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The purpose of this study was to investigate the performance of the parametric bootstrap method and to compare the parametric and nonparametric bootstrap methods for estimating the standard error of equating (SEE) under the common-item nonequivalent groups (CINEG) design with the frequency estimation (FE) equipercentile method under a variety of simulated conditions. When the performance of the parametric bootstrap method was investigated, bivariate polynomial log-linear models were employed to fit the data. With the consideration of the different polynomial degrees and two different numbers of cross-product moments, a total of eight parametric bootstrap models were examined. Two real datasets were used as the basis to define the population distributions and the "true" SEEs. A simulation study was conducted reflecting three levels for group proficiency differences, three levels of sample sizes, two test lengths and two ratios of the number of common items and the total number of items. Bias of the SEE, standard errors of the SEE, root mean square errors of the SEE, and their corresponding weighted indices were calculated and used to evaluate and compare the simulation results. The main findings from this simulation study were as follows: (1) The parametric bootstrap models with larger polynomial degrees generally produced smaller bias but larger standard errors than those with lower polynomial degrees. (2) The parametric bootstrap models with a higher order cross product moment (CPM) of two generally yielded more accurate estimates of the SEE than the corresponding models with the CPM of one. (3) The nonparametric bootstrap method generally produced less accurate estimates of the SEE than the parametric bootstrap method. However, as the sample size increased, the differences between the two bootstrap methods became smaller. When the sample size was equal to or larger than 3,000, the differences between the nonparametric bootstrap method and the parametric bootstrap model that produced the smallest RMSE were very small. (4) Of all the models considered in this study, parametric bootstrap models with the polynomial degree of four performed better under most simulation conditions. (5) Aside from method effects, sample size and test length had the most impact on estimating the SEE. Group proficiency differences and the ratio of the number of common items to the total number of items had little effect on a short test, but had slight effect on a long test.

Pour construire des intervalles de confiance, nous pouvons utiliser diverses approches bootstrap. Nous avons un problème pour le contexte spécifique d’un paramètre de proportion lorsque l’estimateur usuel, la proportion de succès dans l’échantillon ˆp, est nul. Dans un contexte classique d’observations indépendantes et identiquement distribuées (i.i.d.) de la distribution Bernoulli, les échantillons bootstrap générés ne contiennent que des échecs avec probabilité 1 et les intervalles de confiance bootstrap deviennent dégénérés en un seul point, soit le point 0. En contexte de population finie, nous sommes confrontés aux mêmes problèmes lorsqu’on applique une méthode bootstrap à un échantillon de la population ne contenant que des échecs. Une solution possible s’inspire de l’estimateur utilisé dans les méthodes de [Wilson, 1927] et [Agresti et Coull, 1998] où ceux-ci considèrent ˜p l’estimateur qui prend la proportion de succès d’un échantillon augmenté auquel on a ajouté deux succès et deux échecs. La solution que nous introduisons consiste à effectuer le bootstrap de la distribution de ˆp mais en appliquant les méthodes bootstrap à l’échantillon augmenté de deux succès et deux échecs, tant en statistique classique que pour une population finie. Les résultats ont démontré qu’une version de la méthode percentile est la méthode bootstrap la plus efficace afin d’estimer par intervalle de confiance un paramètre de proportion autant dans un contexte i.i.d. que dans un contexte d’échantillonnage avec le plan aléatoire simple sans remise. Nos simulations ont également démontré que cette méthode percentile pouvait compétitionner avantageusement avec les meilleures méthodes traditionnelles. / A few bootstrap approaches exist to create confidence intervals. Some difficulties appear for the specific case of a proportion when the usual estimator, the proportion of success in a sample, is 0. In the classical case where the observations are independently and identically distributed (i.i.d.) from a Bernoulli distribution, the bootstrap samples only contain zeros with probability 1 and the resulting bootstrap confidence intervals are degenerate at the value 0. We are facing the same problem in the survey sampling case when we apply the bootstrap method to a sample with all observations equal to 0. A possible solution is suggested by the estimator found in the confidence intervals of [Wilson, 1927] and [Agresti et Coull, 1998] where they use ˜p the proportion of success in a augmented sample consisting of adding two successes and two failures to the original sample. The proposed solution is to use the bootstrap method on ˆp but where the bootstrap is based on the augmented sample with two additional successes and failures, whether the sample comes from i.i.d. Bernoulli variables or from a simple random sample. Results show that a version of the percentile method is the most efficient bootstrap method to construct confidence intervals for a proportion both in the classical setting or in the case of a simple random sample. Our results also show that this percentile interval can compete with the best traditional methods.

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Master of Science / Department of Computing and Information Sciences / Daniel A. Andresen / As a laboratory associated the English Language Program (ELP) at Kansas State University, the International Technology Commons (ITC) provides English instructions to students who are qualified to begin university work but do not meet the English proficiency standards for the university by using cutting-edge pedagogical technologies. The ITC Information System is a centralized web-based framework that manages the polices, processes, and procedures to make sure that the ITC can fulfill all tasks required to archive its objectives, including checking in/out electronic devices and/or books to students and faculties, registering new students during the enrollment, keeping track of ITC properties and assets, etc. As a full-stack project, the ITC Information System has been designed and implemented by utilizing multiple modern programming languages, frameworks, and platforms. Been serving the ITC since August 2015, the ITC Information System has significantly improved the efficiency of ITC electronic resources, and reduced the man-hours devoting to administrating undergraduate lab monitors. Leadership of the ELP appreciates the outcome and expresses expectation to broaden the scale of this project to serving more instructional divisions.

