Conditional Interval Estimation of the Ratio of Variance Components following Rejection of a Pre-test

Abstract

The conditional confidence interval for a ratio of variance components in the random effects model and the random effects nested design following a preliminary test, is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage pobability of the UCI is not uniformly greater than or less than the nominal level. The UCI is appropriate only when one does not perform any pre-test. However, if a pre-test is performed before the construction of a confidence interval, then the appropriate confidence interval is the CCI because the pre-test affects subsequent inference procedures.

Optimum Critical Value for Pre-Test Estimator

“…This preliminary test estimator has been explored by Bancroft (1944), followed by Bancroft (1964), Han and Bancroft (1968), Judge and Bock (1978), Ali and Saleh (1990), Kibria and Saleh (1993), Saleh and Kibria (1993), Benda (1996), Chiou and Han (1999), Han (2002), Wan and Zou (2003), and recently Kibria and Saleh (2004), among others. Detailed reviews of preliminary test estimation procedures are given by Han et al (1977) and Giles and Giles (1993), among others.…”

Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

“…Meeks and D'agostino (1983) proposed a method to find the conditional confidence interval (CCI) for the mean in the normal distribution. Han (1994, 1995) got a conditional interval for the location and scale parameter for the exponential distribution, Mahdi (2003Mahdi ( ,2004) got a CCI for the shape and scale parameters for the Weibull distribution, further information could be seen in Madhi (2000) and Chiou and Han (1998 Henderson, 1953;Rash and Masata, 2006). Another example is the estimation of risk of extinction or decline of a population that requires estimation of variability of vital rates such as survival and fecundity (Akcakaya, 2002).…”