Author

Chien-Fu Wu

Bio: Chien-Fu Wu is an academic researcher from University of Michigan. The author has contributed to research in topic(s): Estimator & Orthogonal array. The author has an hindex of 35, co-authored 56 publication(s) receiving 5688 citation(s). Previous affiliations of Chien-Fu Wu include Georgia Institute of Technology & University of Waterloo.

Papers
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Journal ArticleDOI
TL;DR: In this paper, a class of weighted jackknife variance estimators for the least square estimator by deleting any fixed number of observations at a time was proposed, and three bootstrap methods were considered.
Abstract: Motivated by a representation for the least squares estimator, we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time. They are unbiased for homoscedastic errors and a special case, the delete-one jackknife, is almost unbiased for heteroscedastic errors. The method is extended to cover nonlinear parameters, regression $M$-estimators, nonlinear regression and generalized linear models. Interval estimators can be constructed from the jackknife histogram. Three bootstrap methods are considered. Two are shown to give biased variance estimators and one does not have the bias-robustness property enjoyed by the weighted delete-one jackknife. A general method for resampling residuals is proposed. It gives variance estimators that are bias-robust. Several bias-reducing estimators are proposed. Some simulation results are reported.

1,616 citations

Journal ArticleDOI
TL;DR: For a linear regression model, the necessary and sufficient condition for the asymptotic consistency of the least squares estimator is known as mentioned in this paper, and the condition is sufficient for the existence of any weakly consistent estimator, including the least square estimator.
Abstract: For a linear regression model, the necessary and sufficient condition for the asymptotic consistency of the least squares estimator is known. An analogous condition for the nonlinear model is considered in this paper. The condition is proved to be necessary for the existence of any weakly consistent estimator, including the least squares estimator. It is also sufficient for the strong consistency of the nonlinear least squares estimator if the parameter space is finite. For an arbitrary compact parameter space, its sufficiency for strong consistency is proved under additional conditions in a sense weaker than previously assumed. The proof involves a novel use of the strong law of large numbers in $C(S)$. Asymptotic normality is also established.

499 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a resampling method based on the balanced repeated replication (BRR) method for stratified multistage multi-stage designs with replacement, in particular for two sampled clusters per stratum.
Abstract: Methods for standard errors and confidence intervals for nonlinear statistics —such as ratios, regression, and correlation coefficients—have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement, in particular, the important special case of two sampled clusters per stratum. These methods include the customary linearization (or Taylor) method and resampling methods based on the jackknife and balanced repeated replication (BRR). Unlike the jackknife or the BRR, the linearization method is applicable to general sampling designs, but it involves a separate variance formula for each nonlinear statistic, thereby requiring additional programming efforts. Both the jackknife and the BRR use a single variance formula for all nonlinear statistics, but they are more computing-intensive. The resampling methods developed here retain these features of the jackknife and the BRR, yet permit extension to more complex designs involving sampling without replace...

415 citations

Journal ArticleDOI
TL;DR: This paper presents a large number of designs of Plackett-Burman designs that have been used in screening experiments for identifying important main effects and some of them have been criticized for their complex aliasing patterns.
Abstract: Traditionally, Plackett-Burman (PB) designs have been used in screening experiments for identifying important main effects. The PB designs whose run sizes are not a power of two have been criticized for their complex aliasing patterns, which according t..

341 citations

Journal ArticleDOI
TL;DR: The delete-1 jackknife is known to give inconsistent variance estimators for nonsmooth estimators such as the sample quantiles as mentioned in this paper, which can be rectified by using a more general jackknife with $d$, the number of observations deleted, depending on a smoothness measure of the point estimator.
Abstract: The delete-1 jackknife is known to give inconsistent variance estimators for nonsmooth estimators such as the sample quantiles. This well-known deficiency can be rectified by using a more general jackknife with $d$, the number of observations deleted, depending on a smoothness measure of the point estimator. Our general theory explains why jackknife works or fails. It also shows that (i) for "sufficiently smooth" estimators, the jackknife variance estimators with bounded $d$ are consistent and asymptotically unbiased and (ii) for "nonsmooth" estimators, $d$ has to go to infinity at a rate explicitly determined by a smoothness measure to ensure consistency and asymptotic unbiasedness. Improved results are obtained for several classes of estimators. In particular, for the sample $p$-quantiles, the jackknife variance estimators with $d$ satisfying $n^{1/2}/d \rightarrow 0$ and $n - d \rightarrow \infty$ are consistent and asymptotically unbiased.

