Julie Zhou

Autologistic regression model for the distribution of vegetation

Modeling the contagious distribution of vegetation and species in ecology and biogeography has been a challenging issue. Previous studies have demonstrated that the autologistic regression model is a useful approach for describing the distribution because patial correlation can readily be accounted for in the model. So far studies have been mainly restrained to the first-orderautologistic model. However, the first-order correlationmodel may sometimes be insufficient as long-range dispersal/migration can play a significant role in species distribution. In this study, we used the second-order autologistic regression model to model the distributions of the subarctic evergreen woodland and the boreal evergreen forest in British Columbia, Canada, in terms of climate covariates. We investigated and compared three estimation methods for the second-ordermodel—the maximum pseudo-likelihood method, the Monte Carlo likeli hood method, and the Markov chain Monte Carlo stochasti capproximation. Detailed procedures for these methods were developed and their performances were evaluated through simulations. The study demonstrates the importance for including the second-order correlation in the autologistic model for modeling vegetation distribution at the large geographical scale; each of the two vegetations studied was strongly autocorrelated not only in the south-north direction but also in the north west-southeast direction. The study further concluded that the assessment of climate change should be performed on the basis of individual vegetation or species because different vegetation or species likely respond differently to different sets of climate variables.

Robust estimation of hedonic models of price and income for investment property

Real estate market data often contain outliers in the observations. Since outliers have a large influence on least squares estimates, robust regression methods have been recommended for this situation. Compares the performance of least squares and least median of squares, a robust method, in the estimation of price/income relationships for apartment buildings. Multiplicative models with multiplicative errors are estimated by means of natural log transformations. The study confirms the importance of employing robust methods for this application and implies this may well be so for real estate data sets more generally.

INTEGER-VALUED, MINIMAX ROBUST DESIGNS FOR APPROXIMATELY LINEAR MODELS WITH CORRELATED ERRORS

We consider finite design spaces and integer-valued discrete designs to construct minimax designs, which are robust against both departures from assumed linear regression response and departures from the assumption of uncorrelated errors. Simulated annealing algorithm is developed to carry out the minimization problems to search for minimax designs. In particular, minimax designs are studied for approximately linear models with errors following moving average (MA) processes. Results are obtained for MA(1) and MA(2) error processes in this paper, and those results can be extended to MA(q) (q ≥ 3) processes. Examples of minimax designs are given for approximately polynomial regression and approximately second order multiple regression.

Minimax regression designs for approximately linear models with autocorrelated errors

We study the construction of regression designs, when the random errors are autocorrelated. Our model of dependence assumes that the spectral density g(~o) of the error process is of the form g(o)= (1 -a)go(~O ) + ~gl(o), where go(CO) is uniform (corresponding to uncorrelated errors), ct ~ [0, 1) is fixed, and gx(to) is arbitrary. We consider regression responses which are exactly, or only approximately, linear in the parameters. Our main results are that a design which is asymptotically (minimax) optimal for uncorrelated errors retains its optimality under autocorrelation if the design points are a random sample, or a random permutation, of points from this distribution. Our results are then a partial extension of those of Wu (Ann. Statist. 9 (1981), 1168-1177), on the robustness of randomized experimental designs, to the field of regression design.

Robust Designs Based on the Infinitesimal Approach

Abstract We introduce an infinitesimal approach to the construction of robust designs for linear models. The resulting designs are robust against small departures from the assumed linear regression response and/or small departures from the assumption of uncorrelated errors. Subject to satisfying a robustness constraint, they minimize the determinant of the mean squared error matrix of the least squares estimator at the ideal model. The robustness constraint is quantified in terms of boundedness of the Gateaux derivative of this determinant, in the direction of a contaminating response function or autocorrelation structure. Specific examples are considered. If the aforementioned bounds are sufficiently large, then (permutations of) the classically optimal designs, which minimize variance alone at the ideal model, meet our robustness criteria. Otherwise, new designs are obtained.

Minimizing the Condition Number to Construct Design Points for Polynomial Regression Models

In this paper we study a new optimality criterion, the

A Robust Criterion for Experimental Designs for Serially Correlated Observations

K

Computing A-optimal and E-optimal designs for regression models via semidefinite programming

-optimality criterion, for constructing optimal experimental designs for polynomial regression models. We focus on the

Confidence intervals based on robust regression

p

On Exact K-optimal Designs Minimizing the Condition Number

th order polynomial regression model with symmetric design space