A new modified Jackknifed estimator for the Poisson regression model

S Türkan, G Özel - Journal of Applied Statistics, 2016 - Taylor & Francis
S Türkan, G Özel
Journal of Applied Statistics, 2016Taylor & Francis
The Poisson regression is very popular in applied researches when analyzing the count
data. However, multicollinearity problem arises for the Poisson regression model when the
independent variables are highly intercorrelated. Shrinkage estimator is a commonly
applied solution to the general problem caused by multicollinearity. Recently, the ridge
regression (RR) estimators and some methods for estimating the ridge parameter k in the
Poisson regression have been proposed. It has been found that some estimators are better …
Abstract
The Poisson regression is very popular in applied researches when analyzing the count data. However, multicollinearity problem arises for the Poisson regression model when the independent variables are highly intercorrelated. Shrinkage estimator is a commonly applied solution to the general problem caused by multicollinearity. Recently, the ridge regression (RR) estimators and some methods for estimating the ridge parameter k in the Poisson regression have been proposed. It has been found that some estimators are better than the commonly used maximum-likelihood (ML) estimator and some other RR estimators. In this study, the modified Jackknifed Poisson ridge regression (MJPR) estimator is proposed to remedy the multicollinearity. A simulation study and a real data example are provided to evaluate the performance of estimators. Both mean-squared error and the percentage relative error are considered as the performance criteria. The simulation study and the real data example results show that the proposed MJPR method outperforms the Poisson ridge regression, Jackknifed Poisson ridge regression and the ML in all of the different situations evaluated in this paper.
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