AISM 53, 469-486
© 2001 ISM
(Received September 6, 1999; revised April 24, 2000)
Abstract. Mixed interval-censored (MIC) data consist of $n$ intervals with end-points $L_i$ and $R_i$, $i=1, \ldots, n$. At least one of them is a singleton set and one is a finite non-singleton interval. The survival time $X_i$ is only known to lie between $L_i$ and $R_i$, $i=1,2,\ldots,n$. Peto (1973, Applied Statistics, 22, 86-91) and Turnbull (1976, J. Roy. Statist. Soc. Ser. B, 38, 290-295) obtained, respectively, the generalized MLE (GMLE) and the self-consistent estimator (SCE) of the distribution function of $X$ with MIC data. In this paper, we introduce a model for MIC data and establish strong consistency, asymptotic normality and asymptotic efficiency of the SCE and GMLE with MIC data under this model with mild conditions.
Key words and phrases: Asymptotic normality, generalized maximum likelihood estimator, mixture distribution, strong consistency.
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