This paper deals with the problem of testing the homogeneity of treatment effects against a simple tree order alternative in a two-way additive heteroscedastic ANOVA model. We propose the likelihood ratio test (LRT) along with two multiple comparison tests based on pairwise differences between control and treatment means. The critical values are estimated using the bootstrap method. The asymptotic validity of the bootstrap is established. Simultaneous confidence intervals for the pairwise differences between control and treatment mean effects are also derived. Furthermore, a robustness study is conducted under non-normal distributions, including Laplace, t, Weibull, and three types of mixture normal distributions. To facilitate the implementation of our proposed methods, we have developed an ‘R’ package and shared it publicly on ‘GitHub’. The performance of the proposed test procedures is demonstrated through applications to a memory-recall dataset from a psychological study and a weight gain dataset from a biomedical experiment.
This paper explores a determinant-based multiple correlation coefficient in multiplicative distortion measurement error models, where an unobservable covariate vector is distorted by a confounding variable-related multiplicative function. As a novel metric for gauging correlation among continuous variables, it proves valuable when specifying a dependent variable and covariates is difficult, especially for equally important variables. We first examine triple-variable scenarios and then extend to p-dimensional vectors under normal and general distributions. Two calibration methods are proposed to generate unobservable variable proxies. We present comprehensive asymptotic results for calibrated estimators and test statistics, with theoretical findings highlighting their asymptotic efficiency. Monte Carlo simulations and a real dataset validate the proposed estimators and test statistics.
This work develops a weighted adaptive spline likelihood framework for partially nonlinear regression under both response and covariate truncation. The simultaneous truncation of response and covariate data leads to a non-standard likelihood in which the truncation adjustment depends on both the parametric and nonparametric components of the model. To address this issue, we propose a weighted penalized M-estimator in which the unknown smooth function is represented using splines with an adaptively selected order. The proposed framework incorporates the truncation mechanism directly into the likelihood and provides a flexible approach for estimating the nonlinear component while accounting for the information loss caused by truncation. Under suitable regularity conditions, the proposed estimator is shown to be uniformly consistent and asymptotically normal. The theoretical results provide statistical justification for the proposed methodology, while the numerical analysis demonstrates its performance under different truncation settings. Overall, the proposed framework provides a practical and flexible approach to partially nonlinear regression with truncated response and covariate data.
It is increasingly feasible to obtain external information from multiple prior studies, and appropriately leveraging such information can assist the analysis of internal individual-level data. However, external information from multiple sources is often heterogeneous, and not all sources are informative for a given internal study. In this paper, we propose a model averaging procedure that optimally utilizes heterogeneous summary information from external studies to improve prediction performance. The procedure incorporates informative external information and downweights uninformative sources through data-driven weight assignments. Notably, our framework does not require the internal model to be correctly specified. We establish weight convergence and asymptotic optimality under correctly specified and misspecified internal models, respectively, and we compare the risk of the proposed model averaging procedure with that of simple equal-weight averaging. Numerical simulations demonstrate superior predictive performance, which we further illustrate using a Beijing housing rental dataset and a skin cutaneous melanoma dataset.
{The significance and novelty of this work are established through methodological development, theoretical analysis, and numerical experiments for quantile regression in streaming data.} Estimating equation and objective function are perhaps the most common tools in classical statistics and machine learning. The optimum frameworks are frequently used for optimizing the statistical inference and learning. Up to now, however, the optimum forms of the online updating have not been well explored. In this paper, these classical optimum notions are utilized to solve the modern issue: online learning. For quantile and quantile regression, a type of optimum frameworks of the online updating estimating equation and objective function are proposed, the notion of expectation derivative and the smoothing techniques are introduced to deal with non-differentiable objective functions, and the relevant iterative algorithms are suggested to implement the estimation procedures. The proposed methods can be applied to the models with possible heterogenous distributions. Theoretically, the asymptotic normality and oracle property are established. The behaviours of the methods are further illustrated by various numerical examples from simulation experiments and real data analysis.
