Randy R. Sitter

A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data

Suppose that the finite population consists of N identifiable units. Associated with the ith unit are the study variable, yi, and a vector of auxiliary variables, xi. The values x1, x2,…, xN are known for the entire population (i.e., complete) but yi is known only if the ith unit is selected in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this article, a unified model-assisted framework has been attempted using a proposed model-calibration technique. The proposed model-calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of Deville and Särndal and/or the generalized regression estimators in the linear model case. The pseudoempirical maximum likelihood estimator of Chen and Sitter, when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estimator but with positive weights. Some existing estimators using auxiliary information are reexamined under this framework. The estimation of the finite population distribution function, using complete auxiliary information, is also considered, and estimators based on a general model are presented. Results of a limited simulation study on the performance of the proposed estimators are reported.

Minimum-aberration two-level fractional factorial split-plot designs

It is often impractical to perform the experimental runs of a fractional factorial in a completely random order, In these cases, restrictions on the randomization of the experimental trials are imposed and the design is said to have a split-plot structure. We rank these fractional factorial split-plot designs similarly to fractional factorials using the aberration criterion to find the minimum-aberration design. We introduce an algorithm that constructs the set of all nonisomorphic two-level fractional factorial split-plot designs more efficiently than existing methods. The algorithm can be easily modified to efficiently produce sets of all nonisomorphic fractional factorial designs, fractional factorial designs in which the number of levels is a power of a prime, and fractional factorial split-plot designs in which the number of levels is a power of a prime.

Bootstrap for Imputed Survey Data

Abstract Most surveys use imputation to compensate for missing data. However, treating the imputed data set as the complete data set and directly applying existing methods (e.g., the linearization, the jackknife, and the bootstrap) for variance estimation and/or statistical inference does not produce valid results, because these methods do not account for the effect of missing data and/or imputation. In this article we show that correct bootstrap estimates can be obtained by imitating the process of imputing the original data set in the bootstrap resampling; that is, by imputing the bootstrap data sets in exactly the same way that the original data set is imputed. The proposed bootstrap is asymptotically valid irrespective of the sampling design, the imputation method, or the type of statistic used in inference. This enables us to use a unified method in a variety of problems, and in fact this is the only method that works without any restriction on the sampling design, the imputation method, or the type ...

Design Issues In Fractional Factorial Split-Plot Experiments

It is often impractical to perform the experimental runs of a fractional factorial in a completely random order. In these cases, restrictions on the randomization of the experimental trials are imposed and the design is said to have a split-plot structure. Similar to fractional factorials, the “goodness” of fractional factorial split-plot designs can be judged using the minimum aberration criterion. However, the split-plot nature of the design implies that not all factorial effects can be estimated with the same precision. In this paper, we discuss the impact of the randomization restrictions on the design. We show how the split-plot structure affects estimation, precision, and the use of resources. We demonstrate how these issues affect design selection in a real industrial experiment.

A Resampling Procedure for Complex Survey Data

Abstract In complex survey data, often the sampling design induces a non-iid structure to the data (e.g., without replacement sampling, stratification, multistage, or unequal probability of selection). Though techniques for variance estimation and confidence intervals do exist, they often are cumbersome to implement or do not extend to complex designs. It would be desirable to have resampling methods that reuse the existing estimation system repeatedly, using computing power to avoid theoretical work, and that can be applied to such data. In recognition of this need, various resampling procedures for variance estimation and confidence intervals in sample survey data (where the sampling is without replacement) have been proposed in the literature. These include the jackknife, the with-replacement bootstrap (BWR), the without-replacement bootstrap (BWO), and the rescaling bootstrap. The BWR and BWO are applicable only to simple sampling designs. Others have shown the asymptotic consistency of jackknife vari...

Robust designs for binary data

This article is concerned with experimental design of statistical models for binary data. Since in most commonly used models for binary data, the information matrix depends on the unknown parameters, the standard optimality criteria used in regression cannot be used. What is typically done to avoid this problem is to assume good initial parameter estimates. The main purpose of this article is to introduce a minimax procedure for obtaining designs that are robust to poor initial parameter estimates. The procedure yields designs with more design points, and larger spread, if precise knowledge of the parameters is unavailable. D-optimality, and Fieller and confidence intervals for the median response dose are used to construct optimality functions for the procedure.

Fractional Factorial Split-Plot Designs for Robust Parameter Experiments

For robust parameter designs, it has been noted that performing the experiment as a split plot often provides cost savings and increased efficiency. Thus experiments are often performed using fractional factorial split-plot designs. We consider how one should best choose such designs for robust parameter experiments and what is meant by maximum resolution and by minimum aberration in this context under various experimental settings.

Fractional resolution and minimum aberration in blocked 2 n−k designs

Systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks. This is accomplished through the use of blocking factors. The concepts of resolution and minimum aberration, design optimization criteria ordinarily used to rank unblocked fractional factorial designs, are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup. Some limited theoretical results are derived, and tables of minimumaberration blocked two-level fractional factorial designs are presented and considered. The relationship between clear effects (effects that are estimable when higher-order effects are assumed negligible) and minimum aberration in the presence of blocking is discussed.

Using the Folded-Over 12-Run Plackett—Burman Design to Consider Interactions

This article demonstrates that the folded-over 12-run Plackett–Burman design is useful for considering up to 12 factors in 24 runs, even if one anticipates that some two-factor interactions may be significant. The properties of this design are investigated, and a sequential procedure for analyzing the data from such a design is proposed. The performance of the procedure is investigated through the analysis of real and constructed examples and through a small simulation study. Applications to other folded-over Plackett–Burman designs are also briefly discussed.

On the accuracy of Fieller intervals for binary response data

Abstract Finney proposed the use of a fiducial interval for the median response dose based on Fiellers theorem. An alternative is to use the asymptotic confidence interval. The simulations by Abdelbasit and Plackett suggest that the two intervals have similar coverage probabilities. We compare the two intervals theoretically and in an expanded simulation study. Our results show that Fieller intervals are generally superior. An attempt is made to characterize how and when the two intervals differ.