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This paper presents a reparameterization of the conventional log-linear regression model. This reparameterization is shown to be more reasonable than the conventional specification. The stochastic assumptions of this reparameterized model are derived from the expected value properties of the dependent variable. Comparison with the conventional method of fitting log-linear models shows the regression intercept and the variance of the regression intercept to be different. A minimum variance unbiased estimate and another consistent estimate of the intercept are derived. [ABSTRACT FROM AUTHOR]

The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared with known numbers of degrees of freedom (different for the two forms). The asymptotic approximations are suitable for moderate sample sizes. The test statistics can be relatively easily computed using the package , or similar MATLAB software. Application of the tests is illustrated on magnetometer and financial data. The asymptotic theory emphasizes the differences between the standard vector linear regression and the functional linear regression. To understand the behavior of the residuals obtained from the functional linear model, the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace, estimation of the optimal subspace, and estimation of the regression kernel. [ABSTRACT FROM AUTHOR]

Bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems. Often, however, the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters. This is for example the situation in subgroup analysis, where the problem is not only to estimate the different components of a parameter vector, but also to identify the parameters that are above, and the others that are below a certain specified cutoff point. We have proposed in this paper Bayes estimates in a very general context that meet this need. These estimates are obtained by matching the first two moments of the histogram of the estimates, and the posterior expectations of the first two moments of the histogram of the parameters, and minimizing, subject to these conditions, the posterior expectation of the Euclidean distance between the estimates and the parameters. Several applications of the main result are provided in the normal and other models. Also, the results are applied to an actual data set. [ABSTRACT FROM AUTHOR]

In this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived. The tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified. Various tests for extra-Poisson and extra-binomial variation are obtained as special cases; the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise. The common occurrence of extra- Poisson and extra-binomial variation has been noted by several authors. However, the Poisson and binomial models remain valid in many instances and, because of their simplicity and appeal, it is of real interest to ascertain when they apply. This paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived, including those by Fisher (1950), Collings and Margolin (1985), and Prentice (1986). It also shows the Pearson statistic to be a score test for overdispersion in a certain situation. [ABSTRACT FROM AUTHOR]

This paper is written with three objectives in mind. First, to point out that the problem of grouping, where a larger number of elements n are combined into m mutually exclusive groups (m ~n) should be recognized as a problem in Integer Programming, and that such recognition can help us in avoiding complete enumeration of stages in grouping from n to n - 1 ... to m, and of alternative possibilities in each stage. Second, to formulate mathematically some simple versions of the relevant Integer Programming Problem, so that the available computer codes can solve it. When the grouping attempts to minimize the within groups sums of squares, the so-called string property is proved to be necessary for the minimum (Lemma 1). It is shown that the string property can be exploited to write the non-linear within group sums of squares as a linear function (Lemma 2). An attempt is made to generalize the string property for the higher dimensional case. Third, to give some numerical examples to clarify the mathematical models and to illustrate the advantages of Integer Programming formulation by comparing with the numerical examples appearing in the literature [8], [13 ]. Zero-one programming where the integer variables can take values of zero or one only appears to be most efficient from the limited experience of the author. The paper is divided into three sections which closely correspond to the three objectives noted above. [ABSTRACT FROM AUTHOR]

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

This paper presents the results of a Monte Carlo study of the accuracy of an approximation to the power of the chi-square goodness of fit test with small but equal expected frequencies. Various combinations of sample size, number of groups, and alpha level are considered, and in most instances the actual power of the test is estimated to be less than the nominal power. The degree of accuracy appears to be more related to the size of the sample than to the size of the expected frequencies. The following rule of thumb is offered for obtaining crude estimates of the actual power from the nominal power for sample sizes from 10 to 50: The actual power of the test equals about eight-tenths of the nominal power. [ABSTRACT FROM AUTHOR]

