C. F. J. Wu

Resampling Inference with Complex Survey Data

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...

Analysis of Designed Experiments with Complex Aliasing

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..

A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing

Experiments using designs with complex aliasing patterns are often performed—for example, twolevel nongeometric Plackett-Burman designs, multilevel and mixed-level fractional factorial designs, two-level fractional factorial designs with hard-to-control factors, and supersaturated designs. Hamada and Wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions. Their strategy provides a restricted search in a rather large model space, however. This article provides an efficient methodology based on a Bayesian variable-selection algorithm for searching the model space more thoroughly. We show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models. The proposed methodology is demonstrated with four examples, three of which come from actual industrial experiments.

A graph-aided method for planning two-level experiments when certain interactions are important

In planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects. In this article, we propose a graph-aided method to solve this problem for two-level experiments. First, we choose the defining relations for a 2 n–k design according to a goodness criterion such as the minimum aberration criterion. Then we construct all of the nonisomorphic graphs that represent the solutions to the problem of simultaneous estimation of main effects and two-factor interactions for the given defining relations. In each graph a vertex represents a factor and an edge represents the interaction between the two factors. For the experiment planner, the job is simple: Draw a graph representing the specified interactions and compare it with the list of graphs obtained previously. Our approach is a substantial improvement over Taguchis linear graphs.

Speech recognition using hidden Markov models with polynomial regression functions as nonstationary states

Proposes, implements, and evaluates a class of nonstationary-state hidden Markov models (HMMs) having each state associated with a distinct polynomial regression function of time plus white Gaussian noise. The model represents the transitional acoustic trajectories of speech in a parametric manner, and includes the standard stationary-state HMM as a special, degenerated case. The authors develop an efficient dynamic programming technique which includes the state sojourn time as an optimization variable, in conjunction with a state-dependent orthogonal polynomial regression method, for estimating the model parameters. Experiments on fitting models to speech data and on limited-vocabulary speech recognition demonstrate consistent superiority of these nonstationary-state HMMs over the traditional stationary-state HMMs. >

An Approach to the Construction of Asymmetrical Orthogonal Arrays

Abstract Use of asymmetrical orthogonal arrays (OAs) for planning industrial experiments with mixed levels has become increasingly popular. In addition to applications to experimental investigations in many disciplines, they can also be used in the balanced repeated-replications method of inference from general stratified survey samples. In this article, we propose a general approach to the construction of asymmetrical OAs with economic run size and flexibility in the choice of factor levels. As applications of this approach, we construct several general classes of arrays that include numerous existing classes of arrays as special cases. A large number of known asymmetrical OAs can be reproduced by our approach in a unified and simple manner. Many new arrays are obtained. A list of asymmetrical OAs with moderate run size is given. Our approach consists of three steps. We first construct an OA as the generalized Kronecker sum of an OA and some difference matrices. We then add, to the constructed OA, co...

Joint monitoring of PID-controlled processes

Statistical process control (SPC) monitoring of the special causes of a process, along with engineering feedback control such as proportional-integral-derivative (PID) control, is a major tool for on-line quality improvement. In this paper, a strategy t..

Nearly orthogonal arrays with mixed levels and small runs

In running a factorial experiment, it may be desirable to use an orthogonal array with different (mixed) numbers of factor levels. Because of the orthogonality requirement, such arrays may have a large run size. By slightly sacrificing the orthogonality requirement, we can obtain nearly orthogonal arrays with economic run size. Some general methods for constructing such arrays are given. For 12, 18, 20, and 24 runs, many orthogonal arrays and nearly orthogonal arrays with mixed levels are constructed and tabulated. Effects of near orthogonality on estimation efficiency and analysis are studied.

Inference from Stratified Samples: Second-Order Analysis of Three Methods for Nonlinear Statistics

Abstract For stratified samples and nonlinear statistics that can be expressed as functions of estimated totals, second-order asymptotic expansions of the linearization, jackknife, and balanced repeated-replication variance estimators are obtained. Based on these, comparisons are made in terms of their biases. Some higher order asymptotic equivalence results are also established. The special case of a combined ratio estimator is investigated in detail. Some results on bias reduction achieved by the jack-knife and balanced repeated-replication estimators of a nonlinear function of totals are also given.

Construction of optimal multi-level supersaturated designs

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu (2001). Optimal supersaturated designs are shown to have a periodic property and general methods for constructing optimal multilevel supersaturated designs are proposed. Inspired by the Addelman-Kempthorne construction of orthogonal arrays, optimal multi-level supersaturated designs are given in an explicit form: columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties.