Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

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.     

Comparison of Confidence Intervals on Between Group Variance in Unbalanced Heteroscedastic One-Way Random Models

A computer algorithm for computing the alternative distributions of the Wilcoxon signed rank statistic under shift alternatives is discussed. An explicit error bound is derived for the numeric integration approximation to these distributions.

A nonparametric process control procedure in which the standard CUSUM procedure is applied to the Wilcoxon signed rank statistic is discussed. In order to implement this procedure, the distribution of the Wilcoxon statistic under shift of the underlying distribution from its point of symmetry needs to be computed. The average run length of the nonparametric and parametric CUSUM are compared.     

Two Adjusted Empirical-Likelihood-Based Methods in Generalized Varying-Coefficient Partially Linear Model

An empirical likelihood method was proposed by Owen and has been extended to many semiparametric and nonparametric models with a continuous response variable. However, there has been less attention focused on the generalized regression model. This article systematically studies two adjusted empirical-likelihood-based methods in the generalized varying-coefficient partially linear models. Based on the popular profile likelihood estimation procedure, the new adjusted empirical likelihood technology for the parameter is established and the resulting statistics are shown to be asymptotically standard chi-square distributed. Further, the adjusted empirical-likelihood-based confidence regions are established, and an efficient adjusted profile empirical-likelihood-based confidence intervals/regions for any components of the parameter, which are of primary interest, is also constructed. Their asymptotic properties are also derived. Some numerical studies are carried out to illustrate the performance of the proposed inference procedures.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

An asymptotic confidence interval for the process capability index Cpm

Abstract

The use of indices as an estimation tool of process capability is long-established among the statistical quality professionals. Numerous capability indices have been proposed in last few years. C_pm constitutes one of the most widely used capability indices and its estimation has attracted much interest. In this paper, we propose a new method for constructing an approximate confidence interval for the index C_pm. The proposed method is based on the asymptotic distribution of the index C_pm obtained by the Delta Method. Under some regularity conditions, the distribution of an estimator of the process capability index C_pm is asymptotically normal.     

Confidence Bounds for Multiplicative Comparisons

Statements that are inherently multiplicative have historically been justified using ratios of random variables. Although recent work on ratios has extended the classical theory to produce confidence bounds conditioned on a positive denominator, this current article offers a novel perspective that eliminates the need for such a condition. Although seemingly trivial, this new perspective leads to improved lower confidence bounds to support multiplicative statements. This perspective is also more satisfying as it allows comparisons that are inherently multiplicative in nature to be properly analyzed as such.     

Some Applications of Order Statistics to Multivariate Analysis II

ABSTRACT

Harter (1979) summarized applications of order statistics to multivariate analysis up through 1949. The present paper covers the period 1950–1959. References in the two papers were selected from the first and second volumes, respectively, of the author's chronological annotated bibliography on order statistics [Harter (1978, 1983)]. Tintner (1950a) established formal relations between four special types of multivariate analysis: (1) canonical correlation, (2) principal components, (3) weighted regression, and (4) discriminant analysis, all of which depend on ordered roots of determinantal equations. During the decade 1950–1959, numerous authors contributed to distribution theory and/or computational methods for ordered roots and their applications to multivariate analysis. Test criteria for (i) multivariate analysis of variance, (ii) comparison of variance–covariance matrices, and (iii) multiple independence of groups of variates when the parent population is multivariate normal were usually derived from the likelihood ratio principle until S. N. Roy (1953) formulated the union–intersection principles on which Roy & Bose (1953) based their simultaneous test and confidence procedure. Roy & Bargmann (1958) used an alternative procedure, called the step–down procedure, in deriving a test for problem (iii), and J. Roy (1958) applied the step–down procedure to problem (i) and (ii), Various authors developed and applied distribution theory for several multivariate distributions. Advances were also made on multivariate tolerance regions [Fraser & Wormleighton (1951), Fraser (1951, 1953), Fraser & Guttman (1956), Kemperman (1956), and Somerville (1958)], a criterion for rejection of multivariate outliers [Kudô (1957)], and linear estimators, from censored samples, of parameters of multivariate normal populations [Watterson (1958, 1959)]. Textbooks on multivariate analysis were published by Kendall (1957) and Anderson (1958), as well as a monograph by Roy (1957) and a book of tables by Pillai (1957).     

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.