This paper takes a few steps toward alleviating problems of data analysis that arise from the fact that elementary expressions for density and cumulative distribution functions (c.d.f.'s) for most stable distributions are unknown. In section 2 results of Bergstrom [3] are used to develop numerical approximations for the c.d.f.'s and the inverse functions of the c.d.f.'s of symmetric stable distributions. Tables of the c.d.f.'s and their inverse functions are presented for twelve values of the characteristic exponent. In section 3 the usefulness of the numerical c.d.f.'s and their inverse functions in estimating the parameters of stable distributions and testing linear models involving stable variables is discussed. Finally, section 4 presents a Monte Carlo study of truncated means as estimates of location. In every case but the Gaussian, some truncated mean is shown to have smaller sampling dispersion than the full mean. [ABSTRACT FROM AUTHOR]

Presents the authors' comments on the paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," by Jianqing Fan, Heng Peng, and Tao Huang, published in the September 2005 issue of the "Journal of the American Statistical Association." Congratulations to the authors for their interesting, innovative, and important contribution on microarray normalization; Analysis of the main contributions made by the authors; Suggestions for some possible extensions to the results of the authors; Views on the goal of significance analysis; Appreciation of the paper for its computational simplicity.

Presents the author's comments on the paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," by Jianqing Fan, Heng Peng and Tao Huang, published in the September 2005 issue of the "Journal of the American Statistical Association." Appreciation of the authors for their significant contribution in enlarging the bag of statistical tools available for normalization; Opinion on the normalization strategy described; Importance of the iterative procedure suggested; Views on the focus of the paper from a methodological standpoint; Contexts in which the methodology described may be applicable.

This article presents a response to several commentaries regarding a study which proposed computations for Bayesian p values in composite null models. In the double use of data and conditioning, Michael Evans and Hal S. Stern both discussed what constitutes double use of the data in computing a p value. They take opposite perspectives on this issue. Evans argues that the only way to avoid double use of the data is to separate the data into two independent subsets, using one subset to fit the model and the other to assess the validity of the model. Because the procedures that we recommend do not formally split the data into two parts, Evans suggests that they can be guilty double use of the data. In contrast, Stern does not feel that it is necessary to worry about double use of the data the extent that we worry, he does not feel that even the posterior predictive p value involves double use of the data. These contrasting positions perfectly highlight what we view to be the main motivation for our paper. We feel that it is very important to avoid a double use of the data, but that separating the data into two independent subsets is a too drastic solution that can lose considerable power. We consider each of these issues in turn.

The author here comments on the research paper by Peter J. Huber, related to the minimax aspects of the bounded-influence regression. In his opinion Huber's paper is a major contribution to robust regression, clarifying the relationships among the various methods that have been proposed. The author here put the asymptotic case in the framework of infinitesimal neighborhood models and use the technique of statistician H. Rieder to rederive the formulas presented in the paper and extend them to the full p-variate case. The asymptotic minimax results in the univariate case are seen to be valid for general loss functions rather than only for Huber's testing-related measure. The relation to errors-in-variables models becomes clear. The author remarks that the p-variate extension suggests that more complicated estimates that choose an appropriate coordinate system in the X space before clipping may improve the solution of a particular section in the paper. The author presents all the formulae and calculations needed to prove his point.

Opinion. Presents the author's view on Carroll and colleagues' paper that considers ambient ozone pollution in Harris County, Texas between 1980 and 1993. Some features of the space-time model that require discussion; Comments about styles of space-time modelling.

Presents the authors' views in response to comments on their paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," published in the September 2005 issue of the "Journal of the American Statistical Association." Acknowledgement of the critics for their comments; Account of progress made in the field of statistical techniques for the design and analysis of microarray data; Explanations for the suggestions made by the critics for inclusion of more statistical understanding of various procedures.

Presents the authors' comments on the paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," by Jianqing Fan, Heng Peng and Tao Huang, published in the September 2005 issue of the "Journal of the American Statistical Association." Appreciation of the authors for their significant contribution to the semiparametric estimation theory; Suggestions for a two-way semilinear model for normalization and analysis of cDNA microarray data; Comments on multiway semilinear models; Description of models for location normalization; Opinion on the relationship between the relationship between the multiway semilinear models and the semilinear in-slide model.

