Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established. Tyler’s M-estimator has been recognized as the ‘most robust’ M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler’s M-estimators for location and shape are generalized by taking account of incomplete data. It is shown that the shape matrix esti...

In this paper, we propose a new ridge-type estimator called the new mixed ridge estimator (NMRE) by unifying the sample and prior information in linear measurement error model with additional stochastic linear restrictions. The new estimator is a generalization of the mixed estimator (ME) and ridge estimator (RE). The performances of this new estimator and mixed ridge estimator (MRE) against th...

In this paper we consider the problem of optimality in manifold reconstruction. A random sample Xn = {X1, . . . , Xn} ⊂ R composed of points lying on a d-dimensional submanifold M , with or without outliers drawn in the ambient space, is observed. Based on the Tangential Delaunay Complex [4], we construct an estimator M̂ that is ambient isotopic and Hausdorffclose to M with high probability. The...

Let (Xj , Yj) n j=1 be a realization of a bivariate jointly strictly stationary process. We consider a robust estimator of the regression function m(x) = E(Y |X = x) by using local polynomial regression techniques. The estimator is a local M-estimator weighted by a kernel function. Under mixing conditions satisfied by many time series models, together with other appropriate conditions, consiste...

We develop two new methods for selecting the penalty parameter L1-penalized high-dimensional M-estimator, which we refer to as analytic and bootstrap-after-cross-validation methods. For both methods, derive nonasymptotic error bounds corresponding M-estimator show that converge zero under mild conditions, thus providing a theoretical justification these demonstrate via simulations finite-sample...

this article examines statistical inference for  where and are independent but not identically distributed pareto of the first kind (pareto (i)) random variables with same scale parameter but different shape parameters. the maximum likelihood, uniformly minimum variance unbiased and bayes estimators with gamma prior are used for this purpose. simulation studies which compare the estimators are ...