Browsing by Subject "Nonparametric statistics"
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Item A class of nonparametric procedures in one-factor experiments(Texas Tech University, 1998-08) Bransom, Jonathan E.This thesis analyzes and develops an algorithm for the adaptive distribution-free procedure for testing ordered alternatives and multiple comparisons. in one-way analysis of variance, including treatment of ties and demonstrates the supremacy of these procedures over typical parametric procedures based on sample means and the well-known Wilcoxon nonparametric procedure based on ranks. Initial data classifies the underlying distribution by tail-weight and amount of skewness. The preliminary classification determines the tailoring of specific scores from where all the inferences are based. The adaptive procedure performs well for a wide range of distributions rather than performing with optimal properties for any of the particular distributions. The preliminary selection of an adaptive procedure should affect characteristics of the final inference. Testing a null hypothesis at a nominal significance level of a after selecting a model wiU frequently result in an overall significance level much greater than a. The model should be selected by determining which corresponding test will produce the largest observed significance level.Item A comparison of some nonparametric scale tests(Texas Tech University, 1980-12) Hwang, E-binNot availableItem A comparison of some nonparametric tests(Texas Tech University, 1974-05) Whiteside, Mary MilamNot availableItem A two-sample nonparametric adaptive test for scale(Texas Tech University, 1977-08) Samudio, EnedinoNot availableItem Approximations to the exact distribution of the Kruskal-Wallis test statistic for unequal sample sizes(Texas Tech University, 1976-12) Wynn, Terry DuaneNot availableItem Bayesian Nonparametric Methods for Protein Structure Prediction(2011-10-21) Lennox, Kristin PatriciaThe protein structure prediction problem consists of determining a protein?s three-dimensional structure from the underlying sequence of amino acids. A standard approach for predicting such structures is to conduct a stochastic search of conformation space in an attempt to find a conformation that optimizes a scoring function. For one subclass of prediction protocols, called template-based modeling, a new protein is suspected to be structurally similar to other proteins with known structure. The solved related proteins may be used to guide the search of protein structure space. There are many potential applications for statistics in this area, ranging from the development of structure scores to improving search algorithms. This dissertation focuses on strategies for improving structure predictions by incorporating information about closely related ?template? protein structures into searches of protein conformation space. This is accomplished by generating density estimates on conformation space via various simplifications of structure models. By concentrating a search for good structure conformations in areas that are inhabited by similar proteins, we improve the efficiency of our search and increase the chances of finding a low-energy structure. In the course of addressing this structural biology problem, we present a number of advances to the field of Bayesian nonparametric density estimation. We first develop a method for density estimation with bivariate angular data that has applications to characterizing protein backbone conformation space. We then extend this model to account for multiple angle pairs, thereby addressing the problem of modeling protein regions instead of single sequence positions. In the course of this analysis we incorporate an informative prior into our nonparametric density estimate and find that this significantly improves performance for protein loop prediction. The final piece of our structure prediction strategy is to connect side-chain locations to our torsion angle representation of the protein backbone. We accomplish this by using a Bayesian nonparametric model for dependence that can link together two or more multivariate marginals distributions. In addition to its application for our angular-linear data distribution, this dependence model can serve as an alternative to nonparametric copula methods.Item Distribution-free interval estimation techniques for slope in simple linear regression(Texas Tech University, 1985-08) Taylor, Gregory ClarkThis work is concerned with estimating the slope parameter, B, in the simple linear regression model. Many of the rank procedures used to find confidence intervals for fl are free of distributional assumptions on the dependent variable. Rank procedures often generate smaller intervals than those given by the classical procedures when the residual distribution is skewed or heavy-tailed. Many of these procedures, such as those discussed by Theil, Sen, and Sievers, are computationally infeasible, even for a computer, when used with samples much larger than 100. This dissertation develops distribution-free procedures which substantially reduce these calculations. The rank-based procedures of Theil, Sen, and Sievers require n(n-1)/2 pairwise slopes to be computed. The new procedures require only n such pairwise slopes to be computed, a comparatively negligible amount of computation. Measures of