Testing spatial randomness based on empirical distribution function: A study on lattice data

In this article, we extended the empirical distribution function based test statistic _Ik$I_k$ of Skaug and Tjostheim [1993. Nonparametric test of serial independence based on the empirical distribution function. Biometrika 80, 591–602] in the time series setting to _Dn$D_n$ for spatial lattice data and derived the asymptotic distribution of the proposed test statistic _Dn$D_n$ under the null hypothesis of spatial independence. The size and power of the proposed test statistic under conditional autoregressive model (CAR) were simulated. We applied _Dn$D_n$, Moran's I and Geary's c   to the transformed and well-studied sudden infant death syndrome data from North Carolina and found that _Dn$D_n$ produced a much smaller p$p$-value in testing spatial independence.     

De-aliasing effects using semifoldover techniques

Semifoldover designs, obtained by semifolding a regular two-level factorial design, have been discussed recently in the literature. In this article, with the use of indicator functions, we investigate various semifoldover designs that are obtained from a general two-level factorial design. We discuss when a main factor or a two-factor interaction can be de-aliased from their aliased two-factor interactions, and extend some of the existing results from regular designs to non-regular designs. Finally, we present some examples to illustrate the results developed here.     

Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model

The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma. This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.     

Quantile dispersion graphs to compare the efficiencies of cluster randomized designs

The purpose of this article is to compare efficiencies of several cluster randomized designs using the method of quantile dispersion graphs (QDGs). A cluster randomized design is considered whenever subjects are randomized at a group level but analyzed at the individual level. A prior knowledge of the correlation existing between subjects within the same cluster is necessary to design these cluster randomized trials. Using the QDG approach, we are able to compare several cluster randomized designs without requiring any information on the intracluster correlation. For a given design, several quantiles of the power function, which are directly related to the effect size, are obtained for several effect sizes. The quantiles depend on the intracluster correlation present in the model. The dispersion of these quantiles over the space of the unknown intracluster correlation is determined, and then depicted by the QDGs. Two applications of the proposed methodology are presented.     

Nonparametric estimation of the shape function in a Gamma process for degradation data

The author considers estimation under a Gamma process model for degradation data. The setting for degradation data is one in which n independent units, each with a Gamma process with a common shape function and scale parameter, are observed at several possibly different times. Covariates can be incorporated into the model by taking the scale parameter as a function of the covariates. The author proposes using the maximum pseudo‐likelihood method to estimate the unknown parameters. The method requires usage of the Pool Adjacent Violators Algorithm. Asymptotic properties, including consistency, convergence rate and asymptotic distribution, are established. Simulation studies are conducted to validate the method and its application is illustrated by using bridge beams data and carbon‐film resistors data. The Canadian Journal of Statistics 37: 102‐118; 2009 © 2009 Statistical Society of Canada     

Least squares estimation of varying‐coefficient hazard regression with application to breast cancer dose‐intensity data

To enhance modeling flexibility, the authors propose a nonparametric hazard regression model, for which the ordinary and weighted least squares estimation and inference procedures are studied. The proposed model does not assume any parametric specifications on the covariate effects, which is suitable for exploring the nonlinear interactions between covariates, time and some exposure variable. The authors propose the local ordinary and weighted least squares estimators for the varying‐coefficient functions and establish the corresponding asymptotic normality properties. Simulation studies are conducted to empirically examine the finite‐sample performance of the new methods, and a real data example from a recent breast cancer study is used as an illustration. The Canadian Journal of Statistics 37: 659–674; 2009 © 2009 Statistical Society of Canada     

Estimation in capture–recapture models when covariates are subject to measurement errors and missing data

For capture–recapture models when covariates are subject to measurement errors and missing data, a set of estimating equations is constructed to estimate population size and relevant parameters. These estimating equations can be solved by an algorithm similar to the EM algorithm. The proposed method is also applicable to the situation when covariates with no measurement errors have missing data. Simulation studies are used to assess the performance of the proposed estimator. The estimator is also applied to a capture–recapture experiment on the bird species Prinia flaviventris in Hong Kong. The Canadian Journal of Statistics 37: 645–658; 2009 © 2009 Statistical Society of Canada     

The t-information and its use in multivariate problems and time-series analysis

The second moment of recently introduced scalar inference function can be viewed as generalized Fisher information of the continuous probability distributions. In this paper we call it the t-information and give some possible applications of the new concept.     

On distribution-weighted partial least squares with diverging number of highly correlated predictors

Summary.  Because highly correlated data arise from many scientific fields, we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. For this, we first develop a distribution-weighted least squares estimator that can recover directions in the central subspace, then use the distribution-weighted least squares estimator as a seed vector and project it onto a Krylov space by partial least squares to avoid computing the inverse of the covariance of predictors. Thus, distrbution-weighted partial least squares can handle the cases with high dimensional and highly correlated predictors. Furthermore, we also suggest an iterative algorithm for obtaining a better initial value before implementing partial least squares. For theoretical investigation, we obtain strong consistency and asymptotic normality when the dimension p of predictors is of convergence rate O { n ^1/2/ log ( n )} and o ( n ^1/3) respectively where n is the sample size. When there are no other constraints on the covariance of predictors, the rates n ^1/2 and n ^1/3 are optimal. We also propose a Bayesian information criterion type of criterion to estimate the dimension of the Krylov space in the partial least squares procedure. Illustrative examples with a real data set and comprehensive simulations demonstrate that the method is robust to non-ellipticity and works well even in 'small n –large p ' problems.     

Vector random fields with compactly supported covariance matrix functions

The objective of this paper is to construct covariance matrix functions whose entries are compactly supported, and to use them as building blocks to formulate other covariance matrix functions for second-order vector stochastic processes or random fields. In terms of the scale mixture of compactly supported covariance matrix functions, we derive a class of second-order vector stochastic processes on the real line whose direct and cross covariance functions are of Pólya type. Then some second-order vector random fields in R^d${\mathbb{R}}^d$ whose direct and cross covariance functions are compactly supported are constructed by using a convolution approach and a mixture approach.