Sufficient Statistics and Exponential Families

SMML estimators for exponential families with continuous sufficient statistics

The minimum message length principle is an information theoretic criterion that links data compression with statistical inference. This paper studies the strict minimum message length (SMML) estimator for d-dimensional exponential families with continuous sufficient statistics, for all d. The partition of an SMML estimator is shown to consist of convex polytopes (i.e. convex polygons when d = 2...

II Sufficient Statistics and Exponential Family

For the parameter estimation problem, we know nothing about the parameter but the observations from such a distribution. Therefore, the observations X1, · · · , Xn is our first hand of information source about the parameter, that is to say, all the available information about the parameter is contained in the observations. However, we know that the estimators we obtained are always functions of...

Reconstruction of Order Statistics in Exponential Distribution

In this article, a new censoring scheme is considered, namely, a middle part of a random sample is censored. A treatment for reconstructing the missing order statistics is investigated. The proposed procedure is studied in detail under exponential distribution which is widely used as a constant failure model in reliability. Different approaches are used to obtain point and interval reconstructo...

Exponential families

Features as Sufficient Statistics

An image is often represented by a set of detected features. We get an enormous compression by representing images in this way. Furthermore, we get a representation which is little affected by small amounts of noise in the image. However, features are typically chosen in an ad hoc manner. \Ve show how a good set of features can be obtained using sufficient statistics. The idea of sparse data re...