Confidence intervals for the difference of means: application to the Behrens-Fisher type problem

A systematic method of the construction of a confidence interval for the difference between two means is given in the exponential and gamma cases. The application of a similar method to the Behrens-Fisher type problem is also given. Further, the numerical calculation of coverage probabilities is done and a comparison of the confidence interval proposed in this paper with that based on the Fisher-Welch-Wald similar test is given. As a result, the method is seen to be reasonable. Received: April 23, 1999; revised version: February 22, 2000     

Model-Selection-Based Detection of Unit Root Allowing for Various Trend-Break Types

In the conventional hypothesis-testing approach to the detection of a unit root and a trend break, selections of the outlier type (additive or innovational) and of the break type (jump or kink) are carried out arbitrarily, because there is no generally accepted statistical technique. To overcome this problem, a model-selection approach using the modified Bayesian information criterion (MBIC) is proposed. Whether the observed time series contains a unit root and a trend break is determined as a result of model selection from among alternative models with and without unit root and trend break. The efficacy of the proposed approach is verified using comprehensive simulations.     

Age–Period–Cohort Decomposition of U.S. and Japanese Birth Rates

Aggregate data on birth rates in the U.S. and Japan, classified by period and by age, are decomposed into age, period, and cohort effects using Bayesian cohort models that were developed to overcome the identification problem in cohort analysis. Main findings are fivefold. First, age, period, and cohort effects movements are all larger in Japan than in the U.S. Second, in both countries, age effects are the largest and are roughly consistent with the life-cycle movements showing an inverted U shape. Third, Easterlin’s cohort size hypothesis roughly fits U.S. birth rates but not Japanese birth rates. Fourth, despite rapid decline of total fertility rates in Japan in last three decades, period effects have been on an upward trend since the early 1990s. Finally, upward and downward cohort effects movements in Japan are derived by rapid economic growth and the Equal Employment Opportunity Law, respectively.     

Estimation of two ordered normal means when a covariance matrix is known

Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67–93] and Peddada et al. [Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703–715]. The estimators are also compared under the Pitman nearness criterion and it is shown that the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error.     

A higher order approximation to a percentage point of the non–central t-distribution

A higher order approximation formula for a percentage point of the noncentral t–distribution with v degrees of freedom is given up to the order o(v^-3), using the Cornish-Fisher expansion for the statistic based on a lin-ear combination of a normal random variable and a chi-random variable. The upper confidence limit and the confidence interval for the non–centrality parameter are given. Numerical results are also obtained.     

LOSS OF INFORMATION ASSOCIATED WITH THE ORDER STATISTICS AND RELATED ESTIMATORS IN THE DOUBLE EXPONENTIAL DISTRIBUTION CASE

Fisher (1934) derived the loss of information of the maximum likelihood estimator (MLE) of the location parameter in the case of the double exponential distribution. Takeuchi & Akahira (1976) showed that the MLE is not second order asymptotically efficient. This paper extends these results by obtaining the (asymptotic) losses of information of order statistics and related estimators, and by comparing them via their asymptotic distributions up to the second order.