Estimators of the variance of the sample mean: Quadratic forms, optimal batch sizes, and linear combinations
Abstract
A classical problem of stochastic simulation is how to estimate the variance of point estimators, the prototype problem being the sample mean from a steady-state autocorrelated process. A variety of estimators for the variance of the sample mean exist, all designed to provide robustness to violations of assumptions, small variance, and reasonable computing requirements. No estimator seems to dominate the others in terms of the statistical properties for all covariance-stationary processes and for all sample sizes. Obtaining good estimators of the variance of the sample mean for all covariance-stationary processes is the primary motivation of the author's dissertation research. The research encompasses three areas: (1) The investigation of some desirable properties of the class of quadratic-form estimators and the derivation of quadratic-form coefficients for some well-known estimators. (2) The investigation of optimal batch sizes and the derivation of an explicit formula for the asymptotic optimal batch size as a function of sample size, estimator type, and the center of gravity of the nonnegative autocorrelations of the data type. (3) The creation of estimators with smaller variance or mean squared error by using linear combinations of known estimators.
Degree
Ph.D.
Advisors
Schmeiser, Purdue University.
Subject Area
Industrial engineering
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