The effects of dependence on nonparametric detection

Abstract

This paper investigates the effects of dependence on rank tests, in particular on a class of recently defined nonparametric tests called "mixed" statistical tests. It is shown that the mixed test statistic is asymptotically normal for Gaussian processes with mild regularity properties justifying the use of asymptotic relative efficiency (ARE) as a figure of merit. Results are presented in terms of variations on three well-known statistics--the one-sample Wilcoxon, the two-sample Mann-Whitney, and the Kendalltau. It is found that the effects of dependence on ARE with respect to a parametric test can be offset to some extent by appropriately grouping sample values. If, however, a constant false-alarm rate is to be attained, either the form of the dependence must be known or some learning scheme must be applied.

Keywords

This publication has 15 references indexed in Scilit:

The effect of autoregressive dependence on a nonparametric test (Corresp.)
IEEE Transactions on Information Theory, 1967
An automatic decision threshold for polarity coincidence arrays
Published by Institute of Electrical and Electronics Engineers (IEEE) ,1966
Nonparametric detection of a signal of known form in additive noise
IEEE Transactions on Information Theory, 1965
On nonparametric signal detectors
IEEE Transactions on Information Theory, 1964
Asymptotic Efficiency of Certain Locally Most Powerful Rank Tests
The Annals of Mathematical Statistics, 1961
On Strong Mixing Conditions for Stationary Gaussian Processes
Theory of Probability and Its Applications, 1960
Asymptotic Normality and Efficiency of Certain Nonparametric Test Statistics
The Annals of Mathematical Statistics, 1958
Most Powerful Rank-type Tests
The Annals of Mathematical Statistics, 1957
A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
Proceedings of the National Academy of Sciences, 1956
A Class of Statistics with Asymptotically Normal Distribution
The Annals of Mathematical Statistics, 1948