Bayesian classification of Neolithic tools

The classification of Neolithic tools by using cluster analysis enables archaeologists to understand the function of the tools and the technological and cultural conditions of the societies that made them. In this paper, Bayesian classification is adopted to analyse data which raise the question whether the observed variability, e.g. the shape and dimensions of the tools, is related to their use. The data present technical difficulties for the practitioner, such as the presence of mixed mode data, missing data and errors in variables. These complications are overcome by employing a finite mixture model and Markov chain Monte Carlo methods. The analysis uses prior information which expresses the archaeologist's belief that there are two tool groups that are similar to contemporary adzes and axes. The resulting mixing densities provide evidence that the morphological dimensional variability among tools is related to the existence of these two tool groups.     

Interpreting forensic DNA mixtures: allowing for uncertainty in population substructure and dependence

We consider the assessment of deoxyribonucleic acid (DNA) profiles from biological samples containing a mixture of DNA from more than one person. The problem has been investigated in the context of likelihood ratios by Weir and co-workers under the assumption of independent alleles in DNA profiles. However, uncertainty about independence may arise from various factors such as population substructure and relatedness. This issue has received considerable attention in recent years. Ignoring this uncertainty may seriously overstate the strength of the evidence and therefore disadvantage innocent suspects. Taking this uncertainty into account, we develop a general formula for calculating the match probabilities of DNA profiles. Thus, we extend the result derived by Weir and co-workers to the dependence situation, which is often more to the benefit of the defendant in comparison with the simple product rule result based on an independence assumption. The effect of dependence of alleles on likelihood ratio estimates can be seen in the analysis of two real data sets.     

On singular elliptical models

The probability density function (pdf) ofsingular elliptical distributions is represented as an integralseries of singular normal distributions. Explicit formulas for the pdf and the cdf of the generalized Chi-square distribution are derived under singular elliptical assumptions extending the result of Díaz-García [(2002). Singular elliptical distribution: density and applications. Commun. Stat.—Theory Methods 31:665–681]. Applications are given of the proposed result for singular mixedmodels.     

Two Graphical Techniques Useful in Detecting Correlation Structure in Repeated Measures Data

Analysis of repeated measures data using a mixed model includes specifying a form for the covariance matrix of the within-subject observations. This reduction in the number of estimated parameters from the unspecified structure may improve the efficiency of inferences made. An implementation of this technique has been incorporated in the MIXED procedure of the SAS® statistical package, and includes a wide range of options for the structure of the covariance matrix. It is demonstrated that draftman's display plots and/or plots in a coordinate system with parallel axes can aid in visualizing the dispersion structure.     

Fourier analysis of irregularly spaced data on Rd

Summary.  The purpose of the paper is to propose a frequency domain approach for irregularly spaced data on R ^d . We extend the original definition of a periodogram for time series to that for irregularly spaced data and define non-parametric and parametric spectral density estimators in a way that is similar to the classical approach. Introduction of the mixed asymptotics, which are one of the asymptotics for irregularly spaced data, makes it possible to provide asymptotic theories to the spectral estimators. The asymptotic result for the parametric estimator is regarded as a natural extension of the classical result for regularly spaced data to that for irregularly spaced data. Empirical studies are also included to illustrate the frequency domain approach in comparisons with the existing spatial and frequency domain approaches.     

Youth perceptions of neighborhood hassles and resources: A mixed method analysis

Empirical investigations exploring the processes and mechanisms of neighborhood influences on child and youth development are needed to contribute to the growing body of research on neighborhood as a context for development. Using a mixed method design, this study examined the relationship between structurally identified resources in three urban public housing neighborhoods, youth perceptions and experiences of resources, and youth report of neighborhood hassles and cohesion. Survey data from 153 ethnically and culturally diverse youth between 6th and 8th grade were analyzed using regression analyses; constant comparative analysis was used to code interviews from a subsample of 22 youth. Results indicated an inverse relationship between the number of neighborhood resources and the level of daily hassles youth report. Analysis of mixed method results further highlights the importance of young people's perceptions of neighborhood influences.     

Linear predictors of future order statistics

In this paper we establish an optimal asymptotic linear predictor which does not involve the finite-sample variance-covariance structure. Extensions to the problem of finding the best linear unbiased and simple linear unbiased predictors for k samples are given. Moreover, we obtain alternative linear predictors by modifying the covariance matrix by either an identity matrix or a diagonal matrix. For normal, logistic and Rayleigh samples of size 10, the alternative linear predictors with these modifications have high efficiency when compared with the best linear unbiased predictor.     

On left-truncating and mixing Poisson distributions

ABSTRACT

The distributions obtained by left-truncating at k a mixed Poisson distribution, denoted kT-MP, and those obtained by mixing previously left-truncated Poisson distributions, denoted M-kTP, are characterized by means of their probability generating function. The main consequence is that every kT-MP distribution is a M-kTP distribution, but not the other way around.     

Bootstrap mean squared error of a small-area EBLUP

Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163–171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior than the Prasad–Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors.