Robust ridge M-estimators with pretest and Stein-rule shrinkage for an intercept term

Shih, Jia-Han; Lin, Ting-Yu; Jimichi, Masayuki; Emura, Takeshi

doi:10.1007/s42081-020-00089-6

Cited by 9 publications

(4 citation statements)

References 32 publications

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“…The idea was proposed by Bancroft [36] who formulated pretest estimators that incorporate a preliminary hypothesis test into estimation. Judge and Bock [37] extensively studied pretest estimators with applications to econometrics; see also more recent works [38][39][40][41][42][43]. Among all, we particularly note that Shih et al [41] proposed the general pretest (GPT) estimator that includes empirical Bayes and Types I-II shrinkage pretest estimators for the univariate normal mean.…”

Section: Estimation Under Sparse Meansmentioning

confidence: 97%

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Taketomi

Konno

Chang

et al. 2021

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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.

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Section: Estimation Under Sparse Meansmentioning

confidence: 97%

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Taketomi

Konno

Chang

et al. 2021

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“…We now consider discrete shrinkage schemes by pre-testing 𝐻 : 𝜇 = 0 vs. 𝐻 : 𝜇 ≠ 0 for 𝑖 = 1,2, … , 𝐺. The idea was proposed by Bancroft [36], who developed pretest estimators (see also more recent works [20,[37][38][39][40][41][42][43]). In the meta-analytic context, Taketomi et al [20] adopted the general pretest (GPT) estimator of Shih et al [41], which is defined as follows:…”

Section: Estimators Under Sparse Meansmentioning

confidence: 99%

meta.shrinkage: An R Package for Meta-Analyses for Simultaneously Estimating Individual Means

et al. 2022

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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.

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“…To overcome this difficulty, Yang and Emura [15] suggested reducing the number of shrinkage parameters for the case of p > n in their formulation of a generalized ridge estimator. The idea behind their approach was to assign two different weights (1 or 0.5) for shrinkage parameters via preliminary tests [22][23][24][25][26]. While this approach has sound statistical performance in sparse and high-dimensional models, no software packages were implemented for the generalized ridge estimator.…”

Section: Introductionmentioning

confidence: 99%

g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

Emura,

Matsumoto,

Uozumi

et al. 2024

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Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data.

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Robust ridge M-estimators with pretest and Stein-rule shrinkage for an intercept term

Cited by 9 publications

References 32 publications

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

meta.shrinkage: An R Package for Meta-Analyses for Simultaneously Estimating Individual Means

g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

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