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

The Design and Analysis of Experiments

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.

/pdf/regression-modeling-strategies-1jyn0f4r32.pdf

Regression Modeling Strategies

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).

Increased Prevalence of Sleep-Disordered Breathing in Adults

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.

/pdf/aic-model-selection-and-multimodel-inference-in-behavioral-192nrc36ut.pdf

AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons

Estimation and inference in two-stage, semi-parametric models of production processes

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.

/pdf/jackknife-bootstrap-and-other-resampling-methods-in-3l6x5quxzs.pdf

Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis

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.

/pdf/asymptotic-theory-of-nonlinear-least-squares-estimation-bzreq5juhn.pdf

Asymptotic Theory of Nonlinear Least Squares Estimation

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...

Resampling Inference with Complex Survey Data

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..

Analysis of Designed Experiments with Complex Aliasing

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.

/pdf/a-general-theory-for-jackknife-variance-estimation-2a2qc57cj2.pdf

Chien-Fu Wu

Papers

Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis

Asymptotic Theory of Nonlinear Least Squares Estimation

Resampling Inference with Complex Survey Data

Analysis of Designed Experiments with Complex Aliasing

A General Theory for Jackknife Variance Estimation