Summarizes information scattered in the technical literature on a subject too new to be included in most textbooks, but which is of interest to statisticians, and those who use statistics in science and education, at an advanced undergraduate or higher level. Overviews recent research on constructin

Confidence intervals on variance components

2. Confidence Intervals on Variance Components

The R e s t r i c t e d E M A l g o r i t h m f o r M a x i m u m L i k e l i h o o d E s t i m a t i o n U n d e r Linear R e s t r i c t i o n s on the Parameters Author(s): Dong K . K i m and J e r e m y M . G . T a y l o r Source: Journal of the American Statistical Association, V o l . 90, No. 430 (Tun., 1995), pp. 708¬ Published b y : American Statistical Association Stable U R L : http://www.jstor.org/stable/2291083 Accessed: 25/05/2011 17:26 Y o u r use of the J S T O R archive indicates your acceptance of J S T O R ' s Terms and Conditions of U s e , available at http://www.jstor.org/page/info/about/policies/terms.jsp. J S T O R ' s Terms and Conditions of U s e provides, i n part, that unless y o u have obtained prior permission, y o u may not download an entire issue of a journal or multiple copies of articles, and y o u may use content i n the J S T O R archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=astata. E a c h copy of any part of a J S T O R transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. J S T O R is a not-for-profit service that helps scholars, researchers, and students discover, use, and b u i l d upon a wide range of content i n a trusted digital archive. W e use information technology and tools to increase productivity and facilitate new forms of scholarship. F o r more information about J S T O R , please contact support@jstor.org. iPv! H 1 American Statistical Association is collaborating with J S T O R to digitize, preserve and extend access to Journal of the American Statistical Association. m STOR http://www.jstor.org

The Restricted EM Algorithm for Maximum Likelihood Estimation Under Linear Restrictions on the Parameters

Christensen, R. (2002), Plane Answers to Complex Questions: The Theory of Linear Models (3rd ed.), New York: Springer-Verlag. Crocker, D. C. (1980), Review of Linear Regression Analysis, by G. A. F. Seber, Technometrics, 22, 130. Datta, B. N. (1995), Numerical Linear Algebra and Applications, Paci c Grove, CA: Brooks/Cole. Draper, N. R. (2002), “Applied Regression Analysis Bibliography Update 2000–2001,” Communications in Statistics: Theory and Methods, 2051– 2075. Golub, G. H., and Van Loan, C. F. (1996), Matrix Computations (3rd ed.), Baltimore, MD: Johns Hopkins University Press. Graybill, F. A. (2000), Theory and Application of the Linear Model, Paci c Grove, CA: Brooks/Cole. Hocking, R. R. (2003), Methods and Applications of Linear Models: Regression and the Analysis of Variance (2nd ed.), New York: Wiley. Porat, B. (1993), Digital Processing of Random Signals, Englewood Cliffs, NJ: Prentice-Hall. Ravishanker, N., and Dey, D. K. (2002), A First Course in Linear Model Theory, Boca Raton, FL: Chapman and Hall/CRC. White, H. (1984), Asymptotic Theory for Econometricians, Orlando, FL: Academic Press.

Components of Variance

To the Editor. —The article by Dr Cappelleri and colleagues 1 suggests that larger trials and meta-analyses of smaller medical intervention studies typically yield the same result. Although assumptions in conventional statistical power analysis predict that large trials gauging a population effect yield parallel results to aggregated smaller trials, questions of treatment integrity yield a different prediction. For example, larger studies may involve more personnel who are less likely to be trained as scientists or who may be less concerned with the scientific integrity of the trial. The hypothesis that larger studies should produce smaller effects is best tested by examining treatment magnitude as a continuous function of the sample size, an analysis that Cappelleri et al did not report. Recent meta-analyses of behavioral intervention studies examining health-risk behaviors provide another opportunity to test this hypothesis. Our search of MEDLINE (1966 through December 1996) and other databases (eg, PsychLIT, January 1974 through September

Large trials vs meta-analysis of smaller trials. authors' reply

The variability among data may have quite complex structure and the splitting of variation into its individual components is important in many areas of applications. In particular, the study of variation through a class of linear models known as random and mixed models is a central topic in statistics with wide ramifications in both theory and applications. Sometimes these models are called components of variance models since the interest in the model lies in investigating the variances of the effects of factor levels which are assumed to be randomly selected from a large population of levels. These variances are also known as variance components since the total variance can be expressed as the sum of these variances and the error variance. Knowledge of the variance components, i.e., the information on the relative importance and magnitude of the sources of variability in the data is of critical importance in many problems since the isolation of the total variance into the individual components of variance would result in the physical elimination of the sources of variability in question.

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A bibliography on variance components an introduction and an update: 1984-2002

Analysis of Variance Model, Effects of Departures from Assumptions Underlying.

In many engineering and quality control studies, such as in lot-to-lot acceptance inspection, in exploratory chemical and physical research, and in Monte Carlo computer simulation, the sample size is not fixed in advance, but is determined in part by the results of the sampling process. A study of this type is called sequential and was first proposed by Wald (1947). Sequential tests of hypotheses are now widely recognized as the most efficient means for comparing treatment effects. It has been estimated that in testing hypotheses sequential sampling commonly reduces the required sample size on the average to approximately 50 percent of that required by a single sampling plan of comparable discriminating power. For instance, suppose the effects of two treatments differ at least by a given amount; and the risks of type I and type II errors are fixed by α and β, respectively. In sequential trials, instead of repeating the experiment at a given number of times, we check after each trial whether we have by now sufficient information to reach a conclusion, i.e., we carry out exactly as many trials as necessary to determine with risks α and β which of the two treatments is superior to the other. The advantages of this procedure are obvious when the single experiments are costly and time consuming; but it is also valuable when the number of observations is limited. For example, in many quality engineering experiments, when a group of specimens are prepared and tested, the cost of preparation, testing and measurement may be so great that the use of a single sampling with a predetermined sample size may be almost prohibitive. On the basis of the results of each of the individual outcomes of one particular experiment, it is determined whether the trial or sequence of trials be continued or a decision can be reached. A general description of sequential sampling plans can be found in Wald (1947) and in many other texts such as Bowker and Lieberman (1972), Doty (1996), Duncan (1989), Ghosh (1970), Ghosh and Sen (1991), Grant and Leavenworth (1980), Guenther (1978), Hald (1981), McWilliams (1989), Mittag and Rinne (1993), Montgomery (2001), Sarkadi and Vincze (1974), and Wetherill and Glazebrook (1986). The Visual BASIC program given here generates truncated Wald’s sampling plan for specified values of the parameters characterising the plan. The program also computes exact operating characteristic (OC) and the average sample size (ASN) for specified values of the lot fraction defective.

Anwer Khurshid

Papers

A bibliography on variance components an introduction and an update: 1984-2002

Analysis of Variance Model, Effects of Departures from Assumptions Underlying.

A visual basic program to determine Wald's sequential sampling plan

International forum a visual basic program to determine wald's sequential sampling plan