arXiv subjects

S. Ejaz Ahmed

Publications and source records attributed to S. Ejaz Ahmed.

3 recordsLinked to original sources

arXiv2017

Liu-type Shrinkage Estimations in Linear Models

In this study, we present the preliminary test, Stein-type and positive part Liu estimators in the linear models when the parameter vector $\boldsymbolβ$ is partitioned into two parts, namely, the main effects $\boldsymbolβ_1$ and the nuisance effects $\boldsymbolβ_2$ such that $\boldsymbolβ=\left(\boldsymbolβ_1, \boldsymbolβ_2 \right)$. We consider the case that a priori known or suspected set of the explanatory variables do not contribute to predict the response so that a sub-model may be enough for this purpose. Thus, the main interest is to estimate $\boldsymbolβ_1$ when $\boldsymbolβ_2$ is close to zero. Therefore, we conduct a Monte Carlo simulation study to evaluate the relative efficiency of the suggested estimators, where we demonstrate the superiority of the proposed estimators.

math.ST↗

arXiv2017

Shrinkage Estimation Strategies in Generalized Ridge Regression Models Under Low/High-Dimension Regime

In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also, it is obtained theoretical properties of the proposed estimators for Low/High Dimensional cases. Furthermore, the performance of the listed estimators is demonstrated by both simulation studies and real-data analysis, and compare its performance with existing penalty methods. We show that the proposed methods compare well to competing regularization techniques.

math.ST↗

arXiv2011

Positive-shrinkage and Pretest Estimation in Multiple Regression: A Monte Carlo study with Applications

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage method combines restricted and unrestricted estimators to obtain the parameter estimates. Such an estimator outperforms the classical maximum likelihood estimators. Any \emph{prior} information may be validated through preliminary test (or pretest), and depending on the validity, may be incorporated in the model as a parametric restriction. Thus, pretest estimator chooses between the restricted and unrestricted estimators depending on the outcome of the preliminary test. Examples using three real life data sets are provided to illustrate the application of shrinkage and pretest estimation. Performance of positive-shrinkage and pretest estimators are compared with unrestricted estimator under varying degree of uncertainty of the prior information. Monte Carlo study reconfirms the asymptotic properties of the estimators available in the literature.

stat.AP↗