asymptotic relative efficiency (ARE) and finite sample efficiency are derived and used to evaluate these "reduced" procedures. In many cases, the reduced procedures have efficiencies of .8 when compared to the procedures described by Theil, Sen, and Sievers. This is a small loss considering the computational gains from using the reduced procedures developed in this dissertation.Item Distribution-free procedures for testing and pairwise comparisons under order restrictions in incomplete blocks(Texas Tech University, 1998-08) Shaw, Carrie Nicole SmartNot availableItem Item Multiple comparison procedures in factorial designs using the aligned rank transformation(Texas Tech University, 2001-05) Abundis, MariselaA factorial design is used for an experiment that involves the study of two or more factors simultaneously, with each factor having two or more levels. The importance of factorial designs is that they permit simultaneous examination of the effects of individual factors and their interactions. All possible combinations of the levels of the factors are investigated in each replication of an experiment. A main effect is defined as the change in response produced by a change in the level of one factor while keeping the remaining factors at a fixed level. Interaction exists between two factors if the difference in response between the levels of one factor is not the same at all levels of the other factors. Thus, the preliminary focus of analysis is testing hypotheses about interaction, equality of row treatment effects, and column treatment effects. If interaction exists, main effects exists as well. If interaction does not exist. then testing main effects should proceed. In Chapter II, we present the analysis of variance for a two-factor factorial fixed effects factorial design. The hypotheses do not provide detailed information about the difference in interactions and main eflfects. Multiple comparison procedures are capable of responding to specific questions about more meaningful comparisons on any of the above effects. These procedures allow the comparisons between groups or pairs of treatment means. The comparisons are made in terms of treatment totals or treatment averages. It must be noted that multiple comparison techniques are not dependent on the rejection of null hypothesis. The testing of interaction between two factors and main eflfects can also be performed by multiple comparison methods. Common multiple comparison procedures that will be implemented are Tukey's Studentized Range Test and Scheflfe's Method. These multiple comparison procedures are discussed in Chapter II. Additionally, we will employ a macro called %SimPower in order to perform multiple comparisons. This macro was developed by Tobias (see Westfall et al.. 1999). %SimPower simulates power for multiple comparisons. It uses complete, minimal, and proportional power definitions. Complete power is defined as the probability of rejecting all false null hypotheses. Minimal power is the probability that at least one false null hypothesis is rejected implying a significant result. Proportional power is the proportion of false null hypotheses detected to all false null hypotheses, that is false nulls expected to be detected. Further discussion is provided in Chapter V. One of the main purposes of this investigation is to carry out multiple comparisons for tw^o-factor factorial designs based on the aligned rank transformation. The aligned rank transform procedure provides a robust and powerful alternative method of data analysis to the classical least squares method. In this investigation, we will study the validity and power of the aligned rank transform technique for multiple comparisons. In Chapter III, we define the classical least squares F-statistic and the aligned rank transform technique. Analysis of two applications based on the least squares and aligned rank transform methods will be examined in Chapter IV. The final conclusio will be provided in Chapter VI. We will utilize the SAS programming language to perform the classical least squares method and the aligned rank transform technique. PROC GLM, PROG REG, and PROC RANK will execute the two techniques. These ideas will be explained in more detail later on.Item Nonparametric analysis of covariance in block designs(Texas Tech University, 1993-05) Chang, Guang-hwaAnalysis of Covariance (ANOCOVA) has been considered as a more effective approach in data analysis than an ordinary Analysis of Variance (ANOVA) for two reasons: (1) increasing the power and precision of the tests through the reduction in error variance, and (2) providing a means of statistically adjusting for pre-existing differences between treatment groups. The parametric analysis of covariance theory was developed with the assumption of normality. If this assumption underlying the parametric model is uncertain, then the applicability of the parametric test is doubtful. Nonparametric ANOCOVA is a robust competitor of the parametric method with less restrictive distributional assumptions. In the past two decades, several nonparametric ANOCOVA tests for one-way layouts have been suggested and shown to be robust and powerful through simulation studies. A number of nonparametric ANOCOVA procedures for higher way layouts have also been studied and the limiting results are usually based on increasing cell sizes. The model that is considered in this research is the ANOCOVA model for Randomized Block Designs (RBD) with one observation per cell, as Yij=ƒÊ+ƒÀi+„„j+0(Xij-X..)