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.     

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.     

Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler

In this paper many convergence issues concerning the implementation of the Gibbs sampler are investigated. Exact computable rates of convergence for Gaussian target distributions are obtained. Different random and non-random updating strategies and blocking combinations are compared using the rates. The effect of dimensionality and correlation structure on the convergence rates are studied. Some examples are considered to demonstrate the results. For a Gaussian image analysis problem several updating strategies are described and compared. For problems in Bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice.     

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.     

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.     

Maximum likelihood analysis of masked series system lifetime data

Component lifetime parameters of a series system are estimated from system lifetimes and masked cause of failure observations. The time and cause of system failures are assumed to follow a competing risks model. The masking probabilities of the minimum random subsets are not subjected to the symmetry assumption. Sufficient regularity conditions are provided, justifying the maximum likelihood analysis. Maximum likelihood estimates of both the lifetime parameters and masking probabilities are generically computed via an EM algorithm. An appropriate set of asymptotically pivotal quantities are also derived. Such maximum likelihood based estimates are further refined by bootstrap. The developed techniques are illustrated by numerical examples of independent Weibull component lifetimes with distinct scale and shape parameters.     

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.     

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.     

Generalized Laplacian Distributions and Autoregressive Processes

Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First- and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters. Various areas of application of these models are discussed.     

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.     

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.     

Design-based analysis of embedded experiments with applications in the Dutch Labour Force Survey

Summary.  Previous research has proposed a design-based analysis procedure for experiments that are embedded in complex sampling designs in which the ultimate sampling units of an on-going sample survey are randomized over different treatments according to completely randomized designs or randomized block designs. Design-based Wald and t -statistics are applied to test whether sample means that are observed under various survey implementations are significantly different. This approach is generalized to experimental designs in which clusters of sampling units are randomized over the different treatments. Furthermore, test statistics are derived to test differences between ratios of two sample estimates that are observed under alternative survey implementations. The methods are illustrated with a simulation study and real life applications of experiments that are embedded in the Dutch Labour Force Survey. The functionality of a software package that was developed to conduct these analyses is described.     

Defining equations for two-level factorial designs

Defining equations are introduced in the context of two-level factorial designs and they are shown to provide a concise specification of both regular and nonregular designs. The equations are used to find orthogonal arrays of high strength and some optimal designs. The latter optimal designs are formed in a new way by augmenting notional orthogonal arrays which are allowed to have some runs with a negative number of replicates before augmentation. Defining equations are also shown to be useful when the factorial design is blocked.     

Asymptotic efficiencies of estiamtors of location a comutational study

Asymptotic efficiencies of four classes of estimators of location are evaluated for a family of distributions consisting of t, lambda and contaminated normal densities. For the class of estimators derived from signed rank tests, maximin efficiencies between pairs of distributions in the family are computed using a formula of Gastwirth ( 1966 ). Asymptotic efficiencies are also evaluated for the scale dependent estimators of the form proposed by Hubcr ( 1964 ) and the efficiencies of procedures utilizing interquantiie ranges.are evaluated. Efficiencies of linear estimators such as trimmed means, BLUE's for the lambda family are computed for each density considered. Efficiencies of linear, polynomial and trigonometric approximations to BLUE weight functions are determined. Using the method of Birnbaum and Laska ( 1967 ) maximin efficiencies are computed using four linear or polynomial terms. On the basis of comparisons of these numerical results, suggestions for robust estimators are given     

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.     

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.     

Adaptive web sampling in ecology

Adaptive sampling strategies for ecological and environmental studies are described in this paper. The motivations for adaptive sampling are discussed. Developments in this area over recent decades are reviewed. Adaptive cluster sampling and a number of its variations are described. The newer class of adaptive web sampling designs and their spatial sampling uses are discussed. Case studies in the use of adaptive sampling strategies with ecological populations are cited. The nature of optimal sampling strategies is described. Design-based and model-based approaches to inference with adaptive sampling strategies are summarized.     

Polynomial Regression and Estimating Functions in the Presence of Multiplicative Measurement Error

We consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Two general methods are considered, with the methods differing in their assumptions about the distributions of the predictor and the measurement errors. Consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory. Diagnostics are presented for distinguishing additive and multiplicative measurement error. Data from a nutrition study are analysed by using the methods. The results from a simulation study are presented and the performances of the methods are compared.     

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.     

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.