This paper suggests Liu-type shrinkage estimators in linear regression model the presence of multicollinearity under subspace information. The performance proposed is compared to estimator terms their relative efficiency via a Monte Carlo simulation study and real data set. results reveal that outperform better than estimator.

Multicollinearity in logistic regression affects the variance of the maximum likelihood estimator negatively. In this study, Liu-type estimators are used to reduce the variance and overcome the multicollinearity by applying some existing ridge regression estimators to the case of logistic regression model. A Monte Carlo simulation is given to evaluate the performances of these estimators when t...

Bootstrap techniques are widely used today in many other fields such as economics, Business Administration, Physics, Engineering, Chemistry, Meteorological, Biological Sciences and Medicine. This paper is concerned with the estimation of linear regression model parameters in the presence of heteroscedasticity using wild bootstrap approaches of Wu and Liu. The empirical evidence has shown that t...

We consider unbiased estimation following a group sequential test for distributions in a one-parameter exponential family. We show that, for an estimable parameter function, there exists uniquely an unbiased estimator depending on the sufficient statistic and based on the truncation-adaptation criterion (Liu and Hall (1999)); moreover, this estimator is identical to one based on the Rao-Blackwe...

The bounded normal mean problem has important applications in nonparametric function estimation. It is to estimate the mean of a normal distribution whose mean is restricted to a bounded interval. The minimax risk for such a problem is generally unknown. It is shown in Donoho, Liu and MacGibbon(1990) that the linear minimax risk provides a good approximation to the minimax risk. We show in this...

We consider a blockwise James-Stein estimator for nonparametric function estimation in suitable wavelet or Fourier bases. The estimator can be readily explained and implemented. We show that the estimator is asymptotically sharp-adaptive in minimax risk over any Sobolev ball containing the true function. Further, for a moderately broad range of bounded sets in Besov space our estimator is asymp...

Several efforts have been made to solve the multicollinearity problem, which arises from correlated regressors in linear regression model. This is because Ordinary Least Squares (OLS) Estimator becomes inefficient presence of multicollinearity.