+cij, i=1,c,n;j=1,c,c, where cij's are either iid or exchangeable and have continuous cdf's. Some nonparametric aligned rank test procedures are proposed in this paper for detecting the treatment effects for the above model. The first test proposed in this paper for ANOCOVA in RBD is based on the ranks of the block-mean-aligned observations. The overall ranking is used and the proposed test statistic has asymptotically a x^ distribution. Based on the same principle in developing the above test, a test for ANOCOVA in Incomplete Block Designs is also proposed. The second test proposed in this paper for ANOCOVA in RBD also uses overall ranking on the aligned observations. A test procedure using within-block rankings on the covariate-aligned observations is also proposed. The Rank Transformation test of Conover and Iman (1981) is briefly discussed in this paper. Through a Monte Carlo simulation study, the aligned rank test based on within block rankings and the Rank Transformation test are shown to be very robust and powerful and are strongly recommended for the model we discussed. It is found that the parametric test does not present good results in most of the non-normal cases and its use is discouraged when the underlying distribution is unknown.Item Nonparametric methods for pairwise comparisons in the randomized complete block design(Texas Tech University, 1998-12) Barefield, Eric W.The main focus of this investigation is to verify the robustness of validity of these tests. By robustness of validity, it is meant the stability of the Type I error rate for small designs as well as conditions under which some of the underlying assumptions are violated. For methods that produce valid tests, further investigations with respect to power are meaningful. Since many nonparametric methods use large sample approximation theory, it may be expected that these methods will perform better as n, the number of blocks, increases. As the number of treatments, p, gets larger, it becomes harder to reject the null hypothesis since this increases the critical value. As we will see, some design structures make rejection of the null hypothesis impossible for certain methods. The methods of interest include the sign statistic, signed rank statistic, rank sum statistic (Aligned Rank statistic using separated rankings and uniform scores). Aligned-Rank Transform, Within-Block ranking, and least squares.Item Nonparametric two-sample testing and estimation of location and scale parameters(Texas Tech University, 1980-08) Nath, Ravinder; Duran, Benjamin; Boullion, Thomas; Davenport, JamesNot availableItem On bandwidth selection for the kernel and local linear smoother methods in functional estimation with current status data(Texas Tech University, 2002-05) Gao, WeiNot availableItem On nonparametric confidence intervals for scale parameters(Texas Tech University, 2001-05) Martinez, Ruby R.In this thesis, the main focus is on nonparametric confidence intervals for scale parameters. The general technique of forming confidence intervals will be discussed. We consider testing a particular hypothesis using an appropriate test statistic. The critical region will be identified and those values of the parameter for which the null hypothesis is accepted will be used to yield a confidence interval. This is a general procedure for determining confidence intervals, and more details will be given in ensuing chapters. This is a general procedure for determining confidence intervals.Item On some nonparametric tests for location and scale.(Texas Tech University, 1974-08) Tsai, Wuu-ShyongNot availableItem On using the kernel method for functional estimation with current status data(Texas Tech University, 1999-12) Taylor, Scott A.To implement Yang's (1999) kernel estimator method, an important issue is the choice of bandwidth. It is well-known that the performance of kernel estimators depend upon the bandwidth. Furthermore, Yang's (1999) method uses the ratio of two kernel estimators which may be more sensitive to the choice of bandwidth. Our goal is to investigate the choice of bandwidth and evaluate the performance of the corresponding kernel estimators. The NPMLE will also be included in the studies for comparison. By comparing the mean square error of the kernel estimator against the NPMLE of Groeneboom and Wellner (1992), the kernel estimator was found to behave quite well under the given testing conditions. This thesis is organized as follows: The NPMLE method for functional estimation is introduced in Chapter II. Yang's kernel estimator method is introduced in Chapter III. In Chapter IV, we explain the procedures for evaluating the best choice of bandwidth. We analyze and display the results from the computer simulations in Chapter V. Finally, conclusions are drawn in Chapter VI.Item Performance of some nonparametric tests under inverse Gaussian alternatives(Texas Tech University, 1984-05) Shen, Chi-chungNot availableItem Power of nonparametric and parametric tests under location/scale alternatives(Texas Tech University, 1996-12) Li, SenNot availableItem Power of nonparametric tests for location/scale in one-factor model(Texas Tech University, 1998-08) Smart, Sandi ReneeNot available