Search results for "Uncertainty"
showing 10 items of 1010 documents
Unacceptable implications of the left haar measure in a standard normal theory inference problem
1978
For a very common statistical problem, inference about the mean of a normal random variable, some inadmissible consequences of the left Haar invariant prior measure, which is that recommended as a suitable prior by Jeffreys’ multivariate rule and by the methods of Villegas and Kashyap, are uncovered and investigated.
Analisis bayesiano de los contrastes de hipotesis parametricos
1985
Classical solutions to parametric hypothesis testing are shown to be particular instances of the Bayesian solution to a decision problem with two alternatives, in which the increase in utility for rejecting a false null is a linear function of the discrepancy between the accepted parametric model and the more likely model under the null.
A matrix-valued Bernoulli distribution
2006
AbstractMatrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.
Asymptotics for pooled marginal slicing estimator based on SIRα approach
2005
Pooled marginal slicing (PMS) is a semiparametric method, based on sliced inverse regression (SIR) approach, for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we consider the SIR"@a version (combining the SIR-I and SIR-II approaches) of the PMS estimator and we establish the asymptotic distribution of the estimated matrix of interest. Then the asymptotic normality of the eigenprojector on the estimated effective dimension reduction (e.d.r.) space is derived as well as the asymptotic distributions of each estimated e.d.r. direction and its corresponding eigenvalue.
ConvergenceClubs: A Package for Performing the Phillips and Sul's Club Convergence Clustering Procedure
2019
This paper introduces package ConvergenceClubs, which implements functions to perform the Phillips and Sul (2007, 2009) club convergence clustering procedure in a simple and reproducible manner. The approach proposed by Phillips and Sul to analyse the convergence patterns of groups of economies is formulated as a nonlinear time varying factor model that allows for different time paths as well as individual heterogeneity. Unlike other approaches in which economies are grouped a priori, it also allows the endogenous determination of convergence clubs. The algorithm, usage, and implementation details are discussed.
Regression models for multivariate ordered responses via the Plackett distribution
2008
AbstractWe investigate the properties of a class of discrete multivariate distributions whose univariate marginals have ordered categories, all the bivariate marginals, like in the Plackett distribution, have log-odds ratios which do not depend on cut points and all higher-order interactions are constrained to 0. We show that this class of distributions may be interpreted as a discretized version of a multivariate continuous distribution having univariate logistic marginals. Convenient features of this class relative to the class of ordered probit models (the discretized version of the multivariate normal) are highlighted. Relevant properties of this distribution like quadratic log-linear e…
Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence
2016
The geometric median, also called L 1 -median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et?al. (2013). This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The L p rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rates of convergence in quadratic mean of the averaged algorithm are also given.
Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
2006
In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estima…
A Software Tool For Sparse Estimation Of A General Class Of High-dimensional GLMs
2022
Generalized linear models are the workhorse of many inferential problems. Also in the modern era with high-dimensional settings, such models have been proven to be effective exploratory tools. Most attention has been paid to Gaussian, binomial and Poisson settings, which have efficient computational implementations and where either the dispersion parameter is largely irrelevant or absent. However, general GLMs have dispersion parameters φ that affect the value of the log- likelihood. This in turn, affects the value of various information criteria such as AIC and BIC, and has a considerable impact on the computation and selection of the optimal model.The R-package dglars is one of the standa…
Deflation-based separation of uncorrelated stationary time series
2014
In this paper we assume that the observed pp time series are linear combinations of pp latent uncorrelated weakly stationary time series. The problem is then to find an estimate for an unmixing matrix that transforms the observed time series back to uncorrelated time series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure that extracts the latent time series one by one. The limiting distribution of this deflation-based SOBI is found under general conditions, and we show how the results can be used for the comparison of es…