# Browsing by Subject "Linear models (Statistics)"

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Item Aligned rank tests for repeated observation models with orthonormal design(Texas Tech University, 2004-08) Omolo, Bernard OgunaShow more Rank tests are known to be distribution-free for simple linear models, where the observations are i.i.d. For general linear models with nuisance parameters, however, the alignment principle can be applied to obtain asymptotically distribution-free rank tests. This is especially so when the centered design matrices have full rank, as is the case in Kraft and van Eeden [19], Adichie [1] and Chiang and Puri [4], among others. Motivated by the example of testing linearity in a nonparametric regression model, however, we will be dealing with models whose centered design matrices are not of full rank. More specifically, the asymptotic distribution of the aligned rank statistics will be obtained under the null hypothesis and local alternatives for testing a linear hypothesis in a repeated observation model with orthonormal design matrix. These asymptotic distributions are of the chi-square type and independent of the choice of aligner, as in the full rank case. Some simulations of the power function when the errors have a Cauchy distribution are included. The theory is presented in a self-contained manner, and based on the Chernoff- Savage rather than the Hajek approach. In principle this would allow us 1o also deal with the asymptotics under fixed alternatives, although this option is not presented to completion. This approach can be extended to scale models as well as multivariatc models. Although these topics are only briefly considered, interesting additional insight, is gained in the independence of the aligner. In the location model, this independence is obtained due to a suitable choice of the test statistic so that cancellation takes place. In the scale model, on the other hand, the aligner docs not e\en appear in the expansion of the basic components of the test statistic due to the particular form of scene functions employed for scale problems.Show more Item Bayesian variable selection for GLM(2002) Wang, Xinlei; Shively, Thomas S.; George, Edward I.Show more Item Essays in monetary and fiscal policy(Texas Tech University, 2004-05) Alzoubi, OmarShow more Not availableShow more Item Item and person parameter estimation using hierarchical generalized linear models and polytomous item response theory models(2003-05) Williams, Natasha Jayne; Koch, William R.; Beretvas, Susan NatashaShow more Item Nonparametric analysis of treatment effects with missing observations /: y Kimberly Lee Drews.(Texas Tech University, 2002-12) Drews, Kimberly LeeShow more Not availableShow more Item Stability of estimates of location and scale parameters in rank regression(Texas Tech University, 2001-05) Bonow, Jessica L.Show more We have several objectives or goals that we want to achieve or accomplish in the thesis. One goal is to determine which scale parameter estunate of the three being examined will be the best estimator of the actual value of r for each error term distribution. We wish to see if the choice of the scale estimate has any influence on the performance on the rank regression tests. We want to perform a hypothesis test on the analysis of covariance model to compare the aligned rank transform, rank regression, and least squares tests, as well as investigate the influence of the scale parameter estimates on the rank regression test. Another goal is to produce the empirical Type I error rates to investigate the robustness of stability of the tests. For the valid tests, the empirical power calculation is used to decide on the superiority of each test. To implement the empirical results and the sunulation study of this thesis, we used SAS, SAS/IML and SAS/MACRO languages. The code and syntax can be found in the appendix.Show more