279 citations

Cited by
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Journal Article
TL;DR: This book by a teacher of statistics (as well as a consultant for "experimenters") is a comprehensive study of the philosophical background for the statistical design of experiment.
Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. \$8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

12,326 citations

BookDOI
01 Jan 2006
TL;DR: Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas.
Abstract: Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas. Regression models are also used to adjust for patient heterogeneity in randomized clinical trials, to obtain tests that are more powerful and valid than unadjusted treatment comparisons.

3,607 citations

Journal ArticleDOI
Paul E. Peppard
TL;DR: The prevalence of sleep-disordered breathing in the United States for the periods of 1988-1994 and 2007-2010 is estimated using data from the Wisconsin Sleep Cohort Study, an ongoing community-based study with participants randomly selected from an employed population of Wisconsin adults.
Abstract: Sleep-disordered breathing is a common disorder with a range of harmful sequelae. Obesity is a strong causal factor for sleep-disordered breathing, and because of the ongoing obesity epidemic, previous estimates of sleep-disordered breathing prevalence require updating. We estimated the prevalence of sleep-disordered breathing in the United States for the periods of 1988–1994 and 2007–2010 using data from the Wisconsin Sleep Cohort Study, an ongoing community-based study that was established in 1988 with participants randomly selected from an employed population of Wisconsin adults. A total of 1,520 participants who were 30–70 years of age had baseline polysomnography studies to assess the presence of sleep-disordered breathing. Participants were invited for repeat studies at 4-year intervals. The prevalence of sleep-disordered breathing was modeled as a function of age, sex, and body mass index, and estimates were extrapolated to US body mass index distributions estimated using data from the National Health and Nutrition Examination Survey. The current prevalence estimates of moderate to severe sleep-disordered breathing (apnea-hypopnea index, measured as events/hour, ≥15) are 10% (95% confidence interval (CI): 7, 12) among 30–49-year-old men; 17% (95% CI: 15, 21) among 50–70-year-old men; 3% (95% CI: 2, 4) among 30–49-year-old women; and 9% (95% CI: 7, 11) among 50–70 year-old women. These estimated prevalence rates represent substantial increases over the last 2 decades (relative increases of between 14% and 55% depending on the subgroup).

2,691 citations

Journal ArticleDOI
TL;DR: In this paper, a coherent data-generating process (DGP) is described for nonparametric estimates of productive efficiency on environmental variables in two-stage procedures to account for exogenous factors that might affect firms’ performance.
Abstract: Many papers have regressed non-parametric estimates of productive efficiency on environmental variables in two-stage procedures to account for exogenous factors that might affect firms’ performance. None of these have described a coherent data-generating process (DGP). Moreover, conventional approaches to inference employed in these papers are invalid due to complicated, unknown serial correlation among the estimated efficiencies. We first describe a sensible DGP for such models. We propose single and double bootstrap procedures; both permit valid inference, and the double bootstrap procedure improves statistical efficiency in the second-stage regression. We examine the statistical performance of our estimators using Monte Carlo experiments.

2,586 citations

Journal ArticleDOI
TL;DR: The information-theoretic (I-T) approaches to valid inference are outlined including a review of some simple methods for making formal inference from all the hypotheses in the model set (multimodel inference).
Abstract: We briefly outline the information-theoretic (I-T) approaches to valid inference including a review of some simple methods for making formal inference from all the hypotheses in the model set (multimodel inference). The I-T approaches can replace the usual t tests and ANOVA tables that are so inferentially limited, but still commonly used. The I-T methods are easy to compute and understand and provide formal measures of the strength of evidence for both the null and alternative hypotheses, given the data. We give an example to highlight the importance of deriving alternative hypotheses and representing these as probability models. Fifteen technical issues are addressed to clarify various points that have appeared incorrectly in the recent literature. We offer several remarks regarding the future of empirical science and data analysis under an I-T framework.

2,545 citations