Search results for "Marginal distribution"
showing 9 items of 19 documents
Derived variables calculated from similar joint responses: some characteristics and examples
1995
Abstract A technique (Cox and Wermuth, 1992) is reviewed for finding linear combinations of a set of response variables having special relations of linear conditional independence with a set of explanatory variables. A theorem in linear algebra is used both to examine conditions in which the derived variables take a specially simple form and lead to reduced computations. Examples are discussed of medical and psychological investigations in which the method has aided interpretation.
A penalized approach for the bivariate ordered logistic model with applications to social and medical data
2018
Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios to be estimated also increases, and estimation gets problematic. In this work we propose a non-parametric approach for the maximum likelihood (ML) estimation of a BOLM, wherein penalties to the differences between adjacent row and column effects are applied. Our proposal is then compared to the Goodman and Dale models. Some simulation results as well as analyses of two real data sets are presented and discussed.
Pairwise Markov properties for regression graphs
2016
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirect…
On easily interpretable multivariate reference regions of rectangular shape
2011
Till now, multivariate reference regions have played only a marginal role in the practice of clinical chemistry and laboratory medicine. The major reason for this fact is that such regions are traditionally determined by means of concentration ellipsoids of multidimensional Gaussian distributions yielding reference limits which do not allow statements about possible outlyingness of measurements taken in specific diagnostic tests from a given patient or subject. As a promising way around this difficulty we propose to construct multivariate reference regions as p-dimensional rectangles or (in the one-sided case) rectangular half-spaces whose edges determine univariate percentile ranges of the…
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.
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…
On (n-l)-wise and joint independence and normality of n Random variables: an example
1981
An example is given of a vector of n random variables such that any (n-1)-dimensional subvector consists of n-1 independent standard normal variables. The whole vector however is neither independent nor normal.
Exploring regression structure with graphics
1993
We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to asgraphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.
Dynamic copula models for the spark spread
2011
We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.