Efficiency of NPMLE in Nonparametric Missing Data Models
نویسندگان
چکیده
Suppose that a random variable X of interest is grouped or censored or missing so that one only observes a coarsening of X, i.e., a random set containing X with probability 1. It is assumed that the coarsening mechanism has the coarsening at random property. Suppose furthermore that the coarsening either equals X itself or that is a set with positive Xprobability. We modify the NPMLE of the distribution of X by demanding that its support is the set of observed data points. We provide a general theorem giving sufficient conditions for efficiency of this NPMLE, or efficiency of the NPMLE after a small data reduction. We apply the theorem to a number of examples.
منابع مشابه
Communication Identity for NPMLE in Missing and Biased Sampling Models
We derive an identity for NPMLE in non-parametric missing data models and biased sampling models, which almost says that the NPMLE is efficient. Application of empirical process theory to the identity provides us with a straightforward consistency and efficiency proof. The identity is illustrated with the random truncation model.
متن کاملIdentity for the NPMLE in censored data models.
We derive an identity for nonparametric maximum likelihood estimators (NPMLE) and regularized MLEs in censored data models which expresses the standardized maximum likelihood estimators in terms of the standardized empirical process. This identity provides an effective starting point in proving both consistency and efficiency of NPMLE and regularized MLE. The identity and corresponding method f...
متن کاملciency of NPMLE in Nonparametric Missing Data
Suppose that a random variable X of interest is grouped or censored or missing so that one only observes a coarsening of X, i.e., a random set containing X with probability 1. It is assumed that the coarsening mechanism has the coarsening at random property. Suppose furthermore that the coarsening either equals X itself or that is a set with positive X-probability. We modify the NPMLE of the di...
متن کاملEstimating the survival function based on the semi-Markov model for dependent censoring.
In this paper, we study a nonparametric maximum likelihood estimator (NPMLE) of the survival function based on a semi-Markov model under dependent censoring. We show that the NPMLE is asymptotically normal and achieves asymptotic nonparametric efficiency. We also provide a uniformly consistent estimator of the corresponding asymptotic covariance function based on an information operator. The fi...
متن کاملNonparametric estimation of a distribution function under biased sampling and censoring
Abstract: This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the algorithm suggested by Vardi (Biometrika, 1989) for size biased data. Application of the algorithm to many models is discussed and a simulation st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999