SCHEDULE

ABSTRACTS

Basic Designs of Experiments for Comparing Precision Agriculture Treatments on Research Fields and on Commercial Fields
G. A. Milliken
Department of Statistics
Kansas State University

Precision agriculture uses the characteristics of the land to determine the optimal set of treatments or prescriptions that should be applied to different areas of a field to provide optimal yield, profit, or optimize some other response variable. A primary goal of precision agriculture research is to determine if the site specific treatments established by the prescription are providing an advantage over either a blanket treatment or other site specific treatments. Often the design of the experiment has the applied rates identical to the prescription rates, i.e., the rates applied correspond exactly to the rates of the prescription. One of the flaws in precision agriculture research is that the prescription is determined and then the treatments are applied accordingly, but there are no areas in the field reserved for applying treatments not defined by the prescription. This causes the prescription and applied treatments to be aliased and one cannot separate the effects of the applied treatments from the prescription treatments. To resolve this problem, one needs to reserve space to include competing treatments in areas where the prescription does not recommend these alternative treatments. The treatment structure of an experiment consists of the applied treatments crossed with the prescribed treatments. The design structure of an experiment consists of the various ways one has to plant, apply treatments and harvest the crop. Constructing models that incorporate these treatment and design structures are demonstrated for precision agriculture experiments and involve aspects of split-plot and strip- plot designs. In addition to spatial correlation structures, site characteristics of the field can be used as covariates to enable one to describe spatial variability. The goal of a commercial field experiment is to evaluate precision agriculture treatments with as little area of the field as possible being assigned to nonprescription treatments, where as for research fields that is not of concern. Basic designs for research fields are discussed followed with a discussion of basic designs for commercial fields. Examples are used to illustrate the concepts.

Applications of re-sampling statistics for cotton insect pest management.
J. L. Willers
USDA-ARS
Mississippi State, MS

Cotton field samples for Tarnished Plant Bug (Lygus lineolaris Miridae: Heteroptera) were analyzed by exhaustive enumeration of m items taken 4 at a time. The value 4 was selected to represent a typical value for the number of samples a commercial cotton consultant would reasonably be expected to collect for each sampling stratum in a commercial cotton field. The resampling technique generated histograms for the m samples in the non-stratified case and three stratified cases. Stratification of samples was accomplished by GIS processing of the insect sample site coordinates and a geo-rectified, classified, remotely sensed image of the cotton field. The resampling results indicate that sample sizes of at least 4 observations can adequately characterize the abundance of this insect pest in a large cotton field whenever remote sensed information is available. Resampling statistics provide better information to the consultant than the estimated mean and its confidence interval whenever sample sizes are small and remotely sensed information is available. Comments on the impact of sample unit size and assessment of patterns of dispersion are also presented.

Modulation Models for Seasonal Life Tables
Xiuling Liu
Department of Experimental Statistics
Louisiana State University
Baton Rouge, LA

Two-dimensional varying coefficient Poisson regression was used to model the death counts of respiratory diseases for women aged 44 to 96 in the United States during the years 1959 to 1998. Due to a strong and varying annual cyclical behavior over time, sine and cosine regressors model the periodicity, but their coefficients are assumed to vary smoothly over the time and age plane. The two dimensional varying coefficient surfaces were estimated using a moderate number of tensor product B-spline bases and the further smoothness was ensured by attaching the difference penalties on rows and columns of tensor product coefficients. The great advantage of the smooth estimation results in a substantial reduction in the dimensions of the varying coefficient surfaces from 76320 to 159. The optimal penalty tuning parameters are chosen based on minimization of AIC. The seasonal effects are summarized with two-dimensional amplitude and phase image plots.

