Vijayan N. Nair

Bio: Vijayan N. Nair is an academic researcher from Bell Labs. The author has contributed to research in topics: Estimator & Least squares. The author has an hindex of 7, co-authored 9 publications receiving 1355 citations.

Taguchi's parameter design: a panel discussion

Abstract: It is more than a decade since Genichi Taguchi's ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchi's methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchi's methodology for implementing it. The topics covered include the importance of vari...

Signal-to-noise ratios, performance criteria, and transformations

Abstract: For the analysis of designed experiments, Taguchi uses performance criteria that he calls signal-to-noise (SN) ratios. Three such criteria are here denoted by SN T , SN L , and SN S . The criterion SN T was to be used in preference to the standard deviation for the problem of achieving, for some quality characteristic y, the smallest mean squared error about an operating target value. Leon, Shoemaker, and Kacker (1987) showed how SN T was appropriate to solve this problem only when σ y was proportional to μ y . On that assumption, the same result could be obtained more simply by conducting the analysis in terms of log y rather than y. A more general transformation approach is here introduced for other, commonly met kinds of dependence between σ y and μ y (including no dependence), and a lambda plot is presented that uses the data to suggest an appropriate transformation. The criteria SN L and SN S were for problems in which the objective was to make the response as large or as small as possible. It is arg...

Analyzing dispersion effects from replicated factorial experiments

Abstract: Recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments. A commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within-replication variance (Bartlett and Kendall 1946). Box and Meyer (1986) introduced a pooling technique for unreplicated two-level experiments. We extend this to replicated two-level experiments and compare its performance with the least squares analysis. We show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory. The pooling technique is generally biased and is not recommended for model identification. The least squares analysis performs well as a model identification tool, but the estimators can be inefficient. In such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood. We derive some prop...

Nonparametric Inference Under Biased Sampling from a Finite Population

Abstract: We consider a biased sampling model that has been found useful in incorporating size biases inherent in many types of discovery data. The model postulates that the data are obtained from a finite population by selecting successively without replacement and with probability proportional to some measure of size. Unlike the ppswor scheme in survey sampling, it is assumed here that the size measure is a function of the unknown population values. In this article, we consider maximum likelihood estimation of the finite population parameters under this biased sampling model. We study the large sample behavior of the MLE's and derive a simple, asymptotically efficient approximation to the MLE. The approximate MLE is structurally similar to the Horvitz-Thompson estimator. We show that information about the order in the sample can be used to make inference even when the population size is unknown, which in fact can be estimated. Small sample behavior of the estimators is investigated through a limited simulation study, and the results are used to analyze oil and gas discovery data from the North Sea basin.

On the Behavior of Some Estimators from Probability Plots

Abstract: Probability plots are popular graphical methods used to assess distributional assumptions. Under a location-scale model, the plot tends to lie on a straight line. A common practice in this situation is to fit a line through the plot and use the intercept and slope of the fitted line as estimates of the location and scale parameters. What are the properties of these estimators? Estimators from weighted least squares lines are considered, and their asymptotic, finite-sample, robustness, and optimality properties are discussed. Included among these are the ordinary least squares estimators and estimators from least squares lines fitted after trimming or Winsorizing some of the extreme order statistics.

The Design and Analysis of Experiments

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

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.