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( h , Φ ) -entropy differential metric

María Luisa Menéndez, Domingo Morales, Leandro Pardo, Miquel Salicrú (1997)

Applications of Mathematics

Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on ( h , Φ ) -entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic...

A copula test space model how to avoid the wrong copula choice

Frederik Michiels, Ann De Schepper (2008)

Kybernetika

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government...

A Gram-Schmidt orthogonalizing process of design matrices in linear models as an estimating procedure of covariance components.

Gabriela Beganu (2005)

RACSAM

Se considera un modelo lineal mixto multivariante equilibrado sin interacción para el que las matrices de las formas cuadráticas necesarias para estimar la covarianza de las componentes se expresan mediante operadores lineales en espacios con producto interior de dimensión finita. El propósito de este artículo es demostrar que las formas cuadráticas obtenidas por el proceso de ortogonalización de Gram-Schmidt de las matrices de diseño son combinaciones lineales de las formas cuadráticas derivadas...

A note on the strong consistency of least squares estimates

Joǎo Lita da Silva (2009)

Discussiones Mathematicae Probability and Statistics

The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.

A study of the tangent space model of the von Mises-Fisher distrubution.

A. Chakak, L. Imhali (2003)

RACSAM

For a random rotation X = M0 eφ(ε) where M0 is a 3 x 3 rotation, ε is a trivariate random vector, and φ(ε) is a skew symmetric matrix, the least squares criterion consists of seeking a rotation M called the mean rotation minimizing tr[(M - E(X))t (M - E(X))]. Some conditions on the distribution of ε are set so that the least squares estimator is unbiased. Of interest is when ε is normally distributed N(0;Σ). Unbiasedness of the least squares estimator is dealt with according to eigenvalues of Σ.

Accelerated Monte Carlo estimation of exceedance probabilities under monotonicity constraints

Nicolas Bousquet (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

The problem of estimating the probability p = P ( g ( X ) 0 ) is considered when X represents a multivariate stochastic input of a monotonic function g . First, a heuristic method to bound p , originally proposed by de Rocquigny (2009), is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of p is considered based on a sequential stochastic exploration of the input space. A maximum likelihood estimator of p build from successive dependent Bernoulli data is defined...

All about the ⊥ with its applications in the linear statistical models

Augustyn Markiewicz, Simo Puntanen (2015)

Open Mathematics

For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

An empirical evaluation of small area estimators.

Álex Costa, Albert Satorra, Eva Ventura (2003)

SORT

This paper compares five small area estimators. We use Monte Carlo simulation in the context of both artificial and real populations. In addition to the direct and indirect estimators, we consider the optimal composite estimator with population weights, and two composite estimators with estimated weights: one that assumes homogeneity of within area variance and squared bias and one that uses area-specific estimates of variance and squared bias. In the study with real population, we found that among...

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