Quantile plots for mean effects in the presence of variance effects for 2k-p designs

In robust parameter design, variance effects and mean effects in a factorial experiment are modelled simultaneously. If variance effects are present in a model, correlations are induced among the naive estimators of the mean effects. A simple normal quantile plot of the mean effects may be misleading because the mean effects are no longer iid under the null hypothesis that they are zero. Adjusted quantiles are computed for the case when one variance effect is significant and examples of 8-run and 16-run fractional factorial designs are examined in detail. We find that the usual normal quantiles are similar to adjusted quantiles for all but the largest and smallest ordered effects for which they are conservative. Graphically, the qualitative difference between the two sets of quantiles is negligible (even in the presence of large variance effects) and we conclude that normal probability plots are robust in the presence of variance effects.     

TEST FOR TREATMENT EFFECT BASED ON BINARY DATA WITH RANDOM SAMPLE SIZES

The problem of testing for treatment effect based on binary response data is considered, assuming that the sample size for each experimental unit and treatment combination is random. It is assumed that the sample size follows a distribution that belongs to a parametric family. The uniformly most powerful unbiased tests, which are equivalent to the likelihood ratio tests, are obtained when the probability of the sample size being zero is positive. For the situation where the sample sizes are always positive, the likelihood ratio tests are derived. These test procedures, which are unconditional on the random sample sizes, are useful even when the random sample sizes are not observed. Some examples are presented as illustration.     

The Econometrics of Piecewise-Linear Budget Constraints

In this article maximum likelihood techniques for estimating consumer demand functions when budget constraints are piecewise linear are exposited and surveyed. Consumer demand functions are formally derived under such constraints, and it is shown that the functions are themselves nonlinear as a result. The econometric problems in estimating such functions are exposited, and the importance of the stochastic specification is stressed, in particular the specification of both unobserved heterogeneity of preferences and measurement error. Econometric issues in estimation and testing are discussed, and the results of the studies that have been conducted to date are surveyed.     

Forecasting Vector ARMA Processes With Systematically Missing Observations

The following two predictors are compared for time series with systematically missing observations: (a) A time series model is fitted to the full series X_t , and forecasts are based on this model, (b) A time series model is fitted to the series with systematically missing observations Y _τ, and forecasts are based on the resulting model. If the data generation processes are known vector autoregressive moving average (ARMA) processes, the first predictor is at least as efficient as the second one in a mean squared error sense. Conditions are given for the two predictors to be identical. If only the ARMA orders of the generation processes are known and the coefficients are estimated, or if the process orders and coefficients are estimated, the first predictor is again, in general, superior. There are, however, exceptions in which the second predictor, using seemingly less information, may be better. These results are discussed, using both asymptotic theory and small sample simulations. Some economic time series are used as illustrative examples.     

On Shifted Geometric INAR(1) Models Based on Geometric Counting Series

Two types of shifted geometric integer valued autoregressive models of order one (SGINAR(1)) are proposed. Both are based on the thinning operator generated by counting series of i.i.d. geometric random variables. Their correlation properties are derived and compared. Also, regression and conditional variance are considered. Nonparametric estimators of model parameters are obtained and their asymptotic characterizations are given. Finally, these two models are applied to a real-life data set and they are compared to some referent INAR(1) models.     

Circular Binary Block Second- and Higher-Order Neighbor Designs

Some new neighbor designs are presented here. Second-order neighbor designs for different configurations are generated in circular binary blocks. Third-order and fourth-order neighbor designs for some cases are also constructed. In all cases, circular blocks are well separated and these designs are obtained through initial block/s. At the end of the study, some models for analysis of these designs are also presented.     

SELECTION OF WEIGHTS FOR WEIGHTED MODEL AVERAGING

We address the task of choosing prior weights for models that are to be used for weighted model averaging. Models that are very similar should usually be given smaller weights than models that are quite distinct. Otherwise, the importance of a model in the weighted average could be increased by augmenting the set of models with duplicates of the model or virtual duplicates of it. Similarly, the importance of a particular model feature (a certain covariate, say) could be exaggerated by including many models with that feature. Ways of forming a correlation matrix that reflects the similarity between models are suggested. Then, weighting schemes are proposed that assign prior weights to models on the basis of this matrix. The weighting schemes give smaller weights to models that are more highly correlated. Other desirable properties of a weighting scheme are identified, and we examine the extent to which these properties are held by the proposed methods. The weighting schemes are applied to real data, and prior weights, posterior weights and Bayesian model averages are determined. For these data, empirical Bayes methods were used to form the correlation matrices that yield the prior weights. Predictive variances are examined, as empirical Bayes methods can result in unrealistically small variances.     

A note on properties of spatial yule-walker estimators

For two-dimensional spatial autoregressive (AR) models, asymptotic properties of the spatial Yule-Walker (YW) estimators (Tjøstheim, 1978) are studied. These estimators although consistent, are shown to be asymptotically biased. Estimators from the first-order spatial bilateral AR model are looked at in more detail and the spatial YW estimators for this model are compared with the exact maximum likelihood estimators. Small sample properties of both estimators are also discussed briefly and some simulation results are presented.     

An Examination of Five Statistical Software Packages for Epidemiology

Five statistical software packages for epidemiology and clinical trials are reviewed. The five packages are EPI INFO, EPICURE, EPILOG PLUS, STATA, and TRUE EPI-STAT. Only DOS versions of these packages are compared and rated (Windows versions are discussed but not rated). Although the packages differ in their target audiences, interfaces, capabilities, and approaches, they are examined according to criteria that are of most interest to epidemiologists, biostatisticians, and others involved in epidemiologic and clinical research. A general discussion with recommendations follows the review of the statistical packages.     

