Search results for "multivariate"
showing 10 items of 1520 documents
Automatic variable selection for exposure-driven propensity score matching with unmeasured confounders.
2020
Multivariable model building for propensity score modeling approaches is challenging. A common propensity score approach is exposure-driven propensity score matching, where the best model selection strategy is still unclear. In particular, the situation may require variable selection, while it is still unclear if variables included in the propensity score should be associated with the exposure and the outcome, with either the exposure or the outcome, with at least the exposure or with at least the outcome. Unmeasured confounders, complex correlation structures, and non-normal covariate distributions further complicate matters. We consider the performance of different modeling strategies in …
Response models for mixed binary and quantitative variables
1992
SUMMARY A number of special representations are considered for the joint distribution of qualitative, mostly binary, and quantitative variables. In addition to the conditional Gaussian models and to conditional Gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters. The possibilities for choosing between the models empirically are examined, as well as the testing of independence and conditional independence and the estimation of parameters. Often the testing of independence is exactly or nearly the same for a number of di…
The asymptotic covariance matrix of the Oja median
2003
The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.
Random Logistic Maps II. The Critical Case
2003
Let (X n )∞ 0 be a Markov chain with state space S=[0,1] generated by the iteration of i.i.d. random logistic maps, i.e., X n+1=C n+1 X n (1−X n ),n≥0, where (C n )∞ 1 are i.i.d. random variables with values in [0, 4] and independent of X 0. In the critical case, i.e., when E(log C 1)=0, Athreya and Dai(2) have shown that X n → P 0. In this paper it is shown that if P(C 1=1)<1 and E(log C 1)=0 then (i) X n does not go to zero with probability one (w.p.1) and in fact, there exists a 0<β<1 and a countable set ▵⊂(0,1) such that for all x∈A≔(0,1)∖▵, P x (X n ≥β for infinitely many n≥1)=1, where P x stands for the probability distribution of (X n )∞ 0 with X 0=x w.p.1. A is a closed set for (X n…
Una solucion bayesiana a la Paradoja de Stein
1982
If we are interested in making inferences about the square norm of the mean in a multivariate normal model, the usual uniform prior for the mean is not sound, as revealed by Stein in his 1959 work. This paper studies in what sense this prior must be modified by using the maximization of missing information procedure (Bernardo, 1979)
Fast and universal estimation of latent variable models using extended variational approximations
2022
AbstractGeneralized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has gained considerable popularity in recent years, e.g., in the analysis of multivariate abundance data in ecology. One of the main features of GLLVMs is their capacity to handle a variety of responses types, such as (overdispersed) counts, binomial and (semi-)continuous responses, and proportions data. On the other hand, the inclusion of unobserved latent variables poses a major computational challenge, as the resulting marginal likelihood function involves an intractable integral for non-normally distributed responses. This has spurred research into a number of approx…
Estimating the decomposition of predictive information in multivariate systems
2015
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…
Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp
2017
Blind source separation (BSS) is a well-known signal processing tool which is used to solve practical data analysis problems in various fields of science. In BSS, we assume that the observed data consists of linear mixtures of latent variables. The mixing system and the distributions of the latent variables are unknown. The aim is to find an estimate of an unmixing matrix which then transforms the observed data back to latent sources. In this paper we present the R packages JADE and BSSasymp. The package JADE offers several BSS methods which are based on joint diagonalization. Package BSSasymp contains functions for computing the asymptotic covariance matrices as well as their data-based es…
The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies
2003
We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform …
Inference based on the affine invariant multivariate Mann–Whitney–Wilcoxon statistic
2003
A new affine invariant multivariate analogue of the two-sample Mann–Whitney–Wilcoxon test based on the Oja criterion function is introduced. The associated affine equivariant estimate of shift, the multivariate Hodges-Lehmann estimate, is also considered. Asymptotic theory is developed to provide approximations for null distribution as well as for a sequence of contiguous alternatives to consider limiting efficiencies of the test and estimate. The theory is illustrated by an example. Hettmansperger et al. [9] considered alternative slightly different affine invariant extensions also based on the Oja criterion. The methods proposed in this paper are computationally more intensive, but surpri…