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1	Exact D-optimal designs for mixture experiments in Scheffe's quadratic models Wu, Shian-Chung 05 July 2006 (has links) The exact D-optimal design problems for regression models has been in-vestigated in many literatures. Huang (1987) and Gaffke (1987) provided a sufficient condition for the minimum sample size for an certain set of candidate designs to be exact D-optimal for polynomial regression models on a compact interval. In this work we consider a mixture experiment with q nonnegative components, where the proportions of components are sub- ject to the simplex restriction $sum_{i=1}^q x_i =1$, $x_i ¡Ù 0$. The exact D-optimal designs for mixture experiments for Scheffe¡¦s quadratic models are investigated. Based on results in Kiefer (1961) results about the exact D-optimal designs for mixture models with two or three ingredients are provided and numerical verifications for models with ingredients between four and nine are presented. Scheffe¡¦s quadratic models information matrix orthonormal polynomial D-optimal design exact D-optimal
2	A comparative study of permutation procedures Van Heerden, Liske 30 November 1994 (has links) The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics) Weather modification Robustness Permutation test Parametric test Monte Carlo study Significance level Power Average confidence interval length Zero measurements Behrens-Fisher problem Scheffe Welch Test statistic Unequal variances 519.56 Statistical hypothesis testing
3	A comparative study of permutation procedures Van Heerden, Liske 30 November 1994 (has links) The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics) Weather modification Robustness Permutation test Parametric test Monte Carlo study Significance level Power Average confidence interval length Zero measurements Behrens-Fisher problem Scheffe Welch Test statistic Unequal variances 519.56 Statistical hypothesis testing
4	Statistical Inference Chou, Pei-Hsin 26 June 2008 (has links) In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications. finite population correction factor statistical hypothesis type I error composite hypothesis power Central limit theorem Basu theorem critical value goodness of fit test likelihood ratio test Lehmann-Scheffe theorem complete statistic ancillary statistic P-value type II error Rao-Blackwell theorem simple hypothesis one-sided test two-sided test significance level sufficient statistic alternative hypothesis testing hypothesis null hypothesis rejection region confidence interval confidence level minimum variance unbiased estimator interval estimation uniformly most powerful test Cramer-Rao inequality likelihood function mean square error moment estimator error of estimation point estimation maximum likelihood estimator bias consistent estimator minimal sufficient statistic factorization theorem unbiased estimator statistic most powerful test test statistics Neyman-Pearson lemma decision rule

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