Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 1, 37-48

ASYMPTOTIC NULL DISTRIBUTIONS OF TESTS FOR CHANGE IN LEVEL IN CORRELATED DATA

By

NEERCHAL K. NAGARAJ, University of Maryland

And

CHADA S. REDDY, University of Minnesota

 

SUMMARY. In the classical change point problem, the observations, X1, X2, , Xn are assumed to be independent. Further it is assumed that we have E(Xi) = m for i = 1,2,., k and E(Xi) = m + d for i = k+1, k+2, , n; for some 1 k<n.the integer k is known as the change point. In this article, we study the asymptotic distributions of certain test statistics (which are locally optimal for independent normal observations) when the observations are associated and strictky stationary. Applications include autoregressive processes. The asymptotic null distributinal results suggest that, even in the modest autocorrelation in the data, the true Type I Error could exceed twice the corresponding value for independent observations. Based on the asymptotic results a correction factor is suggested for the test statistics to account for the correlation.

AMS (1990) subject classification. 62F05,62M10

Key words and phrases. Change point problem, invariance principle, locally optimal invariant tests, associated random variables, Brownian motion, autocovariance function.

FULL PAPER.

This article in Mathematical Reviews.