arXiv subjects

Jibo Wu

Publications and source records attributed to Jibo Wu.

5 recordsLinked to original sources

arXiv2026

Gradient estimate and Liouville theorem for a semilinear parabolic equation with variable coefficient

In this paper, we investigate the semilinear parabolic equation $\partial_t f-\Delta f=a(x,t)f^p$ on a complete Riemannian manifold with Ricci curvature bounded from below. By means of Nash-Moser iteration, we establish Li-Yau type gradient estimates for positive solutions to this equation, where the coefficient function $a$ can be either strictly sign-definite or sign-changing. As an application, we derive Liouville theorems for ancient and eternal solutions on manifolds with nonnegative Ricci curvature, generalizing a number of classical results. Our proof features the incorporation and tuning of two parameters in the auxiliary quantities to accommodate the variable coefficient $a$ and to extend the admissible range of $p$.

math.AP↗

arXiv2017

On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression

In order to overcome multicollinearity, we propose a stochastic restricted Liu-type max- imum likelihood estimator by incorporating Liu-type maximum likelihood estimator (Inan and Erdo- gan, 2013) to the logistic regression model when the linear restrictions are stochastic. We also discuss the properties of the new estimator. Moreover, we give a method to choose the biasing parameter in the new estimator. Finally, a simulation study is given to show the performance of the new estimator.

stat.ME↗

arXiv2017

Preliminary testing derivatives of a linear unified estimator in the logistic regression model

Recently, the well known Liu estimator (Liu, 1993) is attracted researcher's attention in regression parameter estimation for an ill conditioned linear model. It is also argued that imposing sub-space hypothesis restriction on parameters improves estimation by shrinking toward non-sample information. Chang (2015) proposed the almost unbiased Liu estimator (AULE) in the binary logistic regression. In this article, some improved unbiased Liu type estimators, namely, restricted AULE, preliminary test AULE, Stein-type shrinkage AULE and its positive part for estimating the regression parameters in the binary logistic regression model are proposed based on the work Chang (2015). The performances of the newly defined estimators are analysed through some numerical results. A real data example is also provided to support the findings.

math.ST↗

arXiv2017

Efficiency of the principal component Liu-type estimator in logistic regression model

In this paper we propose a principal component Liu-type logistic estimator by combining the principal component logistic regression estimator and Liu-type logistic estimator to overcome the multicollinearity problem. The superiority of the new estimator over some related estimators are studied under the asymptotic mean squared error matrix. A Monte Carlo simulation experiment is designed to compare the performances of the estimators using mean squared error criterion. Finally, a conclusion section is presented.

stat.ME↗

arXiv2017

On the restricted almost unbiased Liu estimator in the Logistic regression model

It is known that when the multicollinearity exists in the logistic regression model, variance of maximum likelihood estimator is unstable. As a remedy, in the context of biased shrinkage ridge estimation, Chang (2015) introduced an almost unbiased Liu estimator in the logistic regression model. Making use of his approach, when some prior knowledge in the form of linear restrictions are also available, we introduce a restricted almost unbiased Liu estimator in the logistic regression model. Statistical properties of this newly defined estimator are derived and some comparison result are also provided in the form of theorems. A Monte Carlo simulation study along with a real data example are given to investigate the performance of this estimator.

math.ST↗