A Novel Approach for Estimating Seemingly Unrelated Regressions with High-Order Autoregressive Disturbances

A seemingly unrelated regression (SUR) model is defined by a system of linear regression equations in which the disturbances are contemporaneously correlated across equations. However, the disturbances can also be serially correlated in each equation of the system. In these cases, estimating SUR becomes more complicated. Some methods have been considered estimating SUR with low-order autoregressive (AR) disturbances. In this article, SUR with high-order AR disturbances are considered and a tapering approach is examined under this situation. Two modified methods for estimating SUR are obtained by using this approach. A comprehensive Monte Carlo simulation study is performed in order to compare small-sample efficiencies of the modified methods with the others given in the literature.     

Spatial model fitting for large datasets with applications to climate and microarray problems

Many problems in the environmental and biological sciences involve the analysis of large quantities of data. Further, the data in these problems are often subject to various types of structure and, in particular, spatial dependence. Traditional model fitting often fails due to the size of the datasets since it is difficult to not only specify but also to compute with the full covariance matrix describing the spatial dependence. We propose a very general type of mixed model that has a random spatial component. Recognizing that spatial covariance matrices often exhibit a large number of zero or near-zero entries, covariance tapering is used to force near-zero entries to zero. Then, taking advantage of the sparse nature of such tapered covariance matrices, backfitting is used to estimate the fixed and random model parameters. The novelty of the paper is the combination of the two techniques, tapering and backfitting, to model and analyze spatial datasets several orders of magnitude larger than those datasets typically analyzed with conventional approaches. Results will be demonstrated with two datasets. The first consists of regional climate model output that is based on an experiment with two regional and two driver models arranged in a two-by-two layout. The second is microarray data used to build a profile of differentially expressed genes relating to cerebral vascular malformations, an important cause of hemorrhagic stroke and seizures.     

Efficiency in estimation of memory

We study the efficiency of semiparametric estimates of memory parameter. We propose a class of shift invariant tapers of order (p,q). For a fixed p, the variance inflation factor of the new tapers approaches 1 as q   goes to infinity. We show that for d∈(−1/2,p+1/2)$d\in (-1/2,p+1/2)$, the proposed tapered Gaussian semiparametric estimator has the same limiting distribution as the nontapered version for d∈(−1/2,1/2)$d\in (-1/2,1/2)$. The new estimator is mean and polynomial trend invariant, and is computationally advantageous in comparison to the recently proposed exact local Whittle estimator. The simulation study shows that our estimator has comparable or better mean squared error in finite samples for a variety of models.