Abstract
In this paper, a new detecting procedure for the change point in the mean is proposed based on a linear kernel smoother. It uses a discontinuous kernel function and has a relative high constant efficiency in an interval of shift value and thus is less sensitive than the simple CUSUM, EWMA, FMA and Shiryayev-Roberts procedures. It also generalizes the FMA procedure.
Similar content being viewed by others
References
Gordon L, Pollak M (1994) An efficient sequential nonparametric scheme for detecting a change of distribution (To appear in Ann Statist)
Lai TL (1974) Control charts based on weighted sums. Ann Statist 2:134–147
Lorden G (1971) Procedures for reacting to a change in distribution. Ann Math Statist 42:1897–1908
Lucas JM, Saccucci MS (1990) Exponentially weighted moving average control charts schemes: Properties and enhancements. Technometrics 32:1–30
McDonald D (1990) A CUSUM procedure based on sequential ranks. Nav Res Log Quart 37:627–646
Pollak M, Siegmund D (1975) Approximations to be expected sample size of certain sequential tests. Ann Statist 3:1267–1282
Pollak M, Siegmund D (1985) A diffusion process and its applications to detecting a change in the drift of Brownian motion. Biometrika 72:267–280
Pollak M, Siegmund D (1986) Convergence of quasi-stationary to stationary distribution for stochastic Markov processes. J Appl Prob 23:215–220
Roberts SW (1966) A comparison of some control chart procedures. Technometrics 8:411–430
Shiryayev AN (1963) On optimum methods in quickest detection problems. Theo Prob Appl 13:22–46
Srivastava MS, Wu Y (1993) Comparison of EWMA, CUSUM and Shiryayev-Roberts procedures for detecting a shift in the mean. Ann Statist 21:645–670
Wu Y (1994) On the design of control charts for detecting the change point. To appear in: Change Point Problems. IMS Lecture Notes (Carlstein Muller and Siegmund eds)
Wu Y, Srivastava MS (1993) On the dynamic sampling plans in on-line control charts. Canad J Statist 21:409–419
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wu, Y. A less sensitive linear detector for the change point based on kernel smoothing method. Metrika 43, 43–55 (1996). https://doi.org/10.1007/BF02613896
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02613896