Tests for symmetry of two-piece normal distribution

In this paper, classical optimum tests for symmetry of two-piece normal distribution is derived. Uniformly most powerful one-sided test for the skewness parameter is obtained when the location and scale parameters are known and is compared with sequential probability ratio test. An ad-hoc test for symmetry and likelihood ratio test for symmetry for large samples, can be found in literature for this distribution. But in this paper, we derive exact likelihood ratio test for symmetry, when location parameter is known. The exact power of the test is evaluated for different sample sizes.     

Censored Exponential Data: Large Deviations for MLEs and Posterior Distributions

In this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models.     

Correlation type gogdness-of-fit statistics with censored sampling

Some comments are made concerning the possible forms of a correlation coefficient type goodness-of-fit statistic, and their relationship with other goodness-of-fit statistics, Critical values for a correlation goodness-of-fit statistic and for the Cramer-von Mises statistic are provided for testing a completely-specified null hypothesis for both complete and censored sampling, Critical values for a correlation test statistic are provided for complete and censored sampling for testing the hypothesis of normality, two parameter exponentiality, Weibull (or, extreme value) and an exponential-power distribution, respectively. Critical values are also provided for a test of one-parameter exponentiality based on the Cramer-von Mises statistic     

The evaluation of bioequivalence using nonparametric procedures

Applications of nonparametric methods to the evaluation of bioequiv-alence for two treatments are presented for independent samples and for a crossover design. Included are procedures for testing for equivalence in location, in dispersion, and in general. Also presented are procedures for the calculation of confidence limits. A general strategy for the evaluation of bioequivalence is developed which involves both hypothesis testing and the calculation of confidencelimits for parameters which characterize departures from equivalene.     

Comparing several experimental groups with a control in the multivariate case

This paper presents a multivariate extension of Dunnett's test for comparing simultaneously k treatment group means with a single control group mean. A test based on Hotelling T²statistics is presented and approximate critical values are evaluated for the case of equal numbers of observations in each group, for the .05 and .01 levels of significance, for 1 to 5 variates, for 1 to 10 treatment groups, and for varying degrees of freedom. The accuracy of the procedure for generating approximate critical values is assessed via simulation studies conducted for selected cases and an example is presented using real data.     

On Non Overlapping Segmentation of the Response Surfaces for Solving Constrained Programming Problems Through Super Convergent Line Series

The solutions of Constrained Programming Problems (linear, quadratic, and cubic) by segmentation of the response surfaces through Super Convergent Line Series were obtained. The line search exchange algorithm was exploited. The response surfaces were explored and segmented up to four segments for linear, six for quadratic, and eight for cubic programming problems, respectively. It was verified and established that the number of segments, S, for which optimal solutions are obtained are two for linear, four for quadratic, and eight for cubic programming problems, respectively.     

A model for comparisons with ordered categorical data

A model developed by Andrich for ordered categorical data is extended to develop tests for treatment effects with paired or matched samples. In particular, this includes analysis for pre-post studies and crossover designs. Some advantages of this model are that it allows for misclassification of subjects, yields reasonable conditional requirements for exact analysis, a normal approximation is good for all but the smallest of sample sizes, and it is relatively simple mathematically. Furthermore, the form of the tests derived are logical extensions of tests for unordered categories.     

Frailty models for survival data

A frailty model is a random effects model for time variables, where the random effect (the frailty) has a multiplicative effect on the hazard. It can be used for univariate (independent) failure times, i.e. to describe the influence of unobserved covariates in a proportional hazards model. More interesting, however, is to consider multivariate (dependent) failure times generated as conditionally independent times given the frailty. This approach can be used both for survival times for individuals, like twins or family members, and for repeated events for the same individual. The standard assumption is to use a gamma distribution for the frailty, but this is a restriction that implies that the dependence is most important for late events. More generally, the distribution can be stable, inverse Gaussian, or follow a power variance function exponential family. Theoretically, large differences are seen between the choices. In practice, using the largest model makes it possible to allow for more general dependence structures, without making the formulas too complicated.This paper is a revised version of a review, which together with ten papers by the author made up a thesis for a Doctor of Science degree at the University of Copenhagen.     

