Family based spatial correlation model

In spatial data analysis, linear, count or binary responses are collected from a large sequence of (spatial) locations. This type of responses from the (spatial) locations may be influenced by certain fixed covariates associated to the location itself as well as certain invisible random effects from the members of the neighboring locations. Also the responses may be subject to certain model errors. In familial/ clustered setup, responses are collected from the members of a large number of independent families, where the pairwise responses within the family are correlated. In a spatial set up, the pairwise responses within a family of locations are correlated similar to the familial setup, but unlike in the familial setup, the responses from neighboring families will also be correlated. In this thesis, unlike in the existing studies, we develop a moving or band correlation structure that reflects the correlations for within and between families. This is done first for linear (continuous) data and then for binary responses. As far as the inference are concerned, we discuss method of moments (MM) and maximum likelihood (ML) approach for the estimation of parameters in linear mixed model setup. Because the exact likelihood estimation approach for the spatial binary models is complicated, we demonstrate how to use the generalized quasi-likelihood ( GQL) approach for such models

Composite Likelihood Inference by Nonparametric Saddlepoint Tests

The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute. However, the strenght of the composite likelihood approach is dimmed when considering hypothesis testing about a multidimensional parameter because the finite sample behavior of likelihood ratio, Wald, and score-type test statistics is tied to the Godambe information matrix. Consequently inaccurate estimates of the Godambe information translate in inaccurate p-values. In this paper it is shown how accurate inference can be obtained by using a fully nonparametric saddlepoint test statistic derived from the composite score functions. The proposed statistic is asymptotically chi-square distributed up to a relative error of second order and does not depend on the Godambe information. The validity of the method is demonstrated through simulation studies

Non-Gaussian Geostatistical Modeling using (skew) t Processes

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) $t$ process we study the second-order and geometrical properties and in the $t$ case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the $t$ process. Moreover we compare the performance of the optimal linear predictor of the $t$ process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australi