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Estimating the Number of Change Points in Exponential Families Distributions
Author(s) -
Lee ChungBow
Publication year - 1997
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.t01-1-00058
Subject(s) - mathematics , estimator , exponential family , statistics , consistency (knowledge bases) , sequence (biology) , term (time) , exponential function , combinatorics , discrete mathematics , mathematical analysis , genetics , physics , quantum mechanics , biology
A simple method is proposed to detect the number of change points in a sequence of independent exponential family random variables. An estimator to maximize some criterion, say SC ( k ), which is to maximize the log‐ likelihood function with some penalty term, is used in detection. Under some mild assumptions, the consistency of the estimator for the true number of change points and the boundedness between the estimated change locations and the true change location are obtained. Some simulated results are given, and the Nile problem is investigated by this method.