Multidimensional Density Smoothing with P-splines
Brian D. Marx
Department of Experimental Statistics
Louisiana State University
Baton Rouge, LA

We propose a simple and effective multidimensional density estimator. Our approach is essentially penalized Poisson regression using a rich tensor product B-spline basis, where the Poisson counts come from processing the data into a multidimensional histogram, often consisting of thousands of bins. The penalty enforces smoothness of the B-spline coefficients, specifically within the rows, columns, layers--depending on the dimension. In this paper, we focus on how a one-dimensional P-spline density estimator can be extended to two-dimensions, and beyond. In higher dimensions we provide a hint on how efficient grid algorithms can be implemented using array regression. Our approach optimizes the penalty weight parameter(s) using information criteria, specifically AIC. Two examples illustrate our method in two-dimensions.

Multivariate Statistical Change Assessment Via A Modified Mahalanobis Distance Applied To Remotely-Sensed, Satellite-Based Data
Fei Lu
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

Changes to the environment are of critical concern in the world today; consequently, monitoring such changes and assessing their impacts are tasks demanding considerably high priority. Many change detection techniques of land cover and land use have been reported in the literature. In this paper, an effective statistical approach for change detection that utilizes a modification to the Mahalanobis distance function is exercised on satellite-based data to assess information of land cover and land use change over a specific area. A GUI capability is discussed to detect, delineate and map areas that have experienced such changes. Two years of data (from satellite overpass in 1999 and 2000) over the Sam Houston National Forest in an area that borders on the west side of Lake Livingston, located in San Jacinto County, was utilized as the data source; this data was gathered by the ETM+ (Enhanced Thematic Mapper Plus) aboard the Landsat 7 satellite. The change detection techniques utilized in this study were implemented using the SAS package.

Some Properties of the Exact and Score Methods for Binomial Proportion and Sample Size Calculation
Jie Peng
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

In this talk, we point out some interesting relations between the exact test and the score test for a binomial proportion p. Based on the properties of the tests, we propose some approximate as well as exact methods of computing sample sizes required for the tests to attain a specified power. Sample sizes required for the tests are tabulated for various values of p to attain a power of 0.80 at level 0.05. We also propose approximate and exact methods of computing sample sizes needed to construct confidence intervals with a given precision. Using the proposed exact methods, sample sizes required to construct 95\% confidence intervals with various precisions are tabulated for p=.05(.05).95 and precisions. The approximate methods for computing sample sizes for score confidence intervals are very satisfactory and the results coincide with those of the exact methods for many cases.

Some Properties of Inferential Procedures for Squared Multiple Correlation Coefficient and Sample Size Calculation
Yanping Xia
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

The problem of hypothesis testing and interval estimation of the squared multiple correlation coefficient (rho)² of a multivariate normal distribution is considered. Available exact methods and their properties are outlined. An exact method of calculating sample size to carry out the exact test (null hypothesis may involve a nonzero value for (rho)²) to attain a given power is given. Sample size calculation for computing confidence interval for (rho)² within a given precision is also provided. Sample sizes for powers and confidence intervals are tabulated for a wide range of parameter configurations and dimension. The methods are illustrated using an example.

Tolerance Factors in Multiple and Multivariate Linear Regressions
Sumona Mondal
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, LA

In this talk, an improved method of computing tolerance factors for constructing tolerance regions in a multivariate linear regression model is proposed. The method is based on a chi-square approximation to the distribution of a linear function of noncentral chi-square variables and simulation. The merits of the proposed approach and the usual simulation method considered in Lee and Mathew (2004, Journal of Statistical Planning and Inference, 126, 253-271) are evaluated using Monte Carlo simulation. The study indicates that the proposed approach is stable and accurate even for small samples, and better than the available methods for computing tolerance factors in multiple linear regression as well as multivariate linear regression.

Bivariate Copulas for Failure Time Data
Fengming Tang
Department of Experimental Statistics
Louisiana State University
Baton Rouge, LA

This talk presents a basic introduction to copulas and illustrates the concepts with three bivariate models that describe lifetime events. This report also describes the relation of three measures of dependence (linear correlation, Kendall tau, and Spearman rho) to the copulas formulation. A cable-insulation failure data are employed to demonstrate the procedure of fitting bivariate censored data to bivariate models specified in terms of their copulas.