Tests for a change-point

SUMMARY The problem considered is that of testing a sequence of independent normal random variables with constant, known or unknown, variance for no change in mean versus alternatives with a single change-point. Various tests, such as those based on the likelihood ratio and recursive residuals, are studied. Power approximations are developed by integrating approximations for conditional boundary crossing probabilities. A comparison of several tests is made.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[2]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[3]  J. Kiefer,et al.  K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests , 1959 .

[4]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[5]  H. Chernoff,et al.  ESTIMATING THE CURRENT MEAN OF A NORMAL DISTRIBUTION WHICH IS SUBJECTED TO CHANGES IN TIME , 1964 .

[6]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[7]  P. Armitage,et al.  Repeated Significance Tests on Accumulating Data , 1969 .

[8]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[9]  L. A. Gardner.  On Detecting Changes in the Mean of Normal Variates , 1969 .

[10]  H. E. Daniels,et al.  The maximum size of a closed epidemic , 1974, Advances in Applied Probability.

[11]  J. Durbin,et al.  Techniques for Testing the Constancy of Regression Relationships Over Time , 1975 .

[12]  D. Siegmund,et al.  Repeated significance tests for a normal mean , 1977 .

[13]  D. Hawkins.  Testing a Sequence of Observations for a Shift in Location , 1977 .

[14]  S. Pocock.  Group sequential methods in the design and analysis of clinical trials , 1977 .

[15]  G. Cobb.  The problem of the Nile: Conditional solution to a changepoint problem , 1978 .

[16]  D. Siegmund.  Estimation following sequential tests , 1978 .

[17]  Keith J. Worsley,et al.  On the Likelihood Ratio Test for a Shift in Location of Normal Populations , 1979 .

[18]  Wilfrid S. Kendall,et al.  Alignments in two-dimensional random sets of points , 1980, Advances in Applied Probability.

[19]  Anthony N. Pettitt,et al.  A simple cumulative sum type statistic for the change-point problem with zero-one observations , 1980 .

[20]  David M. De Long.  Crossing probabilities for a square root boundary by a bessel process , 1981 .

[21]  A. D. Barbour,et al.  Brownian motion and a sharply curved boundary , 1981 .

[22]  Pranab Kumar Sen,et al.  Invariance Principles for Recursive Residuals , 1982 .

[23]  D. Picard,et al.  Tests of Disorder of Regression: Asymptotic Comparison , 1982 .

[24]  Keith J. Worsley,et al.  The power of likelihood ratio and cumulative sum tests for a change in a binomial probability , 1983 .

[25]  D. Siegmund.  Sequential Analysis: Tests and Confidence Intervals , 1985 .

[26]  David E. Matthews,et al.  Asymptotic Score-Statistic Processes and Tests for Constant Hazard Against a Change-Point Alternative , 1985 .

[27]  D. Siegmund.  Boundary Crossing Probabilities and Statistical Applications , 1986 .