Download (.pdf)Multi-level Bootstrapping the SAS® Way
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Bootstrapping is a non-parametric method since specific assumptions are not done about the distribution from which the... more Bootstrapping is a non-parametric method since specific assumptions are not done about the distribution from which the data arise. Also, it is widely used for it can approximate the entire sampling distribution of some estimator; can estimate the bias, or standard error, or a confidence interval of the parameter. The problem of the classical bootstrapping procedure is that it always gives the value of a statistics with high standard errors. Multi-level bootstrapping is proposed as the extended version of bootstrapping. It estimates the parameter of interest from bootstrap resamples giving you a smaller variability or higher reliability as compared to the original bootstrap. To evaluate the multi-level bootstrapping, three samples were generated from a Gaussian distribution; one is for the small sample case, the second for a large sample case and the other is for the unrepresentative sample case. The multi-level bootstrapping is suitable in determining the distribution of a sample when the goal is to achieve low standard errors. For both small and large samples, the multi-level bootstrapping procedure yielded lower standard errors than the classical bootstrapping procedure. In cases where there is an unrepresentative sample, the multi-level bootstrapping procedure produced low standard errors although the estimates are highly biased.
Scalable algorithms for adaptive statistical designs
Reprinted in Scientific Programming 8 (2001), pp. 183-193
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Optimal adaptive designs for delayed response models: exponential case
Appears in MODA6: Model Oriented Data Analysis, A. Atkinson, P. Hackl, W. Mueller, eds., Physica Verlag, 2001, pp. 127-134
Performance of Some Multiple Comparison Tests Under Heteroscedasticity and Dependency
by Anil Dolgun
Journal of Statistical Computation and Simulation , Vol. 80, No. 10, October 2010, 1083–1100. Authors: Demirhan, H., Dolgun, N.A. Demirhan Parlak, Y., Dolgun, M.Ö.
In this article, 18 multiple comparison tests are compared according to powers and type I error measures under some... more In this article, 18 multiple comparison tests are compared according to powers and type I error measures under some violations of analysis of variance assumptions with a Monte Carlo simulation study. Considered violations of assumptions are heterogeneity in subgroup variances and dependency between subgroups. Various numbers of subgroups and subgroup sizes are considered simultaneously with the violations of assumptions. Simulation results are analysed by using visual inspection, graphical representations, decision-tree and correspondence analyses. Wide inferences are drawn on the behaviour of considered tests with respect to measures used. Some general suggestions are given on which tests should be used or avoided under violations of assumptions.
Comparing Diagnostic Tests: Test of Hypothesis for Likelihood Ratios
by Anil Dolgun
Journal of Statistical Computation and Simulation
DOI: 10.1080/00949655.2010.531480
First published on 31 May 2011
Authors: Nimet Anil Dolgun, Harika Gozukara, Ergun Karaagaoglu,
Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the... more Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.