Texas is the leading U.S. producer of cotton, and the U.S. is the largest international market supplier of cotton. Risks and uncertainties plague Texas cotton producers with unpredictable weather, insects, diseases, and price variability. Risk management studies have examined the risk reducing capabilities of alternative management strategies, but few have looked at the interaction of using several strategies in different combinations. The research in this study focuses on managing risk faced by cotton farmers in Texas using irrigation, put options, and yield insurance. The primary objective was to analyze the interactions of irrigation, put options, and yield insurance as risk management strategies on the economic viability of a 1,000 acre cotton farm in the Lower Rio Grande Valley (LRGV) of Texas. The secondary objective was to determine the best combination of these strategies for decision makers with alternative preferences for risk aversion. Stochastic values for yields and prices were used in simulating a whole-farm financial statement for a 1000 acre furrow irrigated cotton farm in the LRGV with three types of risk management strategies. Net returns were simulated using a multivariate empirical distribution for 16 risk management scenarios. The scenarios were ranked across a range of risk aversion levels using stochastic efficiency with respect to a function. Analyses for risk averse decision makers showed that multiple irrigations are preferred, and that yield insurance is strongly preferred at lower irrigation levels. The benefits to purchasing put options increase with yields, so they are more beneficial when higher yields are expected from applying more irrigation applications.

In this thesis, a binary decision tree is used as an approximation of a nonparametric regression curve. The best fitted decision tree is estimated from data via least squares method. It is investigated how and under which conditions the estimator converges. These asymptotic results then are used to create asymptotic convergence regions.

Masters of Science / The multivariate two-sample tests provide a means to test the match between two multivariate distributions. Although many tests exist in the literature, relatively little is known about the relative power of these procedures. The studies reported in the thesis contrasts the effectiveness, in terms of power, of seven such tests with a Monte Carlo study. The relative power of the tests was investigated against location, scale, and correlation alternatives. Samples were drawn from bivariate exponential, normal and uniform populations. Results from the power studies show that there is no single test which is the most powerful in all situations. The use of particular test statistics is recommended for specific alternatives. A possible supplementary non-parametric graphical procedure, such as the Depth-Depth plot, can be recommended for diagnosing possible differences between the multivariate samples, if the null hypothesis is rejected. As an example of the utility of the procedures for real data, the multivariate two-sample tests were applied to photometric data of twenty galactic globular clusters. The results from the analyses support the recommendations associated with specific test statistics.