The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. We established the minimaxity of Baranchick-type estimators for identity covariance matrix and the matrix associated to the loss function is diagonal. In particular the class of James-Stein estimator is presented. The general situation for both matrices cited above is discussed.

In this paper, we study nonparametric local linear estimation of the conditional density of a randomly censored scalar response variable given a functional random covariate. We establish under general conditions the pointwise almost sure convergence with rates of this estimator under $$\alpha $$α -mixing dependence. Finally, to show interests of our results, on the practical point of view, we have conducted a computational study, first on a simulated data and, then on some real data concerning Kidney transplant data.

Let Y be a random real response, which is subject to right censoring by another random variable C . In this paper, we study the nonparametric local linear estimation of the conditional density of a scalar response variable and when the covariable takes values in a semi-metric space. Our main aim is to prove under some regularity conditions both the pointwise and the uniform almost-sure consistencies with convergence rates of the conditional density estimator related by this estimation procedure.

In this paper, we are interested in estimating a multivariate normal mean under the balanced loss function using the shrinkage estimators deduced from the Maximum Likelihood Estimator (MLE). First, we consider a class of estimators containing the James-Stein estimator, we then show that any estimator of this class dominates the MLE, consequently it is minimax. Secondly, we deal with shrinkage estimators which are not only minimax but also dominate the James- Stein estimator.

In this paper, we investigate the problem of the local linear estimation of the conditional ageing intensity function, when the variable of interest is subject to random right-censored. We establish under appropriate conditions the asymptotic normality of this estimator.

This work consists of developing shrinkage estimation strategies for the multivariate normal mean when the covariance matrix is diagonal and known. The domination of the positive part of James–Stein estimator (PPJSE) over James–Stein estimator (JSE) relative to the balanced loss function (BLF) is analytically proved. We introduce a new class of shrinkage estimators which ameliorate the PPJSE, and then we construct a series of polynomial shrinkage estimators which improve the PPJSE; also, any estimator of this series can be ameliorated by adding to it a new term of higher degree. We end this paper by simulation studies which confirm the performance of the suggested estimators.