Existence theorems of a maximum likelihood estimate from a generalized censored data sample
Let T',T be given constants such that \(-\infty \leq T'<T\leq \infty\), and X be a random variable with values in [T',T]. If \((X_ 1,X_ 2,...,X_ n)\) is a random sample from the distribution of X, then the author considers the situation where the only information available for \(X_ i\) is that its value lies in a sub interval \(C_ i\) of [T',T] whose extreme points are random variables. The author defines this collection \(C=\{C_ 1,C_ 2,...,C_ n\}\) as the generalized censored (g.c.) data sample. Next, maximum likelihood (ML) estimation from the g.c. data is taken up. For this purpose, a new approach, called probability content boundary analysis is suggested. The author asserts that this approach is a very general and a unified one in comparison to the usual method of ML equations. This paper includes a large number of propositions, remarks, lemmas and theorems. Also included is a large set of simple illustrative examples to support the results obtained in the paper.
scientific article; zbMATH DE number 3915412