R–estimation of normed bivariate density functions

Normed bivariate density funtions were introduced by HOEFFDING (1940/41). In the present paper estimators for normed bivariate ranks and on a FOURIER series expansion in LEGENDRE polynomials. The estimation of normed bivarate density functions under positive dependence is also described     

Charts for finding upper percentage points of Student's t in the range .01 to .00001

The Bonferroni t-statistic is a versatile tool in multiple comparisons problems. The need for "oddball percentage points" may lead to extensive tables or heavy computation. Charts of t_p as a function of log p enable near two-decimal accuracy for any percentage point between .01 and .00001     

Inferences on the Among-Group Variance Component in Unbalanced Heteroscedastic One-Fold Nested Design

This article studies the hypothesis testing and interval estimation for the among-group variance component in unbalanced heteroscedastic one-fold nested design. Based on the concepts of generalized p-value and generalized confidence interval, tests and confidence intervals for the among-group variance component are developed. Furthermore, some simulation results are presented to compare the performance of the proposed approach with those of existing approaches. It is found that the proposed approach and one of the existing approaches can maintain the nominal confidence level across a wide array of scenarios, and therefore are recommended to use in practical problems. Finally, a real example is illustrated.     

Simultaneous Confidence Regions for Predictions

After observing n independent responses at n corresponding design points in a linear regression setting, one wishes to make a confidence statement about future responses that will apply simultaneously to all possible design points. Two appropriate prediction regions are derived using normal theory.     

Optimal Information Processing and Bayes's Theorem

In this article statistical inference is viewed as information processing involving input information and output information. After introducing information measures for the input and output information, an information criterion functional is formulated and optimized to obtain an optimal information processing rule (IPR). For the particular information measures and criterion functional adopted, it is shown that Bayes's theorem is the optimal IPR. This optimal IPR is shown to be 100% efficient in the sense that its use leads to the output information being exactly equal to the given input information. Also, the analysis links Bayes's theorem to maximum-entropy considerations.     

A note on Bayesian estimation of traffic intensity in single-server Markovian queues

ABSTRACT

In queuing theory, a major interest of researchers is studying the behavior and formation process and analyzing the performance characteristics of queues, particularly the traffic intensity, which is defined as the ratio between the arrival rate and the service rate. How these parameters can be estimated using some statistical inferential method is the mathematical problem treated here. This article aims to obtain better Bayesian estimates for the traffic intensity of M/M/1 queues, which, in Kendall notation, stand for Markovian single-server infinity queues. The Jeffreys prior is proposed to obtain the posterior and predictive distributions of some parameters of interest. Samples are obtained through simulation and some performance characteristics are analyzed. It is observed from the Bayes factor that Jeffreys prior is competitive, among informative and non-informative prior distributions, and presents the best performance in many of the cases tested.     

Chain pooling model selection for two-level fixed effects factorial experiments

As many as three iterated statistical model deletion procedures are considered for an experiment.Population model coeff cients were chosen to simulate a saturated 2⁴experiment having an unfavorable distribution of parameter values.Using random number studies, three model selection strategies were developed, namely, (1) a strategy to be used in anticipation of large coefficients of variation (neighborhood of 65 percent), (2) strategy to be used in anticipation of small coefficients of variation (4 percent or less), and (3) a security regret strategy to be used in the absence of such prior knowledge     

A new approximation to the distribution function of the studentized maximum root

The Studentized maximum root (SMR) distribution is useful for constructing simultaneous confidence intervals around product interaction contrasts in replicated two-way ANOVA. A three-moment approximation to the SMR distribution is proposed. The approximation requires the first three moments of the maximum root of a central Wishart matrix. These values are obtained by means of numerical integration. The accuracy of the approximation is compared to the accuracy of a two-moment approximation for selected two-way table sizes. Both approximations are reasonably accurate. The three-moment approximation is generally superior.     

A test for the equality of k medians against the simple tree alternative under right censorship

We consider a test for the equality of k population medians, θ_i i=1,2,….,k, when it is believed a priori, that θ _i: The observations are subject to right censorhip. The distributions of the censoring variables for each population are assumed to be equal. This test is compared with the general k-sample test proposed by Breslow