Estimation of parameters of a right truncated exponential distribution

The maximum likelihood, moment and mixture of the estimators are for samples from the right truncated exponential distribution. The estimators are compared empirically when all the parameters are unknown; their bias and mean square error are investigated with the help of numerical technique. We have shown that these estimators are asymptotically unbiased. At the end, we conclude that mixture estimators are better than the maximum likelihood and moment estimators.     

Improved unbiased estimators in adaptive cluster sampling

Summary.  The usual design-unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved. Improved unbiased estimators obtained by conditioning on sufficient statistics—not necessarily minimal—are described. First, estimators that are as easy to compute as the usual design-unbiased estimators are given. Estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed. Estimators are compared in examples.     

Homogeneity of Two Straight Lines: Equivalence Approach Using Fitted Regressions

The paper examines the homogeneity of a pair of straight lines, regarded as the expected values of two different linear regressions, from an equivalence point of view. This seems more appropriate than the usual testing of the null hypothesis of homogeneity when the aim is to establish that the lines are close to homogeneous. Upper confidence bounds on the maximum difference between the lines are based on the usual least squares regression estimators, assuming normal distributions. These bounds are constructed for fixed points, or over a fixed interval, and it is concluded that the lines are 1-homogeneous if the bounds are not greater than 1: Also, intervals are constructed over which the lines are concluded to be 1-homogeneous.     

On Comparison Of Estimates Of Dispersion Using Generalized Pitman Nearness Criterion

In this paper, estimates QP dispersion matrix and its functions are compared based on generalized Pitman nearness criterion, Various Iosa functions are considered for the purpose. Locally superior estimates are defined and obtained. Comparison of these estimates are made with other standard ones. It is snown that within certain classes, defined in the paper, these are the best estimatcrs ia the generalized Fitman nearness sense     

The Hazard-Product method of generalization: Application to the gompertz and exponentiated Half-Normal distributions

As new data sources arrive, novel methods of defining undiscovered distributions are increasingly useful. In this presentation, the Hazard-Product method of generalizing survival functions is introduced. Some limitations and considerations are discussed, and a new extensions of the Gompertz and Half-Normal models are proposed. Finally, basic moment and estimation properties of the models are given, and two real data sets are analyzed.     

On Fan's adaptive Neyman tests for comparing two spectral densities

In this paper, we consider tests for assessing whether two stationary and independent time series have the same spectral densities (or same autocovariance functions). Both frequency domain and time domain test statistics for this purpose are reviewed. The adaptive Neyman tests are then introduced and their performances are investigated. Our tests are adaptive, that is, they are constructed completely by the data and do not involve any unknown smoothing parameters. Simulation studies show that our proposed tests are at least comparable to the current tests in most cases. Furthermore, our tests are much more powerful in some cases, such as against the long orders of autoregressive moving average (ARMA) models such as seasonal ARMA series.     

Prediction in Some Poisson Errors in Variables Models

Predictive distributions are developed and illustrated for prediction in some Poisson errors in variables models. Two different situations in which multiplicative treatment effects are appropriate are considered within the context of predicting counts of road accidents. Hierarchical prior structures are investigated, and numerical integration and Gibbs sampling routines are used to derive the predictive and posterior probabilities. Examples of analyses are provided with data from road accidents in Sweden.     

Generalized partially linear varying-coefficient models

Generalized varying-coefficient models are useful extensions of generalized linear models. They arise naturally when investigating how regression coefficients change over different groups characterized by certain covariates such as age. In this paper, we extend these models to generalized partially linear varying-coefficient models, in which some coefficients are constants and the others are functions of certain covariates. Procedures for estimating the linear and non-parametric parts are developed and their associated statistical properties are studied. The methods proposed are illustrated using some simulations and real data analysis.     

A new way of quantifying the symmetry of a random variable: Estimation and hypothesis testing

New measures of skewness for real-valued random variables are proposed. The measures are based on a functional representation of real-valued random variables. Specifically, the expected value of the transformed random variable can be used to characterize the distribution of the original variable. Firstly, estimators of the proposed skewness measures are analyzed. Secondly, asymptotic tests for symmetry are developed. The tests are consistent for both discrete and continuous distributions. Bootstrap versions improving the empirical results for moderated and small samples are provided. Some simulations illustrate the performance of the tests in comparison to other methods. The results show that our procedures are competitive and have some practical advantages.     

On adaptive estimation

Point estimates that are weighted averages of other estimates are considered. They are adaptive because the weights are also functions of the sample observations.In particular, the weights are functions of new measures of peakedness and skewness. Five adaptive estimators are compared (in a Monte Carlo study using the swindle) to some of the usual estimators, including those robust ones of Huber and Tukey. In addition, the swindle constant is considered in some detail. All of the adaptive estimators do extremely well with an adaptive biweight statistic being the best one in this study. Suggestions are made about future directions in this area.     

Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates

Two- or multi-phase study designs are often used in settings involving failure times. In most studies, whether or not certain covariates are measured on an individual depends on their failure time and status. For example, when failures are rare, case–cohort or case–control designs are used to increase the number of failures relative to a random sample of the same size. Another scenario is where certain covariates are expensive to measure, so they are obtained only for selected individuals in a cohort. This paper considers such situations and focuses on cases where we wish to test hypotheses of no association between failure time and expensive covariates. Efficient score tests based on maximum likelihood are developed and shown to have a simple form for a wide class of models and sampling designs. Some numerical comparisons of study designs are presented.