Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value-at-risk. The variance of the weight sample quantile estimator is usually a difficult quantity to compute. In this paper, we present the exact convergence rate and asymptotic distributions of the bootstrap variance estimators for quantiles of weighted empirical distributions. Under regular...

In recent years, the use of vector variance as a measure of multivariate variability has received much attention in wide range of statistics. This paper deals with a more economic measure of multivariate variability, defined as vector variance minus all duplication elements. For high dimensional data, this will increase the computational efficiency almost 50 % compared to the original vector va...

Given a sample from a discretely observed compound Poisson process we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. Asymptotic expansions of the bias and variance of the estimator are given and pointwise weak consistency and asymptotic normality are established. We also derive the minimax conve...

We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. Another example is the number of protected nodes. The offs...

We derive an asymptotic expression for the variance of the number of 2-protected nodes (neither leaves nor parents of leaves) in a binary trie. In an unbiased trie on n leaves we find, for example, that the variance is approximately .934n plus small fluctuations (also of order n); but our result covers the general (biased) case as well. Our proof relies on the asymptotic similarities between a ...

This paper develops a robust testing procedure for the nonparametric kernel method in the presence of temporal dependence of unknown forms. We …rst propose a new variance estimator that corrects the …nite sample bias caused by temporal dependence. The new variance estimator is novel in the sense that it is not only robust to temporal dependence in …nite samples but also consistent in large samp...

In this contribution we study the statistical properties of a number of closed-loop identiication methods and parameterizations. A focus will be on asymptotic variance expressions for these methods. By studying the asymptotic variance for the parameter vector estimates we show that indirect methods fail to give better accuracy than the direct method. Some new results for bias distribution in cl...

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and...

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. ...