Unbiased Estimation of the Reciprocal Mean for Non-negative Random Variables

07/03/2019
by   Sarat Moka, et al.
0

Many simulation problems require the estimation of a ratio of two expectations. In recent years Monte Carlo estimators have been proposed that can estimate such ratios without bias. We investigate the theoretical properties of such estimators for the estimation of β = 1/E Z, where Z ≥ 0. The estimator, β(w), is of the form w/f_w(N) ∏_i=1^N (1 - w Z_i), where w < 2β and N is any random variable with probability mass function f_w on the positive integers. For a fixed w, the optimal choice for f_w is well understood, but less so the choice of w. We study the properties of β(w) as a function of w and show that its expected time variance product decreases as w decreases, even though the cost of constructing the estimator increases with w. We also show that the estimator is asymptotically equivalent to the maximum likelihood (biased) ratio estimator and establish practical confidence intervals.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/21/2020

Uncertainty on the Reproduction Ratio in the SIR Model

The aim of this paper is to understand the extreme variability on the es...
research
02/19/2019

Simulation study of estimating between-study variance and overall effect in meta-analysis of odds-ratios

Random-effects meta-analysis requires an estimate of the between-study v...
research
03/17/2021

Best estimator for bivariate Poisson regression

INTRODUCTION: Wald's, the likelihood ratio (LR) and Rao's score tests an...
research
01/17/2021

Variance Estimation and Confidence Intervals from High-dimensional Genome-wide Association Studies Through Misspecified Mixed Model Analysis

We study variance estimation and associated confidence intervals for par...
research
07/15/2020

Quantifying and Reducing Bias in Maximum Likelihood Estimation of Structured Anomalies

Anomaly estimation, or the problem of finding a subset of a dataset that...
research
07/03/2019

Estimating a probability of failure with the convex order in computer experiments

This paper deals with the estimation of a failure probability of an indu...
research
06/14/2022

Unbiased Estimation using the Underdamped Langevin Dynamics

In this work we consider the unbiased estimation of expectations w.r.t. ...

Please sign up or login with your details

Forgot password? Click here to reset