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Consistency of the <i>φ</i>-Divergence Based Change Point Estimator
Pan-African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya
Department of Statistics and Actuarial Sciences, JKUAT, Nairobi, Kenya
Department of Mathematics, Statistics and Actuarial Sciences, Machakos University, Machakos, Kenya
Department of Statistics and Actuarial Sciences, JKUAT, Nairobi, Kenya
- 1 Pan-African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya
- 2 Department of Statistics and Actuarial Sciences, JKUAT, Nairobi, Kenya
- 3 Department of Mathematics, Statistics and Actuarial Sciences, Machakos University, Machakos, Kenya
- 4 Department of Statistics and Actuarial Sciences, JKUAT, Nairobi, Kenya
Open Journal of Statistics·Volume 10 (2020)·Pages 832–849·Published 26 October 2020·DOI10.4236/ojs.2020.105048
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Abstract
This paper utilizes a change-point estimator based on the φ - divergence. Since we seek a near perfect translation to reality, then locations of parameter change within a finite set of data have to be accounted for since the assumption of stationary model is too restrictive especially for long time series. The estimator is shown to be consistent through asymptotic theory and finally proven through simulations. The estimator is applied to the generalized Pareto distribution to estimate changes in the scale and shape parameters.
KeywordsChange PointConsistencyφ-DivergenceKullback-LeiblerGeneralized Pareto Distribution
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