TITLE:
Statistically Dual Distributions and Estimation
AUTHORS:
Sergey Bityukov, Nikolai Krasnikov, Saralees Nadarajah, Vera Smirnova
KEYWORDS:
Distribution Theory, Confidence Distribution, Measurement, Error Theory, Data Analysis: Algorithms and Implementation, Data Management
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
8,
2014
ABSTRACT:
The reconstruction
of a parameter by the measurement of a random variable depending on the
parameter is one of the main tasks in statistics. In statistical inference, the
concept of a confidence distribution and, correspondingly, confidence density
has often been loosely referred to as a distribution function on the
parameter space that can represent confidence intervals of all levels for a
parameter of interest. In this short note, the notion of statistically dual
distributions is discussed. Based on properties of statistically dual
distributions, a method for reconstructing the confidence density of a
parameter is proposed.