New Parsimonious Multivariate Spatial Model: Spatial Envelope

Envelope Models for Parsimonious and Efficient Multivariate Linear Regression

We propose a new parsimonious version of the classical multivariate normal linear model, yielding a maximum likelihood estimator (MLE) that is asymptotically less variable than the MLE based on the usual model. Our approach is based on the construction of a link between the mean function and the covariance matrix, using the minimal reducing subspace of the latter that accommodates the former. T...

A New Improved Parsimonious Multivariate Markov Chain Model

We present a new improved parsimonious multivariate Markov chain model. Moreover, we find a new convergence condition with a new variability to improve the prediction accuracy and minimize the scale of the convergence condition. Numerical experiments illustrate that the new improved parsimonious multivariate Markov chain model with the new convergence condition of the new variability performs b...

A Spatial Model for Multivariate Lattice Data

In this article, we develop Markov random field models for multivariate lattice data. Specific attention is given to building models that incorporate general forms of the spatial correlations and cross-correlations between variables at different sites. The methodology is applied to the problem of environmental equity. Using a Bayesian hierarchical model that is multivariate in form, we examine ...

Multivariate Spatial Process Models

Multivariate Spatial Outlier Detection

A spatial outlier is a spatially referenced object whose non-spatial attribute values are significantly different from the values of its neighborhood. Identification of spatial outliers can lead to the discovery of unexpected, interesting, and useful spatial patterns for further analysis. Previous work in spatial outlier detection focuses on detecting spatial outliers with a single attribute. I...