In this paper, we highlight properties of Bayesian models in which the prior puts positive mass on all Kullback-Leibler neighborhoods of all densities. These properties are concerned with model choice via the Bayes factor, density estimation and the maximization of expected utility for decision problems. In four illustrations we focus on the Bayes factor and show that whatever models are being compared, the [log(Bayes factor)]/[sample size] converges to a non-random number which has a nice interpretation. A parametric versus semiparametric model comparison provides a fifth illustration. [ABSTRACT FROM AUTHOR]

Comments on a paper which extended the wavelet-based methods to the hierarchical analysis of functional data. Functions generated by the hierarchical model; Implications of the model structure on the potential functional forms.

Comments on a paper which developed a model for clustered functional data through a hierarchical nonparametric mixed-effects structure. Types of data that constitute clustered functional data; Features of the general nonparametric approach; Estimation methods.

We develop a log-linear model for categorical response subject to nonignorable nonresponse. The paper differs from Fay (1986) in its focus on estimation and hypothesis testing in a regression setting, as opposed to imputation in a multivariate setting. We present several new results concerning the existence of solutions on the boundary of the parameter space and the construction of confidence intervals for estimates. We illustrate the method by estimating the proportion of voters preferring Truman in a 1948 preelection poll (Mosteller, Hyman, McCarthy, Marks, and Truman 1949). Results may depend strongly on the model assumed for nonresponse; goodness-of-fit tests are available for comparing alternative models. [ABSTRACT FROM AUTHOR]

The article presents authors' reply comments on various papers related to nonexperimental data and estimation of structural effects. Authors thank researcher John Geweke for his instructive comments and in reply only want to make sure that the relation between Geweke's third paragraph and authors' article is correctly understood. Authors' language did suggest, however, that meaningful statements about correlation with excluded variables would usually involve a very large sufficient set and in the case, authors find Geweke's example instructive. In response to the comment of researcher A.P. Dawid, authors are glad that he likes parts of their, but authors disagree with Dawid's comment on observational studies. Authors feel that selection of observations is not the important new feature in observational studies. The one and only new feature that is important is that the "treatments" or "factors" are not randomized. Selection of observations is not even new, because missing values can make estimates of causal effects inconsistent even when treatments are randomized.

The article comments on the paper by Murray Aitkin, Nan Laird and Brian Francis which presents an analyses of survival of patients in the Stanford Heart Transplantation Program, published in the June 1983 issue of the "Journal of the American Statistical Association." The author congratulates the authors for their careful and thorough analysis of the Stanford heart transplant survival data. There are many statistical issues involved in this area, and also many important medical and ethical questions. The comments are concentrated on the statistical problems, returning only briefly at the end to the current activity regarding larger societal concerns with heart transplantation. Aitkin, Laird, and Francis have made a number of choices in their approach to this reanalysis, and the author would like to comment on several of them. Each transition is examined separately. Aitkin, Laird, and Francis are careful to analyze waiting time for a heart, pretransplant survival, and post-transplant survival separately, before proceeding to comparisons. In particular, this approach enables them to detect a trend in pretransplant survival with calendar time of acceptance, more recent patients being the more healthy. This is an important complication for any assessment of trends in post-transplant survival. However, more could have been done along these lines.

Auditors wishing to estimate the total amount of errors in a set of accounts have tended to use estimation procedures which rely on approximate normality for large sample sizes. Since this reliance is often not well-founded for sample sizes used in auditing practice, efforts have been made to circumvent this difficulty. This paper will briefly describe these efforts and then present a new approach based on the multinomial probability distribution which yields confidence bounds with known confidence levels for all sample sizes. [ABSTRACT FROM AUTHOR]

In regression models, the underlying theory frequently leads to specification of more than one functional form for the conditional mean of the response. The main problem in such cases is whether the differences between the models are sufficiently large relative to the variance of the disturbance term to warrant efforts to discriminate between the models or collect new data in order to discriminate. This paper, after refining the notion of differences between models, suggests several alternative statistics which might be useful in this problem and derives their asymptotic distributions. [ABSTRACT FROM AUTHOR]