On a data-dependent choice of the tuning parameter appearing in certain goodness-of-fit tests

We propose a data-dependent method for choosing the tuning parameter appearing in many recently developed goodness-of-fit test statistics. The new method, based on the bootstrap, is applicable to a class of distributions for which the null distribution of the test statistic is independent of unknown parameters. No data-dependent choice for this parameter exists in the literature; typically, a fixed value for the parameter is chosen which can perform well for some alternatives, but poorly for others. The performance of the new method is investigated by means of a Monte Carlo study, employing three tests for exponentiality. It is found that the Monte Carlo power of these tests, using the data-dependent choice, compares favourably to the maximum achievable power for the tests calculated over a grid of values of the tuning parameter.     

Empirical Bayes procedures for stabilizing maps of U.S. cancer mortality rates

"The geographic mapping of age-standardized, cause-specific death rates is a powerful tool for identifying possible etiologic factors, because the spatial distribution of mortality risks can be examined for correlations with the spatial distribution of disease-specific risk factors. This article presents a two-stage empirical Bayes procedure for calculating age-standardized cancer death rates, for use in mapping, which are adjusted for the stochasticity of rates in small area populations. Using the adjusted rates helps isolate and identify spatial patterns in the rates. The model is applied to sex-specific data on U.S. county cancer mortality in the white population for 15 cancer sites for three decades: 1950-1959, 1960-1969, and 1970-1979. Selected results are presented as maps of county death rates for white males."     

How does the DerSimonian and Laird procedure for random effects meta-analysis compare with its more efficient but harder to compute counterparts?

The procedure suggested by DerSimonian and Laird is the simplest and most commonly used method for fitting the random effects model for meta-analysis. Here it is shown that, unless all studies are of similar size, this is inefficient when estimating the between-study variance, but is remarkably efficient when estimating the treatment effect. If formal inference is restricted to statements about the treatment effect, and the sample size is large, there is little point in implementing more sophisticated methodology. However, it is further demonstrated, for a simple special case, that use of the profile likelihood results in actual coverage probabilities for 95% confidence intervals that are closer to nominal levels for smaller sample sizes. Alternative methods for making inferences for the treatment effect may therefore be preferable if the sample size is small, but the DerSimonian and Laird procedure retains its usefulness for larger samples.     

Union-Intersection testing for outliers in multivariate normal data

The union-intersection approach to multivariate test construction is used to develop an alternative to Wilks' likelihood ratio test statistic for testing for two or more outliers in multivariate normal data. It is shown that critical values of both statistics are poorly approximated by Bonferroni bounds. Simulated critical values are presented for both statistics for significance levels 1% and 5%, for sample sizes 10(5)30, 40, 50, 75 and 100 for 2, 3, 4 and 5 dimensions. A power comparison of the two tests in the slippage of the mean model for generating outliers indicates that the union-intersection test is the more powerful when the slippages are close to collinear. Although Wilks' test remains the preference for general use, the union-intersection test could be valuable when such special structure in the data is suspected.     

Complete censuses and samples

"Complete decennial censuses are needed for small areas and other domains. Sample surveys yield diverse and timely data. Censuses can also be combined with samples, and sometimes with data from registers, for diverse estimates that are detailed over both space and time, and hence are timely for small domains. Methods of 'postcensal estimates' for small domains are described. We note uses of censuses for improving samples and of samples for improving censuses, and propose a method for cumulating data from 'rolling' (or rotating) periodic (weekly, monthly or quarterly) samples specifically designed to cover the population in detail over designed spans (annual and quinquennial)."     

Repeated confidence intervals and prediction intervals using stochastic curtailment

Jennlson and Turnbull (1984,1989) proposed procedures for repeated confidence intervals for parameters of interest In a clinical trial monitored with group sequential methods. These methods are extended for use with stochastic curtailment procedures for two samples in the estimation of differences of means, differences of proportions, odds ratios, and hazard ratios. Methods are described for constructing 1) confidence intervals for these estimates at repeated times In the course of a trial, and 2) prediction intervals for predicted estimates at the end of a trial. Specific examples from several clinical trials are presented.     

