The current note discusses the consistency proof for the penalized maximum likelihood estimator of a Gaussian mixture from the paper ‘Inference for multivariate normal mixtures’ by J. Chen and X. Tan. A soft spot in that proof is identified and a rigorous alternative proof based on a uniform...

Strong consistency of the least-squares estimates in stochastic regression models is established assuming errors with variance not necessarily defined. The errors will be considered identically distributed having absolute moment of order r, 0r⩽2 and, additionally, pairwise independent whenever...

Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived...

Consider the partial linear models of the formY=X[tau][beta]+g(T)+e, where thep-variate explanatoryXis erroneously measured, and bothTand the responseYare measured exactly. LetXbe the surrogate variable forXwith measurement error. Let the primary data set be that containing independent...

Chirp signals play an important role in the statistical signal processing. Recently Kundu and Nandi (2008) [8] derived the asymptotic properties of the least squares estimators of the unknown parameters of the chirp signals model in the presence of stationary noise. Unfortunately they did not...

How to include censored data in a statistical analysis is a recurrent issue in statistics. In multivariate extremes, the dependence structure of large observations can be characterized in terms of a non parametric angular measure, while marginal excesses above asymptotically large thresholds...

We study the estimation of some linear functionals which are based on an unknown lifetime distribution. The observations are assumed to be generated under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring...

We derive formulae for the higher order tail moments of the lower truncated multivariate standard normal (MVSN), Student’s t, lognormal and a finite-mixture of multivariate normal distributions (FMVN). For the MVSN we propose a recursive formula for moments of arbitrary order as a...

We consider a large class of transformation models introduced by Gu et al. (2005)  [14]. They proposed an estimation procedure for calculating the maximum partial marginal likelihood estimator (MPMLE) of regression parameters. A big advantage of MPMLE is that it avoids estimating two...

In this article, a novel adaptive estimation is proposed for varying coefficient models. Unlike the traditional least squares based methods, the proposed approach can adapt to different error distributions. An efficient EM algorithm is provided to implement the proposed estimation. The...