Advances and Applications in Statistics
Volume 7, issue 2, Pages 157 - 174
(August 2007)
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ESTIMATION OF THE CHANGE-POINTS OF THE MEAN RESIDUAL LIFE FUNCTION
Sara Diallo (France)
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Abstract: Estimators for location and size of a discontinuity or change-point in a smooth mean residual life model are proposed. The proposed estimators also apply to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak convergence of a stochastic process in local differences to a Gaussian process is established for properly scaled versions of estimators for the location of a change-point. The continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change-point estimators. |
Keywords and phrases: mean residual life function, jump size, kernel estimation, weak convergence, smoothing, Hille?s theorem, survival function. |
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