Changepoint Problems Under Random Censorship

Abstract

Let X 1, …, X [nθ], X [nθ] + 1, …, X n be a sequence of independent random variables (the “lifetimes”) such that X j ˜ F 1 for 1 ≤ j ≤ [nθ] and X j ˜ F 2 for [nθ] + 1 ≤ j ≤ n, with F 1 ≠ F 2 unknown. In this paper we investigate an estimator θ n for the changepoint θ if the X's are subject to censoring. The rate of almost sure convergence of θ n to θ is established and a test for the hypothesis θ = 0, i.e. “no change”, is proposed.

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