Random Sets and Confidence Procedures

نویسندگان

  • WILLIAM A. BARNETT
  • W. A. BARNETT
چکیده

The set of confidence procedures is identified as a fundamental subset of the set of random sets. This is accomplished by defining a simple a-field on the codomain of a set-valued mapping such that the mapping is a confidence procedure if it is measurable relative to that a-field. The confidence procedure becomes Borei measurable when the a-field is generated by a topology that we also define. The resulting topology and a-fields are shown to be natural choices on &(R) — {0 }. The motivation for the approach is the same as that motivating the use of statistics in point estimation. The theory of confidence procedures in set estimation is shown to be a simple extension of the theory of statistics in point estimation.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Geometric Approach to Confidence Sets for Ratios: Fieller’s Theorem, Generalizations, and Bootstrap

We present a geometric method to determine confidence sets for the ratio E(Y )/E(X) of the means of random variables X and Y . This method reduces the problem of constructing confidence sets for the ratio of two random variables to the problem of constructing confidence sets for the means of one-dimensional random variables. It is valid in a large variety of circumstances. In the case of normal...

متن کامل

Comparing confidence-based and conventional scoring methods: The case of an English grammar class

This study aimed at investigating the reliability, predictive validity, and self-esteem and gender bias of confidence-based scoring. This is a method of scoring in which the test takers receive a positive or negative point based on their rating of their confidence in an answer. The participants, who were 49 English-major students taking their grammar course, were given 8 multiple-choice tests d...

متن کامل

Universal Confidence Sets for Solutions of Optimization Problems

We consider random approximations to deterministic optimization problems. The objective function and the constraint set can be approximated simultaneously. Relying on concentration-of-measure results we derive universal confidence sets for the constraint set, the optimal value and the solution set. Special attention is paid to solution sets which are not single-valued. Many statistical estimato...

متن کامل

Random Procedures for Dominating Sets in Graphs

We present and analyze some random procedures for the construction of small dominating sets in graphs. Several upper bounds for the domination number of a graph are derived from these procedures.

متن کامل

Propagation Models and Fitting Them for the Boolean Random Sets

In order to study the relationship between random Boolean sets and some explanatory variables, this paper introduces a Propagation model. This model can be applied when corresponding Poisson process of the Boolean model is related to explanatory variables and the random grains are not affected by these variables. An approximation for the likelihood is used to find pseudo-maximum likelihood esti...

متن کامل

ذخیره 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 2008