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N-dimensional measures of dependence.

Edward F. Wolff (1980)

Stochastica

In recent joint papers with B. Schweizer, we used the notion of a copula to introduce a family of symmetric, nonparametric measures of dependence of two random variables. Here, we present n-dimensional extensions of these measures and of Spearman's ro. We study them vis-a-vis appropriate higher dimensional analogues of Rényi's axioms for measures of dependence, determine relations among them, and in some cases establish reduction formulae for their computation.

Nearest neighbor classification in infinite dimension

Frédéric Cérou, Arnaud Guyader (2006)

ESAIM: Probability and Statistics

Let X be a random element in a metric space (F,d), and let Y be a random variable with value 0 or 1. Y is called the class, or the label, of X. Let (Xi,Yi)1 ≤ i ≤ n be an observed i.i.d. sample having the same law as (X,Y). The problem of classification is to predict the label of a new random element X. The k-nearest neighbor classifier is the simple following rule: look at the k nearest neighbors of X in the trial sample and choose 0 or 1 for its label according to the majority vote. When ( ℱ , d ) = ( ℝ d , | | . | | ) , Stone...

Near-exact distributions for the generalized Wilks Lambda statistic

Luís M. Grilo, Carlos A. Coelho (2010)

Discussiones Mathematicae Probability and Statistics

Two near-exact distributions for the generalized Wilks Lambda statistic, used to test the independence of several sets of variables with a multivariate normal distribution, are developed for the case where two or more of these sets have an odd number of variables. Using the concept of near-exact distribution and based on a factorization of the exact characteristic function we obtain two approximations, which are very close to the exact distribution but far more manageable. These near-exact distributions...

Necessary and sufficient condition for the existence of a Fréchet mean on the circle

Benjamin Charlier (2013)

ESAIM: Probability and Statistics

Let ( 𝕊 1 , d 𝕊 1 S 1 , d S 1 ) be the unit circle in ℝ2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure μto admit a well defined Fréchet mean on ( 𝕊 1 , d 𝕊 1 S 1 , d S 1 ). We derive a new sufficient condition of existenceP(α, ϕ) with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.

Negative dependence structures through stochastic ordering.

Abdul-Hadi N. Ahmed (1990)

Trabajos de Estadística

Several new multivariate negative dependence concepts such as negative upper orthant dependent in sequence, negatively associated in sequence, right tail negatively decreasing in sequence and upper (lower) negatively decreasing in sequence through stochastic ordering are introduced. These concepts conform with the basic idea that if a set of random variables is split into two sets, then one is increasing whenever the other is decreasing. Our concepts are easily verifiable and enjoy many closure...

Neural network realizations of Bayes decision rules for exponentially distributed data

Igor Vajda, Belomír Lonek, Viktor Nikolov, Arnošt Veselý (1998)

Kybernetika

For general Bayes decision rules there are considered perceptron approximations based on sufficient statistics inputs. A particular attention is paid to Bayes discrimination and classification. In the case of exponentially distributed data with known model it is shown that a perceptron with one hidden layer is sufficient and the learning is restricted to synaptic weights of the output neuron. If only the dimension of the exponential model is known, then the number of hidden layers will increase...

Neuromorphic features of probabilistic neural networks

Jiří Grim (2007)

Kybernetika

We summarize the main results on probabilistic neural networks recently published in a series of papers. Considering the framework of statistical pattern recognition we assume approximation of class-conditional distributions by finite mixtures of product components. The probabilistic neurons correspond to mixture components and can be interpreted in neurophysiological terms. In this way we can find possible theoretical background of the functional properties of neurons. For example, the general...

New copulas based on general partitions-of-unity and their applications to risk management

Dietmar Pfeifer, Hervé Awoumlac Tsatedem, Andreas Mändle, Côme Girschig (2016)

Dependence Modeling

We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows, in contrast to finite partition-of-unity copulas, for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.

New estimates and tests of independence in semiparametric copula models

Salim Bouzebda, Amor Keziou (2010)

Kybernetika

We introduce new estimates and tests of independence in copula models with unknown margins using φ -divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of χ 2 -divergence has good properties in terms of efficiency-robustness.

Non-central generalized F distributions

Célia Nunes, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

The quotient of two linear combinations of independent chi-squares will have a generalized F distribution. Exact expressions for these distributions when the chi-square are central and those in the numerator or in the denominator have even degrees of freedom were given in Fonseca et al. (2002). These expressions are now extended for non-central chi-squares. The case of random non-centrality parameters is also considered.

Non-exchangeable random variables, Archimax copulas and their fitting to real data

Tomáš Bacigál, Vladimír Jágr, Radko Mesiar (2011)

Kybernetika

The aim of this paper is to open a new way of modelling non-exchangeable random variables with a class of Archimax copulas. We investigate a connection between powers of generators and dependence functions, and propose some construction methods for dependence functions. Application to different hydrological data is given.

Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

Zofia Hanusz, Joanna Tarasińska (2015)

Biometrical Letters

Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.

Note on the estimation of parameters of the mean and the variance in n -stage linear models

Júlia Volaufová (1988)

Aplikace matematiky

The paper deals with the estimation of the unknown vector parameter of the mean and the parameters of the variance in the general n -stage linear model. Necessary and sufficient conditions for the existence of the uniformly minimum variance unbiased estimator (UMVUE) of the mean-parameter under the condition of normality are given. The commonly used least squares estimators are used to derive the expressions of UMVUE-s in a simple form.

Notes on the bias of dissimilarity indices for incomplete data sets: the case of archaelogical classification.

Angela Montanari, Stefania Mignani (1994)

Qüestiió

The problem of missing data is particularly present in archaeological research where, because of the fragmentariness of the finds, only a part of the characteristics of the whole object can be observed. The performance of various dissimilarity indices differently weighting missing values is studied on archaeological data via a simulation. An alternative solution consisting in randomly substituting missing values with character sets is also examined. Gower's dissimilarity coefficient seems to be...

Notes on the evolution of feature selection methodology

Petr Somol, Jana Novovičová, Pavel Pudil (2007)

Kybernetika

The paper gives an overview of feature selection techniques in statistical pattern recognition with particular emphasis on methods developed within the Institute of Information Theory and Automation research team throughout recent years. Besides discussing the advances in methodology since times of Perez’s pioneering work the paper attempts to put the methods into a taxonomical framework. The methods discussed include the latest variants of the optimal algorithms, enhanced sub-optimal techniques...

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