Rank tests for changepoint problems

SUMMARY We consider procedures based on quadratic form rank statistics to test for one or more changepoints in a series of independent observations. Models incorporating both smooth and abrupt changes are introduced. Various test statistics are suggested, their asymptotic null distributions are derived and tables of significance points are given. A Monte Carlo study shows that the asymptotic significance points are applicable to moderately sized samples.

[1]  T. W. Anderson,et al.  Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes , 1952 .

[2]  G. S. Watson,et al.  Goodness-of-fit tests on a circle. II , 1961 .

[3]  F. B. Hildebrand.  Advanced Calculus for Applications , 1962 .

[4]  Michel Loève,et al.  Probability Theory I , 1977 .

[5]  P. Sen,et al.  Theory of rank tests , 1969 .

[6]  Richard A. Johnson,et al.  Nonparametric Tests for Shift at an Unknown Time Point , 1968 .

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

[8]  G. Martynov.  Computation of Distribution Functions of Quadratic Forms of Normally Distributed Random Variables , 1976 .

[9]  Ian B. MacNeill,et al.  Properties of Sequences of Partial Sums of Polynomial Regression Residuals with Applications to Tests for Change of Regression at Unknown Times , 1978 .

[10]  A. Pettitt.  A Non‐Parametric Approach to the Change‐Point Problem , 1979 .

[11]  D. A. Hsu,et al.  Detecting Shifts of Parameter in Gamma Sequences with Applications to Stock Price and Air Traffic Flow Analysis , 1979 .

[12]  Mukhtar M. Ali,et al.  The Identical Distribution Hypothesis for Stock Market Prices—Location- and Scale-Shift Alternatives , 1982 .

[13]  S. Zacks.  Classical and Bayesian Approaches to the Change-Point Problem: Fixed Sample and Sequential Procedures. , 1982 .

[14]  Edna Schechtman.  A nonparametric test for detecting changes in location , 1982 .

[15]  F. Lombard.  Asymptotic distributions of rank statistics in the change-point problem , 1983 .

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

[17]  Detecting a shift in location: Some robust tests , 1983 .

[18]  Douglas A. Wolfe,et al.  Nonparametric statistical procedures for the changepoint problem , 1984 .

[19]  J. Kline,et al.  The cusum test of homogeneity with an application in spontaneous abortion epidemiology. , 1985, Statistics in medicine.