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...

We consider an efficient estimation of an unknown parameter appearing in both the drift and the diffusion coefficient for a d-dimensional dynamical system with small noise. Asymptotic properties of an M -estimator obtained from an approximate quadratic martingale estimating function are stated. The sample path is observed at equidistant times k/n, k = 0, 1, . . . , n. The type of asymptotics co...

A leading multivariate extension of the univariate quantiles is the so-called “spatial” or “geometric” notion, for which sample versions are highly robust and conveniently satisfy a Bahadur-Kiefer representation. Another extension of univariate quantiles has been to univariate U-quantiles, on the basis of which, for example, the well-known Hodges-Lehmann location estimator has a natural formula...

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index H∈(0,1)/{12}. Under some assumptions on drift coefficient, we obtain asymptotic normality and moment convergence maximum likelihood estimator parameter when a dispersion coefficient ε→0.

We identify a large sample of isolated bright galaxies and their fainter satellites in the 2dF Galaxy Redshift Survey (2dFGRS). We analyse the dynamics of ensembles of these galaxies selected according to luminosity and morphological type by stacking the positions of their satellites and estimating the velocity dispersion of the combined set. We test our methodology using realistic mock catalog...

Cross-traffic data rate over the tight link of a path can be estimated using different active probing packet dispersion techniques. Many of these techniques send large amounts of probing traffic but use just a tiny fraction of the measurements to estimate the long-run cross-traffic average. In this paper, we are interested in short-term cross-traffic estimation using bandwidth efficient techniq...

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...

We consider the chain ladder reserving method in a Bayesian set up, which allows for combining individual claims development data with portfolio information as for instance development patterns from industry-wide data. We derive the Bayes estimators and the credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the expone...

Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with such a procedure. We introduce different models which ar...