Search results for "uncertainty."
showing 10 items of 972 documents
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…
Spatial data of Ixodes ricinus instar abundance and nymph pathogen prevalence, Scandinavia, 2016-2017.
2020
ticks carry pathogens that can cause disease in both animals and humans, and there is a need to monitor the distribution and abundance of ticks and the pathogens they carry to pinpoint potential high risk areas for tick-borne disease transmission. In a joint Scandinavian study, we measured Ixodes ricinus instar abundance at 159 sites in southern Scandinavia in August-September, 2016, and collected 29,440 tick nymphs at 50 of these sites. We additionally measured abundance at 30 sites in August-September, 2017. We tested the 29,440 tick nymphs in pools of 10 in a Fluidigm real-time PCR chip to screen for 17 different tick-associated pathogens, 2 pathogen groups and 3 tick species. We present…
A critical evaluation of the current “p-value controversy”
2017
This article has been triggered by the initiative launched in March 2016 by the Board of Directors of the American Statistical Association (ASA) to counteract the current p-value focus of statistical research practices that allegedly "have contributed to a reproducibility crisis in science." It is pointed out that in the very wide field of statistics applied to medicine, many of the problems raised in the ASA statement are not as severe as in the areas the authors may have primarily in mind, although several of them are well-known experts in biostatistics and epidemiology. This is mainly due to the fact that a large proportion of medical research falls under the realm of a well developed bo…
Analysis and modelling of wind speed in New York
2010
In this paper we propose an ARMA time-series model for the wind speed at a single spatial location, and estimate it on in-sample data recorded in three different wind farm regions in New York state. The data have a three-hour granularity, but based on applications to financial wind derivatives contracts, we also consider daily average wind speeds. We demonstrate that there are large discrepancies in the behaviour of daily average and three-hourly wind speed records. The validation procedure based on out-of-sample observations reflects that the proposed model is reliable and can be used for various practical applications, like, for instance, weather prediction, pricing of financial wind cont…
Optimal designs for a one-way layout with covariates
2000
Abstract For the general class of Φ q -criteria optimal designs are characterized which reflect the inherent symmetry in a one-way layout with covariates. In particular, the eigenvalues of the covariance matrices are related to those in suitably chosen marginal models depending on the underlying interaction structure.
Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores
1994
After some discussion of the purposes of testing multivariate normality, the paper concentrates on two different approaches to testing linearity: on repeated regression tests of non-linearity and on exploiting properties of a dichotomized normal distribution. Regression tests of linearity are used to examine the adequacy of linear scoring systems for explanatory variables, initially recorded on an ordinal scale. Examples from recent psychological and medical research are given in which the methods have led to some insight into subject-matter.