There are growing demands to use prior and sample information for parameter estimation of a regression model in order to maintain consistency with underlying theory. To meet such demands, this paper provides an inequality constrained least-squares (ICLS) estimation, specifies an untrancated variance-covariance matrix of the ICLS estimates, and discusses their statistical properties in large-and small-sample cases. Finally, the ICLS and the ordinary least-squares OLS estimates are compared in terms of sample bias, sample mean-square error MSE and sample variance of the estimates by a Monte Carlo study. [ABSTRACT FROM AUTHOR]

The decision-theoretic approach to point estimation involves the choice of an estimate to minimize the expected loss associated with the estimate. The purpose of this paper is to indicate the influence of risk aversion on point estimates for classes of payoff functions including the piecewise linear and quadratic payoff functions. Increased risk aversion results in a point estimate closer to zero for a quadratic pay. off function and a lower estimate with a piecewise linear payoff function, for example. [ABSTRACT FROM AUTHOR]

Matrix differentiation, the procedure of finding partial derivatives of the elements of a matrix function with respect to the elements of the argument matrix, is the subject matter of this paper. The method followed here amounts to linking the differentials of the matrix function and the argument matrix, and then identifying matrices of partial derivatives. The basic assumption made is mathematical independence of the elements of the argument matrix. Matrix functions are divided into two categories: Kronecker matrix products and non-Kronecker (= ordinary) matrix products. Three definitions of partial derivatives matrices are used, to be denoted by D[sub 1], D[sub 2] and D[sub 3] in this abstract. D[sub 2] and D[sub 3] are applied to Kronecker products, D[sub 1] is applied to ordinary products. This is a matter of efficiency only. D[sub 1] is developed first. Transforming matrices into column vectors turns out to be very convenient. D[sub 2] and D[sub 3] are developed then. D[sub 3] is a generalisation of D[sub 1]. [ABSTRACT FROM AUTHOR]

In the early years of the eighteenth century A. De Moivre, N. Bernoulli, and P. R. Montmort found three solutions for the following problem of games of chance: Two players, A and B, play a series of games. In each game, independently of the others, either A wins a counter from B with probability p or B wins a counter from A with probability q (p + q = 1). The series ends if either A wins a total number of a counters from B or B wins a total number of b counters from A. What is the probability that A wins the series in at most n games? Denote this probability by P[sub n](a,b). In this paper simple and elementary proofs are given for the various formulas for P[sub n](a,b). Furthermore, it is shown how these formulas can be applied in the theories of order statistics, random walks, storage, queues, Brownian motion, and dams. [ABSTRACT FROM AUTHOR]

This paper develops a theoretical framework for the unrelated question randomized response technique suggested by Walt R. Simmons. The statistical efficiency of this technique is compared with the Warner technique under situations of both truthful and untruthful responses. Methods of allocating the total sample to each of two subsamples required by the unrelated question approach are developed. Recommendations are made concerning choices of values for those parameters which can be assigned at the discretion of the investigator. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to make the reader aware of the applicability and advantage of a particular mathematical model. The application is typified by an example and the advantage is via confidence intervals; that is, shorter confidence intervals are possible using the model than if one ignores it, providing the applicability is valid. It is also shown that an improved estimate can be obtained through use of the model. Let f(y|mu, sigma) be a normal density with mean mu and variance sigma[sup 2] and let g(mu|lambda, beta) be a normal density with mean lambda and variance beta[sup 2]. A sequence y[sub 1], y[sub 2],..., y[sub n+1] of independent observations from the mixture off and g can be considered as follows: An unobservable mu [sub i] is first drawn from g(mu|lambda, beta) and then y[sub i] which can be observed is drawn from f(y|mu[sub i], sigma). Confidence intervals on mu[sub n+1] are obtained which are based on the observations y[sub 1],..., y[sub n+1] and which are shorter than the standard interval based on y[sub n+1] only for any n. Shorter intervals are obtained for two cases: (i) lambda unknown, sigma, beta known; (ii) only sigma/beta = c known. [ABSTRACT FROM AUTHOR]

