Search Results (5)

Spatial regression models are widely available across several disciplines, such as functional magnetic resonance imaging analysis, econometrics, and house price analysis. In nature, sparsity occurs when a limited number of factors strongly impact overall variation. Sparse covariance structures are common in spatial regression models. The spatial error model is a significant spatial regression model that focuses on the geographical dependence present in the error terms rather than the response variable. This study proposes an effective approach using the pretest and shrinkage ridge estimators for estimating the vector of regression coefficients in the spatial error mode, considering insignificant coefficients and multicollinearity among regressors. The study compares the performance of the proposed estimators with the maximum likelihood estimator and assesses their efficacy using real-world data and bootstrapping techniques for comparison purposes. Full article

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. Full article

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. Full article

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease. Full article

This paper considers estimation and inference concerning the autoregressive coefficient ( $\rho$ ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. Our main objective is to construct confidence intervals for $\rho$ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. The starting point for our confidence procedure is the estimating equation of the Anderson–Hsiao (AH) IV procedure. It is well known that the AH IV estimation suffers from weak instrumentation when $\rho$ is near unity. But it is not so well known that AH IV estimation is still consistent when $\rho =1$ . In fact, the AH estimating equation is very well-centered and is an unbiased estimating equation in the sense of Durbin (1960), a feature that is especially useful in confidence interval construction. We show that a properly normalized statistic based on the AH estimating equation, which we call the $\mathbb{M}$ statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. To further improve the informativeness of our confidence procedure in the unit root and near unit root regions and to alleviate the problem that the AH procedure has greater variation in these regions, we use information from unit root pretesting to select among alternative confidence intervals. Two sequential tests are used to assess how close $\rho$ is to unity, and different intervals are applied depending on whether the test results indicate $\rho$ to be near or far away from unity. When $\rho$ is relatively close to unity, our procedure activates intervals whose width shrinks to zero at a faster rate than that of the confidence interval based on the $\mathbb{M}$ statistic. Only when both of our unit root tests reject the null hypothesis does our procedure turn to the $\mathbb{M}$ statistic interval, whose width has the optimal $N^{-1/2}{T}^{-1/2}$ rate of shrinkage when the underlying process is stable. Our asymptotic analysis shows this pretest-based confidence procedure to have coverage probability that is at least the nominal level in large samples uniformly over the parameter space. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings. Full article