Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses

It is known that collinearity among the explanatory variables in generalized linear models (GLMs) inflates the variance of maximum likelihood estimators. To overcome multicollinearity in GLMs, ordinary ridge estimator and restricted estimator were proposed. In this study, a restricted ridge estimator is introduced by unifying the ordinary ridge estimator and the restricted estimator in GLMs and its mean squared error (MSE) properties are discussed. The MSE comparisons are done in the context of first-order approximated estimators. The results are illustrated by a numerical example and two simulation studies are conducted with Poisson and binomial responses.     

Adaptive ridge estimator in a linear regression model with spherically symmetric error under constraint

Abstract

We consider adaptive ridge regression estimators in the general linear model with homogeneous spherically symmetric errors. A restriction on the parameter of regression is considered. We assume that all components are non negative (i.e. on the positive orthant). For this setting, we produce under general quadratic loss such estimators whose risk function dominates that of the least squares provided the number of regressors in the least fore.     

Moments of the trace of a noncentral wishart matrix

Several articles have appeared on the moments of the trace of a noncentral Wishart matrix. Partial results are given in these papers but the representations of these partial results are often too cumbersome for any practical use. In this paper general results are given in compact form which are readily usable in practical problems.     

On the inadmssibelity of ridge estimator in a linear model

The necessary and sufficient conditions for the inadmissibility of the ridge regression is discussed under two different criteria, namely, average loss and Pitman nearness. Although the two criteria are very different, same conclusions are obtained. The loss functions considered in this article are th likelihood loss function and the Mahalanobis loss function. The two loss functions are motivated from the point of view of classification of two normal populations. Under the Mahalanobis loss it is demonstrated that the ridge regression is always inadmissible as long as the errors are assumed to be symmetrically distributed about the origin.     

Sparse alternatives to ridge regression: a random effects approach

In a calibration of near-infrared (NIR) instrument, we regress some chemical compositions of interest as a function of their NIR spectra. In this process, we have two immediate challenges: first, the number of variables exceeds the number of observations and, second, the multicollinearity between variables are extremely high. To deal with the challenges, prediction models that produce sparse solutions have recently been proposed. The term ‘sparse’ means that some model parameters are zero estimated and the other parameters are estimated naturally away from zero. In effect, a variable selection is embedded in the model to potentially achieve a better prediction. Many studies have investigated sparse solutions for latent variable models, such as partial least squares and principal component regression, and for direct regression models such as ridge regression (RR). However, in the latter, it mainly involves an L₁ norm penalty to the objective function such as lasso regression. In this study, we investigate new sparse alternative models for RR within a random effects model framework, where we consider Cauchy and mixture-of-normals distributions on the random effects. The results indicate that the mixture-of-normals model produces a sparse solution with good prediction and better interpretation. We illustrate the methods using NIR spectra datasets from milk and corn specimens.     

A note on the moments of stochastic shrinkage parameters in ridge regression

The purpose of this note is to gain insight on the performance of two well known operational Ridge Regression estimators by deriving the moments of their stochastic shrinkage parameters. We also show that, under certain conditions, one of them has bounded moments.     

Residents,recreationists, ridge regression,and revenues:the five r's of florida's motor- tax

Ridge regression is applied to the question of how to revise Florida's motor-fuel tax to remedy the shortfall of its transportation revenues. Along the way a model of gasoline consumption by residents and tourists is presented, and the differences in consumption patterns between the two types of purchasers are reported.     

The approximation of an unbiased test with a small level for the bioequivalence problem

In the bioequivalence problem. Brown. Hwang and Munk (1997) constructed an unbiased level a test and other tests which are uniformly more powerful than the two one-sided tests procedures when a iscomparatively larger. In this paper, for a small level, an unbiased test is shown to be approxirnately constructeQ lor tnis prooiem oy using tneir Metnog. ine numerical construction is also given.     

On the minimum mean squared error estimators in a regression model

In this paper we analyze the properties of two estimators oroposed by Farebrother (1975) for linear regression models.     

原子吸收光谱法测定茶水和茶叶中的微量元素

采用空气 -乙炔火焰原子吸收法测定了冲泡茶水、水煎茶液及茶叶中一些微量元素的含量 .结果表明 ,4次冲泡茶水可提取 K 1 90 0 0— 2 2 0 0 0 μg/g,Mg90 0— 1 30 0 μg/g,Mn,Ca均为 40 0— 80 0 μg/g,Na80— 2 0 0 μg/g,Fe,Zn都为 2 5— 58μg/g,Ni,Cu,Sr均为 2— 7μg/g.将茶叶用沸水冲泡和水煎处理后 ,测得的微量元素含量基本相同 ,而后者处理茶叶比灰化法处理简单、快速 ,可利用此法测定饮茶时饮入的微量元素含量 ,对指导人们科学饮茶有实际意义