On the Restricted Liu Estimator in the Logistic Regression Model

Abstract

The logistic regression model is used when the response variables are dichotomous. In the presence of multicollinearity, the variance of the maximum likelihood estimator (MLE) becomes inflated. The Liu estimator for the linear regression model is proposed by Liu to remedy this problem. Urgan and Tez and Mansson et al. examined the Liu estimator (LE) for the logistic regression model. We introduced the restricted Liu estimator (RLE) for the logistic regression model. Moreover, a Monte Carlo simulation study is conducted for comparing the performances of the MLE, restricted maximum likelihood estimator (RMLE), LE, and RLE for the logistic regression model.

A novel multivariate performance optimization method based on sparse coding and hyper-predictor learning

“…To make the objective function a smooth function, we fix the sparse code elements in the diagonal matrix as the elements of the previous iteration. Moreover, we note that τ y ′′ is also a function of s i as shown in (8). We also first calculate by using sparse codes solved in the previous iteration, and then fix it when we consider s i in the current iteration.…”

Liu-Type logistic estimator under Stochastic Linear Restrictions

“…(11) Later, following Duffy and Santner (1989), Restricted Logistic Liu estimator (RLLE) by Siray et al, (2015), Restricted Logistic Ridge Estimator (RLRE) by , Restricted Liu-Type Logistic Estimator (RLTLE) by were proposed in the presence of exact linear restrictions in addition to sample model (1). These estimators are defined as (12) (13) (14) When the linear restrictions are stochastic as in (10) in addition to the logistic regression model (1) ( Third type), Nagarajah and Wijekoon (2015) proposed the Stochastic Restricted Maximum Likelihood Estimator (SRMLE).…”

“…Some of the bised estimators proposed in the literature under the first type are namely the Logistic Ridge Estimator (LRE) ( Schaefer et al, 1984), the Principal Component Logistic Estimator (PCLE) (Aguilera et al,2006), the Modified Logistic Ridge Estimator (MLRE) ( Nja et al, 2013), the Logistic Liu Estimator (LLE) ( Mansson et al, 2012), the Liu-Type Logistic Estimator (LTLE) ( Inan and Erdogan, 2013), the Almost Unbiased Ridge Logistic Estimator (AURLE) , the Almost Unbiased Liu Logistic Estimator (AULLE) (Xinfeng 2015) and the Optimal Generalized Logistic Estimator (OGLE) (Varathan and Wijekoon, 2017). When the exact linear restrictions are available in addition to the sample logistic model (second type), the Restricted Maximum Likelihood Estimator (RMLE) by Duffy and Santner (1989), the Restricted Logistic Liu Estimator (RLLE) by Siray et al (2015), the Modified Restricted Liu Estimator by Wu (2015), the Restricted Logistic Ridge Estimator (RLRE) and the Restricted Liu-Type Logistic Estimator (RLTLE) by have been proposed in the literature. When the restrictions on the parameters are stochastic (third type), Nagarajah and Wijekoon (2015) introduced the new estimator called Stochastic Restricted Maximum Likelihood Estimator (SRMLE), and derived the superiority conditions of SRMLE over the LRE, LLE and RMLE.…”

Stochastic Restricted Maximum Likelihood Estimator in Logistic Regression Model

“…Following RMLE in (11) and the Mixed Estimator (ME) in (9) in the Linear Regression Model, we propose a new estimator which is named as the Stochastic Restricted Maximum Likelihood Estimator (SRMLE) when the linear stochastic restriction (10) is available in addition to the logistic regression model (1).…”

“…Duffy and Santer (1989) [9] introduce a Restricted Maximum Likelihood Estimator (RMLE) by incorporating the exact linear restriction on the unknown parameters. Recently Şiray et al (2015) [1] proposes a new estimator called Restricted Liu Estimator (RLE) by replacing MLE by RMLE in the logistic Liu estimator.…”