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## Editorial

### Statistical Methods and Applications (2007-06-01) 16: 5 , June 01, 2007

## The MAP test for multimodality

### Journal of Classification (1994-03-01) 11: 5-36 , March 01, 1994

We introduce a test for detecting multimodality in distributions based on minimal constrained spanning trees. We define a Minimal Ascending Path Spanning Tree (MAPST) on a set of points as a spanning tree that has the minimal possible sum of lengths of links with the constraint that starting from any link, the lengths of the links are non-increasing towards a root node. We define similarly MAPSTs with more than one root. We present some algorithms for finding such trees. Based on these trees, we devise a test for multimodality, called the MAP Test (for Minimal Ascending Path). Using simulations, we estimate percentage points of the MAP statistic and assess the power of the test. Finally, we illustrate the use of MAPSTs for determining the number of modes in a distribution of positions of galaxies on photographic plates from a rich galaxy cluster.

## A Cautionary Note on Likelihood Ratio Tests in Mixture Models

### Annals of the Institute of Statistical Mathematics (2000-09-01) 52: 481-487 , September 01, 2000

We show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation. Different starting strategies and stopping rules yield completely different estimators of the parameters. This is demonstrated for the likelihood ratio test of homogeneity against two-component exponential mixtures, when the test statistic is calculated by the EM algorithm.

## Local expectations of the population spectral distribution of a high-dimensional covariance matrix

### Statistical Papers (2014-05-01) 55: 563-573 , May 01, 2014

This paper discusses the relationship between the population spectral distribution and the limit of the empirical spectral distribution in high-dimensional situations. When the support of the limiting spectral distribution is split into several intervals, the population one gains a meaningful division, and general functional expectations of each part from the division, referred as local expectations, can be formulated as contour integrals around these intervals. Basing on these knowledge we present consistent estimators of the local expectations and prove a central limit theorem for them. The results are then used to analyze an estimator of the population spectral distribution in recent literature.

## On Optimal Designs for High Dimensional Binary Regression Models

### Optimum Design 2000 (2001-01-01) 51: 275-285 , January 01, 2001

We consider the problem of deriving optimal designs for generalised linear models depending on several design variables. Ford, Torsney and Wu (1992) consider a two parameter/single design variable case. They derive a range of optimal designs, while making conjectures about *D*-optimal designs for all possible design intervals in the case of binary regression models. Motivated by these we establish results concerning the number of support points in the multi-design-variable case, an area which, in respect of non-linear models, has uncharted prospects.

## Prediction by conditional simulation: models and algorithms

### Space, Structure and Randomness (2005-01-01) 183: 39-68 , January 01, 2005

Prediction here refers to the behavior of a regionalized variable: average ozone concentration in April 2004 in Paris, maximum lead concentration in an industrial site, recoverable reserves of an orebody, breakthrough time from a source of pollution to a target, etc. Dedicating a whole chapter of a book in honor to Georges Matheron to prediction by conditional simulation is somewhat paradoxical. Indeed performing simulations requires strong assumptions, whereas Matheron did his utmost to weaken the prerequisites for the prediction methods he developed. Accordingly, he never used them with the aim of predicting and they represented a marginal part of his activity. The turning bands method, for example, is presented very briefly in a technical report on the Radon transform to illustrate the one-to-one mapping between *d*-dimensional isotropic covariances and unidimensional covariances^{1} [44]. As for the technique of conditioning by kriging, it is nowhere to be found in Matheron’s entire published works, as he merely regarded it as an immediate consequence of the orthogonality of the kriging estimator and the kriging error.

## Statistics of random processes I: General theory

### Metrika (1983-12-01) 30: 100 , December 01, 1983

## Dickey-Fuller Tests

### International Encyclopedia of Statistical Science (2011-01-01): 385-388 , January 01, 2011

## Nonparametric Bayes Estimation

### Bayesian Theory and Methods with Applications (2011-01-01) 1: 79-121 , January 01, 2011

For a long time there were a lot of unsuccessful efforts directed toward the solution of many nonparametric problems with the help of the Bayes approach. This can be explained mainly by difficulties a researcher encounter, when he attempts to find a suitable prior distribution, determined on a sample space. Such a distribution in nonparametric problems is chosen in the form of a set of probability distributions on the given sample space. The first work in this field where some progress has been achieved belongs to Ferguson. Ferguson formulated the requirements which must be imposed on a prior distribution