayesian methods are employed to construct point and interval estimators of the process capability index C , with performance evaluated via Monte Carlo simulation under multiple interval type-II censoring} This paper investigates the estimation of the process capability index Cs for the log-logistic distribution under a newly proposed multiple interval type-II censoring scheme. Three estimation approaches are considered: maximum likelihood estimation, maximum product of spacings, and Bayesian inference. Within the Bayesian framework, both the likelihood and product of spacings functions are employed under two loss functions, namely the squared error loss and the linear exponential (LINEX) loss, assuming gamma prior distributions for the model parameters. In addition to point estimation, interval estimation is carried out by constructing approximate confidence intervals using classical methods and comparing them with highest posterior density credible intervals obtained from Bayesian procedures. Furthermore, percentile bootstrap confidence intervals based on both the likelihood function and the product of spacings function are also obtained. A comprehensive Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the proposed estimators. Further, the optimal multiple interval type-II censoring plan is examined under different optimality criteria. Finally, the practical applicability of the proposed methods is demonstrated through the analysis of two real-life data sets.
With the advancement and development of science and technology, critical equipment in the aerospace and electronics fields has gradually evolved toward multifunctionality, long life, and high reliability. In practical applications, influenced by factors such as changes in their physical and chemical properties, structural modifications, or environmental stress, the degradation processes of equipment exhibit significant differences across various life stages, resulting in a multi-phase degradation pattern. Since degradation modelling serves as the foundation of performance degradation theory, the accuracy of the degradation model in describing performance degradation laws determines the precision of product life assessment and remaining useful life prediction. Therefore, it is important to detect change points in the degradation process and evaluate product reliability or predict remaining useful life based on degradation models incorporating change points. Targeting degradation processes with nonlinear drift terms and two-phase degradation patterns, this paper investigates the change point detection problem for Wiener processes based on the Wiener process. The nonlinear drift term of the Wiener process is approximated using B-spline functions, and a generalized gradient projection algorithm(GPA) is proposed to calculate the maximum likelihood estimates of related parameters. The convergence of the proposed GPA algorithm is rigorously established. For the change point detection problem in Wiener process parameters, a change point detection method based on the MIC criterion is proposed, and the asymptotic distribution of the corresponding statistic is derived. Following simulation studies, extensive sensitivity analysis is conducted to evaluate the robustness of the proposed method. The results demonstrate that the MIC-based change point detection method exhibits superior robustness across various parameter settings, maintaining stable and reliable testing power even under challenging conditions such as small sample sizes and change points located at the boundaries. The proposed method is then applied to the accelerated degradation test data analysis of MOS tubes in the Tiangong series spacecraft. The results indicate that the degradation pattern of the spacecraft MOS tubes changes after the application of stress, necessitating adjustments to the degradation model to accurately predict the remaining useful life of the MOS tubes.
We propose a general additive-multiplicative rate model for recurrent event data with a terminal event, enhancing flexibility by incorporating both additive and multiplicative effects on the rate function. To address regional heterogeneity often present in large-scale medical studies, cluster-specific baseline rate and hazard functions are utilized for recurrent and terminal events, respectively. Parameter estimation is performed using the inverse probability survival weighting approach. Theoretical results establish the asymptotic properties of the estimators, and simulation studies are conducted to assess finite-sample performance. Results demonstrate that the proposed method yields unbiased estimators and effectively characterizes region-specific heterogeneity. The practical value of the model is illustrated by applying it to cardiovascular disease data from diabetic patients.
This paper focuses on the application of the Bayesian jackknife empirical likelihood method to survey data collected from general single-stage unequal probability sampling and stratified sampling designs. We examine parameters characterized by U-statistics and establish the regularity conditions under which the posterior distribution, derived from the Bayesian jackknife pseudo-empirical likelihood under different priors, converges asymptotically to a normal distribution. We also investigate the impact of incorporating auxiliary information, as well as the use of design weights and calibration weights. Through simulations and real data analysis, we evaluate the effectiveness of the Bayesian jackknife pseudo-empirical likelihood credible intervals. Our results demonstrate that the proposed methodology not only offers significant advantages over methods that ignore the sampling design but also outperforms jackknife pseudo-empirical likelihood approaches.
Likelihood-based inference for three-dimensional Poisson point processes requires numerical approximation of the integral term in the log-likelihood through a cubature scheme algorithm. The quality of this approximation, and hence the accuracy of the resulting statistical inference, depends on a small set of tuning parameters controlling the cubature construction. Despite their practical importance, the literature provides little guidance on how these parameters should be selected in order to obtain reliable first-order inference. This paper addresses this issue for purely spatial three-dimensional Poisson point process models. We formalize the cubature scheme in $ \mathbb {R}<^>3 $ R3 and conduct an extensive simulation study across multiple Poisson process scenarios, process sizes, and cubature configurations. Cubature settings are evaluated by combining parameter mean squared error with a second-order diagnostic based on the three-dimensional inhomogeneous K-function and the Global Envelope Test. The simulation results are then aggregated into empirically grounded practical recommendations for selecting the dummy-point ratio, the tessellation resolution, and the dummy-point layout. Finally, a real three-dimensional spatial application illustrates how cubature choices consistent with these recommendations can lead to stable parameter estimates, reliable fitted intensities, and satisfactory diagnostic performance.
{A new class of semiparametric higher-order spatial autoregressive models is proposed to make a significant contribution to spatial econometrics.} In this paper, we propose a new class of semiparametric higher-order spatial autoregressive models by allowing regression function to possess partially linear spatially varying coefficient structure. The proposed model is sufficiently flexible to simultaneously capture different types of spatial correlation and more accurately characterize spatial heterogeneity of regression relationship. We develop a computationally efficient and heteroskedasticity-robust estimation method for the proposed model by utilizing generalized method of moments (GMM) and local linear smoothing method, and derive asymptotic distribution of resulting estimators. Moreover, we develop a generalized likelihood ratio testing method to check whether coefficient functions in the proposed model have interesting parametric forms, in which a bootstrap procedure is suggested to appropriate null distribution of resulting test statistic. Simulation studies show that the proposed estimation and testing methods work quite well in finite samples. The Boston housing price data are analysed to demonstrate usefulness of the proposed model and its estimation and testing methods.
{Primary techniques: ECME (Expectation-Conditional Maximization Either) algorithm and MCMC (Markov Chain Monte Carlo) Bayesian technique for parameter estimation in tail-inflated VAR(p) model}. {Area of novelty: Extension of VAR modelling under multivariate tail-inflated normal innovations with applications to econometrics and environmental statistics}. This paper proposes a framework for multiple time series data sets, called the multivariate tail-inflated normal vector autoregressive model of order p ( $ { m MTIN-VAR}(p) $ MTIN-VAR(p), which is developed to enhance forecast accuracy in the presence of asymmetric, heavy-tailed innovations. The difference between the traditional Gaussian-based model and the $ { m MTIN-VAR}(p) $ MTIN-VAR(p) model is the incorporation of fat-tailed and skewed error structures in the proposed model. To fit the model, two estimation procedures, based on the ECME algorithm and the Bayesian method, were developed. The applicability of the $ { m MTIN-VAR}(p) $ MTIN-VAR(p) model was demonstrated using extensive simulation studies coupled with an empirical application, where it is seen that the proposed model showed signs of superiority over standard VAR model. In particular, more accurate forecasts were consistently obtained with the ECME procedure with minimal computational complexity. In contrast to Bayesian MCMC, which requires significant runtime and tuning, the ECME algorithm requires few iterations to converge and yet produces better predictive performance, which makes it ideal for real-time decision-making environments.
