Estimating sample mean under interval uncertainty and constraint on sample varience

Authors

Misha Koshelev, Baylor College of MedicineFollow
Ali Jalal-Kamali, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow

Publication Date

2011

Comments

Published in: International Journal of Approximate Reasoning 52(2011) 1136-1146

Abstract

Traditionally, practitioners start a statistical analysis of a given sample x₁, … , x_n by computing the sample mean E and the sample variance V. The sample values x_i usually come from measurements. Measurements are never absolutely accurate and often, the only information that we have about the corresponding measurement errors are the upper bounds Δ_i on these errors. In such situations, after obtaining the measurement result , the only information that we have about the actual (unknown) value x_i of the ith quantity is that x_i belongs to the interval . Different values x_i from the corresponding intervals lead, in general, to different values of the sample mean and sample variance. It is therefore desirable to find the range of possible values of these characteristics when x_i ∈ x_i.

Often, we know that the values x_i cannot differ too much from each other, i.e., we know the upper bound V₀ on the sample variance V : V ⩽ V₀. It is therefore desirable to find the range of E under this constraint. This is the main problem that we solve in this paper.