Variance estimation in the particle filter Particle filters provide sampling based approximations of marginal likelihoods and filtering expectations in hidden Markov models. However, estimating the Monte Carlo variance of these approximations, without generating multiple independent realizations of the approximations themselves, is not straightforward. We present an unbiased estimator of the va...

Abstract: For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = ∑ k μ(k)P k. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker’s and Metropolis algorithms...

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for ...

We consider the ARMA(1,1) model and deal with the estimation of the residual variance. Results are known for the maximum likelihood(ML) es-timators under normality, both for known and unknowm mean, in which case the asymptotic biases depend on the number of parameters(including the mean) and on the true residual variance, but not on the values of the remaining parameters. For moment and least s...

Error variance estimation plays an important role in statistical inference for high dimensional regression models. This paper concerns with error variance estimation in high dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to sp...

We present two improvements on the technique of importance sampling. First we show that importance sampling from a mixture of densities, using those densities as control variates, results in a useful upper bound on the asymptotic variance. That bound is a small multiple of the asymptotic variance of importance sampling from the best single component density. This allows one to beneet from the g...

This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for estimating the parameters based on Type-I and Typ...

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. We present results on the asymptotic variance of estimators obtained using approximate Bayesian computation in a large-data limit. Our key...

I show how any reversible Markov chain on a finite state space that is irreducible, and hence suitable for estimating expectations with respect to its invariant distribution, can be used to construct a non-reversible Markov chain on a related state space that can also be used to estimate these expectations, with asymptotic variance at least as small as that using the reversible chain (typically...