A generalized Liu-type estimator for logistic partial linear regression model with multicollinearity

Dayang Dai; Dabuxilatu Wang; Dayang Dai; Dabuxilatu Wang

doi:10.3934/math.2023600

AIMS Mathematics

2023, Volume 8, Issue 5: 11851-11874. doi: 10.3934/math.2023600

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Research article

A generalized Liu-type estimator for logistic partial linear regression model with multicollinearity

Dayang Dai ,
Dabuxilatu Wang ^,

School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China

Received: 27 December 2022 Revised: 17 February 2023 Accepted: 27 February 2023 Published: 20 March 2023
MSC : 62J07, 62G05, 62F10

This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matrix (MSEM) criterion. Moreover, the optimal choices of biasing parameters and function of biasing parameter are given. Numerical simulations demonstrate that the proposed GLTE performs better than the existing estimators. An application on a set of real data arising from the study of Indian Liver Patient is shown for illustrating our theoretical results.
- Liu estimator,
- logistic partial linear model,
- multicollinearity,
- profile likelihood,
- ridge estimator
Citation: Dayang Dai, Dabuxilatu Wang. A generalized Liu-type estimator for logistic partial linear regression model with multicollinearity[J]. AIMS Mathematics, 2023, 8(5): 11851-11874. doi: 10.3934/math.2023600

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Abstract

This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matrix (MSEM) criterion. Moreover, the optimal choices of biasing parameters and function of biasing parameter are given. Numerical simulations demonstrate that the proposed GLTE performs better than the existing estimators. An application on a set of real data arising from the study of Indian Liver Patient is shown for illustrating our theoretical results.

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