In a linear regression model, when errors are autocorrelated, several asymptotically efficient estimators of parameters have been suggested in the literature. In this paper we study their small sample efficiency using Monte Carlo methods. While none of these estimators turns out to be distinctly superior to the others over the entire range of parameters, there is a definite gain in efficiency to be had from using some two-stage procedure in the presence of moderate high levels of serial correlation in the residuals and very little loss from using such methods when the true rho is small. Where computational costs are a consideration a mixed strategy of switching to a second stage only if the estimated rho is higher than some critical value is suggested and is shown to perform quite well over the whole parameter range. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to examine the mean square error criterion for rejecting or adopting restrictions on the parameter space in a regression model, and to develop a uniformly most powerful testing procedure for the criterion. We present a tabulation of critical points for the test for one restriction and selected points of the power function. The mean square error criterion suggests a framework for thinking about the problem of multicollinearity in a linear model. To this end we present some examples to illustrate the linkage of the mean square error criterion with multicollinearity. [ABSTRACT FROM AUTHOR]

The sequence of births occurring in a closed female population subject to constant schedules of fertility and mortality can be represented as [Multiple line equation(s) cannot be represented in ASCII text] where only one coefficient (Q[sub 0]) and one exponent (r[sub 0]) are real. Convergence to a stable population occurs a few years after all complex components in B(t) have become negligible relative to the one real component. The rate of convergence of B(t) to a real exponential function depends on the age schedules of fertility and mortality, and on the initial age distribution. Methods of determining the coefficients and exponents of the terms of B(t) by use of a large computer are described in this paper, and various significant characteristics of the terms are given. Methods are described for visualizing how convergence would occur in a particular human population on the basis of recorded features of its fertility, mortality, and age composition. [ABSTRACT FROM AUTHOR]

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]

This paper presents a method of constructing conservative joint confidence regions for the parameters of a linear model and the volumes of these regions are compared with the volume of an exact confidence region. Confidence regions on the entire surface are obtained from the confidence region on the parameters. The procedures are illustrated for the case of a simple linear model. [ABSTRACT FROM AUTHOR]

This paper carries on work in [2] and [4] on the asymptotic effects of small specification error in simultaneous equation estimation. The specification errors considered are inherent in the approximate nature of econometric models. It is shown that for any parameter and small enough specification error, the probability limits of two-stage least squares and limited-information maximum-likelihood, while different, lie on the same side of the true parameter value, the difference between them being of the second order of smalls relative to the effects of the specification error on either one of them. A method of consistently estimating the sign of the difference of the effects of specification error on the two estimators is given and a procedure suggested for choosing an estimator to reduce those effects. Two relatively simple examples are worked out. [ABSTRACT FROM AUTHOR]

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done. [ABSTRACT FROM AUTHOR]

In applied problems one often wishes to compare the mortality experience of two or more groups of individuals who are known not to be comparable with respect to a covariable. This paper presents an approach to this problem by assuming that the force of mortality for each individual is a function of the covariable. Extension to the case where more than one covariable is present is indicated. It is also suggested that the present method is adaptable to an actuarial type analysis. [ABSTRACT FROM AUTHOR]

The Revenue Act of 1954 permitted entrepreneurs for the first time to make use of the double declining balance (DDB) and sum of the year's digits (SYD) methods of depreciation in place of the customary straight line method (SL). The tax advantages from using such methods are well known.(n1) In spite of these advantages, however, the accelerated methods in many cases appear to have been adopted only slowly over the years. Clearly any attempt to determine the effect on investment of such provisions must rely on knowledge of the extent of their use. Unfortunately there is no direct information available, nor do estimates exist, for the two-digit manufacturing industries on the fraction of investment in each year since 1954 written off by accelerated methods. In this paper an attempt is made simultaneously to estimate such figures on an annual basis and to fit a learning curve to them.(n2) [ABSTRACT FROM AUTHOR]

