A comparison of estimators of the gain in efficiency achieved by importance sampling
Date
1975
Authors
Cumberbirch, Peter Mark
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Abstract
The problem investigated is that of estimating the 'relative gain' in efficiency achieved.by importance, or probability proportional to estimated size (ppes) sampling, a variance reduction technique: Monte Carlo sampling experiments are conducted in an exploratory study of several estimation procedures, each of which originates from either a one-sample or a two-sample approach to the problem.
The two-sample approach reduces to the usual variance comparison problem, although the sampled distributions are somewhat more restricted in this case. Assumptions of normality and of identical distributions, except, for location and scale, however, are violated; consequently robust estimation procedures are required. Jack-knife techniques, both with and without the natural log transformation, as well as slightly modified versions of the Box and Box-Andersen methods of variance comparison, are implemented in the Monte Carlo study. For comparative purposes, the classical F method is also included.
The two-sample Monte Carlo results indicate that the jackknife technique with the natural log transformation, and the Box method with subsample 10, are the leading competitors among the two-sample procedures. The jackknife proves to be the more powerful of the two, but tends to yield significance levels below the nominal level. The Box method, on the other hand, is more conservative and provides significance levels much nearer the nominal level.
For the one-sample approach, P . V. Sukhatme and B.V. Sukhatme have suggested an estimation technique based on a single sample which yields an estimator that allows negative estimates of t he variance ratio to occur. As an alternative to the Sukhatme estimator, a non-negative, one-sample estimator is proposed.
The Sukhatme estimator and jackknifed versions of the Sukhatme estimator, the non-negative estimator and the natural log of the non-negative estimator are compared. Results of the Monte Carlo experiments for the one-sample procedures tend to indicate that the non-negative estimator is superior to the Sukhatme estimator.