Uniform validity of saddlepoint expansion on compact sets

This paper shows that Daniels's (1954) saddlepoint expansion for the density of a sample mean is, for all practical purposes, always uniformly valid on compact subsets in the interior of the domain of the mean. This uniform validity is the key for establishing the relation between the saddlepoint expansion for the density function and Lugannani and Rice's expansion for the tail probability, and for establishing the validity of a high-order asymptotic expansion for the density of a standardized mean.     

Robust and scale-free effect sizes for non-Normal two-sample comparisons,with applications in e-commerce

The effect size (ES) has been mainly introduced and investigated for changes in location under an assumption of Normality for the underlying population. However, there are many circumstances where populations are non-Normal, or depend on scale and shape and not just a location parameter. Our motivating application from e-commerce requires an ES which is appropriate for long-tailed distributions. We review some common ES measures. We then introduce two novel alternative ES for two-sample comparisons, one scale-free and one on the original scale of measurement, and analyse some theoretical properties. We examine these ES for two-sample comparison studies under an assumption of Normality and investigate what happens when both location and scale parameters differ. We explore ES for phenomena for non-Normal situations, using the Weibull family for illustration. Finally, for an application, we assess differences in customer behaviour when browsing E-commerce websites.     

A multistage analysis strategy for a clinical trial to assess successively more stringent criteria for a primary endpoint with a low event rate

This paper describes how a multistage analysis strategy for a clinical trial can assess a sequence of hypotheses that pertain to successively more stringent criteria for excess risk exclusion or superiority for a primary endpoint with a low event rate. The criteria for assessment can correspond to excess risk of an adverse event or to a guideline for sufficient efficacy as in the case of vaccine trials. The proposed strategy is implemented through a set of interim analyses, and success for one or more of the less stringent criteria at an interim analysis can be the basis for a regulatory submission, whereas the clinical trial continues to accumulate information to address the more stringent, but not futile, criteria. Simulations show that the proposed strategy is satisfactory for control of type I error, sufficient power, and potential success at interim analyses when the true relative risk is more favorable than assumed for the planned sample size. Copyright © 2013 John Wiley & Sons, Ltd.     

Methods for national population forecasts: a review

"Three widely used classes of methods for forecasting national populations are reviewed: demographic accounting/cohort-component methods for long-range projections, statistical time series methods for short-range forecasts, and structural modeling methods for the simulation and forecasting of the effects of policy changes. In each case, the major characteristics, strengths, and weaknesses of the methods are described. Factors that place intrinsic limits on the accuracy of population forecasts are articulated. Promising lines of additional research by statisticians and demographers are identified for each class of methods and for population forecasting generally."     

Energy Use in Institutional Buildings: Estimates From State Energy-Audit Surveys

This article examines the determinants of energy demand for nearly 9,000 institutional buildings in the United States. The data were collected, as part of the federal Institutional Conservation Program, by state energy offices using mail surveys. The article presents energy demand estimates adjusted for differences in state surveys as well as for nonresponse bias, as functions of energy prices, building characteristics, and fuel-type variables for approximations of the installed heating ventilation and air-conditioning equipment. Energy price elasticities are found to vary from ?.28 for schools to ?1.05 for hospitals.     

A note on influence diagnostics in AR(1) time series models

The purpose of this paper is to develop influence diagnostics for AR(1) models under the innovative and the data perturbation schemes. There are four main contributions. First, we derive analytical expressions for the slope and curvature statistics. Second, we establish a relationship between the slope and curvature showing that the standardised slope and standardised curvature are equal for the innovative perturbation scheme, and these vectors are nearly identical for several values of the autoregressive parameter, for the data perturbation scheme. Third, we present a connection between the influence statistics and the tests for outlier detection. Fourth, for the innovative perturbation scheme, we derive the asymptotic distribution of a new influence statistic, whereas for the data perturbation scheme, the distribution of the influence statistics is obtained via Monte Carlo simulation. We additionally discuss practical guidelines for the use of local influence statistics, which are illustrated on a chemical process data set.