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## The Spectral Analysis of Stationary Interval Functions

### Selected Works of David Brillinger (2012-01-01): 25-55 , January 01, 2012

We consider stationary. additive. interval functions X(Δ). These are vector valued stochastic processes having real intervals Δ = (α, β] as domain, having finite dimensional distributions invariant under time translation and satisfying

## Multivariate Ranks-Based Concordance Indexes

### Advanced Statistical Methods for the Analysis of Large Data-Sets (2012-01-01) , January 01, 2012

The theoretical contributions to a “good” taxation have put the attention on the relations between the efficiency and the vertical equity without considering the “horizontal equity” notion: only recently, measures connected to equity (iniquity) of a taxation have been introduced in literature. The taxation problem is limited to the study of two quantitative characters: however the concordance problem can be extended in a more general context as we present in the following sections. In particular, the aim of this contribution consists in defining concordance indexes, as dependence measures, in a multivariate context. For this reason a *k*-variate (*k* > 2) concordance index is provided recurring to statistical tools such as ranks-based approach and multiple linear regression function. All the theoretical topics involved are shown through a practical example.

## Excel 2010 for Social Science Statistics

### Excel 2010 for Social Science Statistics (2012-01-01) , January 01, 2012

## Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions

### Journal of Classification (2012-10-01) 29: 363-401 , October 01, 2012

Cluster-weighted modeling (CWM) is a mixture approach to modeling the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both theoretical and numerical point of view; in particular, we show that Gaussian CWM includes mixtures of distributions and mixtures of regressions as special cases. Further, we introduce CWM based on Student-*t* distributions, which provides a more robust fit for groups of observations with longer than normal tails or noise data. Theoretical results are illustrated using some empirical studies, considering both simulated and real data. Some generalizations of such models are also outlined.

## Implied distributions in multiple change point problems

### Statistics and Computing (2012-07-01) 22: 981-993 , July 01, 2012

A method for efficiently calculating exact marginal, conditional and joint distributions for change points defined by general finite state Hidden Markov Models is proposed. The distributions are not subject to any approximation or sampling error once parameters of the model have been estimated. It is shown that, in contrast to sampling methods, very little computation is needed. The method provides probabilities associated with change points within an interval, as well as at specific points.

## Back Matter - Statistik und Ökonometrie für Wirtschaftswissenschaftler

### Statistik und Ökonometrie für Wirtschaftswissenschaftler (2012-01-01) , January 01, 2012

## In memoriam Joseph B. Kruskal*

### Journal of Classification (2012-04-01) 29: 4-6 , April 01, 2012

## Modelling Rater Differences in the Analysis of Three-Way Three-Mode Binary Data

### Challenges at the Interface of Data Analysis, Computer Science, and Optimization (2012-01-01): 123-131 , January 01, 2012

Using a basic latent class model for the analysis of three-way three- mode data (i.e. raters by objects by attributes) to cluster raters is often problematic because the number of conditional probabilities increases rapidly when extra latent classes are added. To solve this problem, Meulders et al. (J Classification 19:277–302, 2002) proposed a constrained latent class model in which object-attribute associations are explained on the basis of latent features. In addition, qualitative rater differences are introduced by assuming that raters may only take into account a subset of the features. As this model involves a direct link between the number of features *F* and the number of latent classes (i.e., 2^{F}), estimation of the model becomes slow when many latent features are needed to fit the data. In order to solve this problem we propose a new model in which rater differences are modelled by assuming that features can be taken into account with a certain probability which depends on the rater class. An EM algorithm is used to locate the posterior mode of the model and a Gibbs sampling algorithm is developed to compute a sample of the observed posterior of the model. Finally, models with different types of rater differences are applied to marketing data and the performance of the models is compared using posterior predictive checks (see also, Meulders et al. (Psychometrika 68:61–77, 2003)).

## Identifying Jumps in Asset Prices

### Handbook of Computational Finance (2012-01-01): 371-399 , January 01, 2012

For over a hundred years, diffusion differential equations have been used to model the changes in asset prices. Despite obvious fundamental problems with these equations, such as the requirement of continuity, they often provide adequate local fits to the observed asset price process. There are, however, several aspects of the empirical process that are not fit by simple diffusion equations.

## Two sample inference for the mean and covariance functions

### Inference for Functional Data with Applications (2012-01-01) 200: 65-77 , January 01, 2012

Due to possibly different FPC’s structures, working with two functional samples may be difficult. An important contribution has been made by Benko *et al.* (2009) who developed bootstrap procedures for testing the equality of mean functions, the FPC’s, and the eigenspaces spanned by them. In this chapter, we present asymptotic procedures for testing the equality of the means and the covariance operators in two independent samples. Section 5.1 focuses on testing the equality of mean functions. It shows that instead of statistics which have chi–square limits, those that converge to weighted sums of squares of independent standard normals can also be used. In other chapters we focus on statistics converging to chi–square distributions, but analogous versions converging to weighted sums of normals can be readily constructed.