Yung Wun Na. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Statistical Modeling --- p.4 / Chapter 2.1 --- Capture Recapture Model --- p.4 / Chapter 2.1.1 --- Petersen Estimate --- p.5 / Chapter 2.1.2 --- Chapman Estimate --- p.8 / Chapter 2.2 --- The Bootstrap Method --- p.9 / Chapter 2.2.1 --- The Bootstrap Percentile Method --- p.10 / Chapter 2.3 --- The Double Bootstrap Method --- p.12 / Chapter 2.3.1 --- The Robbins-Monro Method --- p.12 / Chapter 2.3.2 --- Confidence Interval generated by the Robbins-Monro Method --- p.13 / Chapter 2.3.3 --- Three Different Approaches --- p.16 / Chapter 3 --- Empirical Study --- p.19 / Chapter 3.1 --- Introduction --- p.19 / Chapter 3.2 --- Double Bootstrap Method --- p.20 / Chapter 3.2.1 --- Petersen Estimate --- p.20 / Chapter 3.2.2 --- Chapman Estimate --- p.27 / Chapter 3.2.3 --- Comparison of Petersen and Chapman Estimates --- p.31 / Chapter 3.3 --- Conclusion --- p.33 / Chapter 4 --- Simulation Study --- p.35 / Chapter 4.1 --- Introduction --- p.35 / Chapter 4.2 --- Simulation Results of Double Bootstrap Method --- p.36 / Chapter 5 --- Conclusion and Discussion --- p.52 / References --- p.60

Au Tsz-yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 76-79). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Forecasting Time Series --- p.1 / Chapter 1.2 --- Importance of Multiple Forecasts --- p.2 / Chapter 1.3 --- Methodology of Forecasting for Autoregressive Models --- p.3 / Chapter 1.4 --- Bootstrap Approach --- p.9 / Chapter 1.5 --- Objectives --- p.12 / Chapter 2 --- "Bootstrapping Simultaneous Prediction Intervals, Case A: p known" --- p.15 / Chapter 2.1 --- TS Procedure --- p.16 / Chapter 2.2 --- CAO Procedure --- p.18 / Chapter 2.3 --- MAS Procedure --- p.20 / Chapter 3 --- "Bootstrapping Simultaneous Prediction Intervals, Case B: p unknown" --- p.24 / Chapter 3.1 --- TS Procedure --- p.25 / Chapter 3.2 --- CAO Procedure --- p.27 / Chapter 3.3 --- MAS Procedure --- p.28 / Chapter 4 --- Simulation Study --- p.29 / Chapter 4.1 --- Design of The Experiment --- p.29 / Chapter 4.2 --- Simulation Results --- p.33 / Chapter 5 --- A Real-Data Case --- p.36 / Chapter 5.1 --- Case A --- p.37 / Chapter 5.2 --- Case B --- p.42 / Chapter 6 --- Conclusion --- p.46 / Chapter A --- Tables of Simulation Results for Case A --- p.49 / Chapter B --- Tables of Simulation Results for Case B --- p.62 / Chapter C --- References --- p.76

Lui Ying Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Introduction to bootstrap and efficiency bootstrap simulation --- p.5 / Chapter 2.1 --- Background of bootstrap --- p.5 / Chapter 2.2 --- Basic idea of bootstrap --- p.7 / Chapter 2.3 --- Variance reduction methods --- p.10 / Chapter 2.3.1 --- Control variates --- p.10 / Chapter 2.3.2 --- Common random numbers --- p.12 / Chapter 2.3.3 --- Antithetic variates --- p.14 / Chapter 2.3.4 --- Importance Sampling --- p.15 / Chapter 2.4 --- Efficient bootstrap simulation --- p.17 / Chapter 2.4.1 --- Linear approximation --- p.18 / Chapter 2.4.2 --- Centring method --- p.19 / Chapter 2.4.3 --- Balanced resampling --- p.20 / Chapter 2.4.4 --- Antithetic resampling --- p.21 / Chapter 3 --- Methodology --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Cluster analysis --- p.24 / Chapter 3.3 --- Regression estimator and mixture experiment --- p.25 / Chapter 3.4 --- Estimate of standard error and bias --- p.30 / Chapter 4 --- Simulation study --- p.45 / Chapter 4.1 --- Introduction --- p.45 / Chapter 4.2 --- Ratio estimation --- p.46 / Chapter 4.3 --- Time series problem --- p.50 / Chapter 4.4 --- Regression problem --- p.54 / Chapter 5 --- Conclusion and discussion --- p.60 / Reference --- p.63

This paper discusses results of a computer simulation to investigate several different tests when sampling several distributions. The hypothesis H0: μ=0 was tested against H0: μ≠0, using the usual t-test, trimmed t-test, the Jackkinfe, the Boostrap and signed-rank test. The p-values and empirical power show that the Bootstrap is as good as the t-test. The Jackknife procedure is too liberal, always obtaining small p-values. The signed-rank is a fairly good test if the data follows the Cauchy Distribution.

This study investigated the extent to which rules proposed by Tong and Brennan (2007) for estimating standard errors of estimated variance components held up across a variety of G theory designs, variance component structures, sample size patterns, and data types. Simulated data was generated for all combinations of conditions, and point estimates, standard error estimates, and coverage for three types of confidence intervals were calculated for each estimated variance component and relative and absolute error variance across a variety of bootstrap procedures for each combination of conditions. It was found that, with some exceptions, Tong and Brennan's (2007) rules produced adequate standard error estimates for normal and polytomous data, while some of the results differed for dichotomous data. Additionally, some refinements to the rules were suggested with respect to nested designs. This study provides support for the use of bootstrap procedures for estimating standard errors of estimated variance components when data are not normally distributed.