Tiefeng Ma

Inferences on the common mean of several inverse Gaussian populations

This paper presents procedures for hypothesis testing and interval estimation for the common mean of several inverse Gaussian populations when the scalar parameters are unknown and unequal. The proposed approaches are hybrids between the generalized inference method and the large-sample theory. Some simulation results are presented to compare the performance of the proposed approaches with that of the existing approach. The simulation results indicate that one of the proposed approaches performs better than the existing approach in most cases. Furthermore, our approaches can be simply carried out by a few simulation steps. Finally, the proposed approaches are illustrated by using three examples.

Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions

The local influence method has proven to be a useful and powerful tool for detecting influential observations on the estimation of model parameters. This method has been widely applied in different studies related to econometric and statistical modelling. We propose a methodology based on the Lagrange multiplier method with a linear penalty function to assess local influence in the possibly heteroskedastic linear regression model with exact restrictions. The restricted maximum likelihood estimators and information matrices are presented for the postulated model. Several perturbation schemes for the local influence method are investigated to identify potentially influential observations. Three real-world examples are included to illustrate and validate our methodology.

Spatial system estimators for panel models: A sensitivity and simulation study

System of panel models are popular models in applied sciences and the question of spatial errors has created the recent demand for spatial system estimation of panel models. Therefore we propose new diagnostic methods to explore if the spatial component will change significantly the outcome of non-spatial estimates of seemingly unrelated regression (SUR) systems. We apply a local sensitivity approach to study the behavior of generalized least squares (GLS) estimators in two spatial autoregression SUR system models: a SAR model with SUR errors (SAR-SUR) and a SUR model with spatial errors (SUR-SEM). Using matrix derivative calculus we establish a sensitivity matrix for spatial panel models and we show how a first order Taylor approximation of the GLS estimators can be used to approximate the GLS estimators in spatial SUR models. In a simulation study we demonstrate the good quality of our approximation results.

Inferences on the reliability in balanced and unbalanced one-way random models

In this article, the hypothesis testing and interval estimation for the reliability parameter are considered in balanced and unbalanced one-way random models. The tests and confidence intervals for the reliability parameter are developed using the concepts of generalized p-value and generalized confidence interval. Furthermore, some simulation results are presented to compare the performances between the proposed approach and the existing approach. For balanced models, the simulation results indicate that the proposed approach can provide satisfactory coverage probabilities and performs better than the existing approaches across the wide array of scenarios, especially for small sample sizes. For unbalanced models, the simulation results show that the two proposed approaches perform more satisfactorily than the existing approach in most cases. Finally, the proposed approaches are illustrated using two real examples.

Estimation of means of multivariate normal populations with order restriction

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case.

Fast learning rates for sparse quantile regression problem

Learning with coefficient-based regularization has attracted a considerable amount of attention recently in both machine learning and statistics. This paper presents a kernelized version of a quantile estimator integrated with coefficient-based regularization, which can be solved efficiently by a simple linear programming. Fast convergence rates are obtained under mild condition on the underlying distribution. Besides, this algorithm can be adapted easily to large scale problems and sparse solution is often achieved as that of Lasso. In our work we make the following main contributions: girst, improved learning rates are obtained by employing so called variance bounds, which is optimal in the literatures of learning theory; second, we establish stronger convergence rates by employing self-calibration inequalities; third, our learning rates can also be derived by a simple data-dependent parameter selection method; finally, the performance of the classical and our new algorithms are compared respectively in a simulation study and an actual problem.

A model-free variable selection method for reducing the number of redundant variables

ABSTRACT Under the sufficient dimension reduction () framework, we propose a model-free variable selection method for reducing the number of redundant predictors. The method adopts the distance correlation as a dependence measure to quantify the relevance and redundancy of a predictor, and searches for a set of the relevant but non-redundant predictors. Two forward screening algorithms are given to find an approximate solution to the set of the relevant but non-redundant predictors. The screening consistency of the proposed method and algorithms has been fully studied. The effectiveness of the proposed method and algorithms is illustrated by the simulation experiments and two real examples. The experimental results show that the proposed method can effectively exclude the redundant predictors and yield a more parsimonious subset of the relevant predictors.

Sensitivity analysis in linear models

Abstract In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

Improved anovae of the covariance matrix in general linear mixed models

In this paper, the problem of estimating the covariance matrix in general linear mixed models is considered. A new class of estimators is proposed. It is shown that this new estimator dominates the analysis of variance estimate under two squared loss functions. Finally, some simulation results to compare the performance of the proposed estimator with that of the analysis of variance estimate are reported. The simulation results indicate that this new estimator provides a substantial improvement in risk under most situations.