Explore the vast range of titles available.

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion such as AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for this distribution. Similar impossibility results are also obtained for the conditional distribution of linear functions (e.g., predictors) of the post-model-selection estimator.

In this paper, we consider an estimation problem of the regression coefficients in multiple regression models with several unknown change-points. Under some realistic assumptions, we propose a class of estimators which includes as a special cases shrinkage estimators (SEs) as well as the unrestricted estimator (UE) and the restricted estimator (RE). We also derive a more general condition for the SEs to dominate the UE. To this end, we generalize some identities for the evaluation of the bias and risk functions of shrinkage-type estimators. As illustrative example, our method is applied to the \"gross domestic product\" data set of 10 countries whose USA, Canada, UK, France and Germany. The simulation results corroborate our theoretical findings.

Traditional specification testing does not always improve subsequent inference. We demonstrate by means of computer experiments under which circumstances, and how severely, data-driven model selection can destroy the size properties of subsequent parameter tests, if they are used without adjusting for the model-selection step. The investigated models are representative of macroeconometric and microeconometric workhorses. The model selection procedures include information criteria as well as sequences of significance tests (“general-to-specific”). We find that size distortions can be particularly large when competing models are close, with closeness being defined relatively to the sample size.

This paper compares the performance characteristics of penalty estimators, namely, LASSO and ridge regression (RR), with the least squares estimator (LSE), restricted estimator (RE), preliminary test estimator (PTE) and the Stein-type estimators. Under the assumption of orthonormal design matrix of a given regression model, we find that the RR estimator dominates the LSE, RE, PTE, Stein-type estimators and LASSO estimator uniformly, while, similar to Hansen (2013), neither LASSO nor LSE, PTE and Stein-Type estimators dominates the other. Our conclusions are based on the analysis of L_2-risks and relative risk efficiencies (RRE) together with the RRE related tables and graphs.

A fundamental strategy to diminish variations in manufacturing process urged the practitioners to characterize the quality of a process by a relationship between the response variable and one or more explanatory variables instead of a single quality characteristic; this state is known as a profile or a function. Profile monitoring mainly aims to test the stability of this relationship. Many researches have been carried out to study the different sampling techniques in the performance of linear profile under the maximum likely hood (MLE) estimation strategy, whereas using different estimation strategy has not been discussed so far. This paper is dedicated to introduce Bayesian estimation strategies with a proposal of novel control charts for jointly monitoring the linear profile. We considered restricted and pretest estimators, besides the estimation of distrust probability under the null hypothesis. Analytical and numerical results showed that the proposed estimators outperformed the MLE method. The proposed control charts have been used to monitor the two-phase flow in the oil industry to control the relationship between the flow rate and the pressure difference between two points.

Meta-analyses combine the estimators of individual means to estimate the common mean of a population. However, the common mean could be undefined or uninformative in some scenarios where individual means are “ordered” or “sparse”. Hence, assessments of individual means become relevant, rather than the common mean. In this article, we propose simultaneous estimation of individual means using the James–Stein shrinkage estimators, which improve upon individual studies’ estimators. We also propose isotonic regression estimators for ordered means, and pretest estimators for sparse means. We provide theoretical explanations and simulation results demonstrating the superiority of the proposed estimators over the individual studies’ estimators. The proposed methods are illustrated by two datasets: one comes from gastric cancer patients and the other from COVID-19 patients.

Meta-analysis is an indispensable tool for synthesizing statistical results obtained from individual studies. Recently, non-Bayesian estimators for individual means were proposed by applying three methods: the James–Stein (JS) shrinkage estimator, isotonic regression estimator, and pretest (PT) estimator. In order to make these methods available to users, we develop a new R package meta.shrinkage. Our package can compute seven estimators (named JS, JS+, RML, RJS, RJS+, PT, and GPT). We introduce this R package along with the usage of the R functions and the “average-min-max” steps for the pool-adjacent violators algorithm. We conduct Monte Carlo simulations to validate the proposed R package to ensure that the package can work properly in a variety of scenarios. We also analyze a data example to show the ability of the R package.

We consider the problem of pooling means from multiple random samples from log-normal populations. Under the homogeneity assumption of means that all mean values are equal, we propose improved large sample asymptotic methods for estimating p log-normal population means when multiple samples are combined. Accordingly, we suggest estimators based on linear shrinkage, pretest, and Stein-type methodology, and consider the asymptotic properties using asymptotic distributional bias and risk expressions. We also present a simulation study to validate the performance of the suggested estimators based on the simulated relative efficiency. Historical data from finance and weather are used to in the application of the proposed estimators.

The purpose of this paper is to discuss the problem of estimation and testing the equality of two autoregressive parameters of two first-order autoregressive processes AR(1), where for each process, the observations are made at different time points. The primary interest is to propose the testing procedures for the homogeneity of autocorrelation parameters ρ1 and ρ2. Furthermore, we are interested in estimating ρ1 under uncertain and weak prior information about the possible equality of ρ1 and ρ2, though we may not have full confidence in the tenacity of this information. A large sample test for the homogeneity of the parameters is developed. Pooled “P” (or restricted estimator) and preliminary test “PT” estimators are proposed, and their properties are investigated and compared with the unrestricted estimator “UE” of ρ1.

The t-ratio has not one but two uses in econometrics, which should be carefully distinguished. It is used as a test and also as a diagnostic. I emphasize that the commonly-used estimators are in fact pretest estimators, and argue in favor of an improved (continuous) version of pretesting, called model averaging.