Rank Tests for Changepoint Problems

Abstract

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A nonparametric location–scale statistic for detecting a change point

“…Lombard [11] showed that the process defined by [28]. It is well-known that the W τ statistic and the M τ statistic are uncorrelated.…”

“…Lombard [11] discussed procedures based on quadratic form rank statistics to test for one or more change points and derived the asymptotic distribution of the general linear rank statistics in the change-point problem. Aly and Abd-Rabou [12] discussed some rank test statistics assuming that the sample size is random by theoretically and via simulation.…”

Testing Epidemic Changes of Infinite Dimensional Parameters

“…Tests constructed in Lombard [9] and Gombay [5] are based on rank statistics. Theorem 2 suggests tests based on the dyadic increments of empirical process.…”

On the power of nonparametric changepoint-tests

“…To name only a few papers, see for example Bhattacharya and Brockwel (1976), Bhattacharya (1987), Bhattacharya and Frierson (1981), Carlstein (1988), Cs6rg6 and Horvhth (1987, 1988a, 1988b, Darkhovskh (1976), Deshayes and Picard (1981), Diimbgen (1991), Hinkley (1970), Lombard (1987), Lorden (1971), Page (1954Page ( , 1955, Pettitt (1979) or Siegmund (1988). Most of these papers have one feature in common: They do not investigate the power of the tests.…”