Changepoint Problems Under Random Censorship

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.