The Poisson maximum likelihood (PML) is used to estimate the coefficients of regression model (PRM). Since resulting estimators are sensitive outliers, different studies have provided robust alleviate this problem. Additionally, PML estimator multicollinearity. Therefore, several biased been cope with problem, such as ridge estimator, Liu Kibria–Lukman and modified estimator. Despite being prop...

We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the Uncorrelated Weights Bootstrap (UBS). We find a representation of the UBS dispersion matrix and show that the bootstrap estimator is consistent if p/n → 0 where p is the dimension of the parameter and n is the sample size. For fixed dimension we sh...

In an extension of the work of Liu and Singh (1992), we consider resampling estimates for the variance of the least squares estimator in linear regression models. Second order terms in asymptotic expansions of these estimates are derived. By comparing the second order terms, certain generalised bootstrap schemes are seen to be theoretically better than other resampling techniques under very gen...

Maximum likelihood is the most widely used statistical estimation technique. Recent work by Jiao, Venkat, Han, and Weissman [1] introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements both in theory and in practice over the maximum likelihood estimator (MLE), particularly in high dimensional scenarios involving para...

We advocate the use of a new distribution family—the transelliptical—for robust inference of high dimensional graphical models. The transelliptical family is an extension of the nonparanormal family proposed by Liu et al. (2009). Just as the nonparanormal extends the normal by transforming the variables using univariate functions, the transelliptical extends the elliptical family in the same wa...

1 Department of Pharmacy, Xuzhou Medical College, 84 West Huaihai Road, Xuzhou, 221002, Jiangsu, China 2 Jiangsu Province Key Laboratory of Anesthesiology, Xuzhou Medical College, 84 West Huaihai Road, Xuzhou, Jiangsu 221002, China 3 Environment Protection Research Institute of Xuzhou, Xuzhou, Jiangsu Province, China 4 Department of Anesthesia, Xuzhou Medical College, 84 West Huaihai Road, Xuzh...

A detailed analysis of minimax estimates of arbitrary linear functionals based on infinite dimensional Gaussian models has been provided by Donoho and Liu. In particular it has been shown that if the parameter space is convex then linear estimates can always be found which have maximum mean squared error within a small constant multiple of the minimax value. These linear estimates do however ha...

The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recent progress has been made in Richard and Montanari [2014], Zhang and Xia [2017] and Liu et al. [2017] demonstrating that minimax optimal singular spaces estimation and low rank tensor recovery ...