Generalized p-Values and Generalized Confidence Intervals for Variance Components in General Random Effect Model with Balanced Data

Abstract

Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type I error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type I error probability.

Measurement of dispersion of PM 2.5 in Thailand using confidence intervals for the coefficient of variation of an inverse Gaussian distribution

“…Since the GCI approach was first introduced by Weerahandi (1993) , several researchers have used it to provide statistical inferences ( Tsui & Weerahandi, 1989 ; Weerahandi, 1993 ; Weerahandi, 1995 ; Ye & Wang, 2007 ; Krishnamoorthy & Tian, 2008 ). After that, Ye, Ma & Wang (2010) presented the generalized pivot quantity (GPQ) criterion for the parameters and the constructed confidence intervals for the common mean of several inverse Gaussian populations.…”