We derive Neyman's locally asymptotically most powerful test criterion to test a linear hypothesis, and in particular, obtain such criteria to test linear hypotheses in binomial and multinomial experiments. We also discuss testing log-linear hypotheses in the parameters of a multinomial experiment, and give a simple criterion for testing the hypothesis of no second order interaction in a p x q x r (p, q, r, > 2) contingency table. Asymptotic tests of the hypotheses mentioned above are available in the literature, but the tests proposed in this paper are simple and are based on explicit optimality consideration. [ABSTRACT FROM AUTHOR]

In this paper confidence bands are given for simple linear model. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval. [ABSTRACT FROM AUTHOR]

In this paper we review the derivation of the predictive density function for the normal multiple regression model, state and prove a general theorem on optimal point prediction, and show how the predictive density can be employed in the analysis of an illustrative investment problem. Then we derive the predictive density function for the multivariate normal regression model and indicate how it can be used in the analysis of several problems. [ABSTRACT FROM AUTHOR]

The multivariate acceptance sampling problem is discussed and a solution for a particular sub-class of the general problem developed. This is where the related quality variables have a multivariate normal distribution with known covariance matrix, and where the specification region may be set in the form of a general ellipsoid. Single sampling acceptance procedures by variables for fraction defective are developed. Methods are given for determining the sample size n and acceptance number c so as to achieve desired operating characteristics. [ABSTRACT FROM AUTHOR]

Presents the author's comments on the paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," by Jianqing Fan, Heng Peng, and Tao Huang, published in the September 2005 issue of the "Journal of the American Statistical Association." Opinion that the paper presents an interesting method for normalizing data from cDNA microarrays; Criticism of the Q-Q-plot for being unconvincing; Suggestions for carrying out studies to determine the practical utility of the proposed methods.

The article presents the author's comments on the paper "Model Selection and Semiparametric Interference for Bivariate Failure-Time Data," by Weijing Wang and Martin T. Wells. Wang and Wells have presented an interesting method for selecting the Archimedean copula (AC) model for bivariate failure time data in the presence of right cursoring. The intent of these comments is to call attention to the issue of whether one should standardize statistics in model selection procedures when nuisance parameters are estimated. The model selection procedure proposed by Wang and Wells is but one example in which this issue arises. This situation occurs in other statistical models, such as in parametric model discrimination with right-censored data where the nuisance parameters are the parametric model parameters and the discrimination statistics are based on generalized residuals. The question of whether or not to standardize the statistics before using them for selecting the model, which is an analogous problem to that encountered by Wang and Wells, arises. It is thus of prime interest to further study this aspect more rigorously and substantively so that a definitive resolution on whether or not to standardize can be made.

The article presents a comment on the research paper by Peter J. Huber, related to the minimax aspects of the bounded-influence regression. According to authors the focus the paper by Huber is indicated in the first sentence of Huber's introduction, that is, "how to cope with the problems caused by influential points in multiple regression. The discussion on this point by various statisticians seems to shed additional light on the conflict between decision theoretic and data analytic points of view mentioned briefly by Huber. Methods of accommodation are designed to allow for the possibility of contamination through suitable choice of both the model and the method of estimation. They rely on estimators that can tolerate a small amount of contamination, often of a specific type. The distinction between accommodation and identification is often overlooked, since a method of accommodation may produce statistical by-products that are apparently useful for identification. Although bounded-influence regression is a method of accommodation, some statisticians indicate that the ability to identify cases based on the resulting weights may be its most useful aspect.

In this article authors comment on the paper entitled "Minimax Aspects of Bounded-Influence Regression," by Peter J. Huber. Authors remark that they would like to thanks Huber for a very stimulating analysis of their results. They were surprised by Huber's remark, both at the end and beginning of the research paper, that bounded-influence regression is not concerned with gross errors in the explanatory variables. According to them Huber's set up is not so symmetric. His minimax framework leads to a specific gross-error distribution for y, but assumes that the x's are error-free. Huber's main thesis is that leverage groups should be treated differently from individual leverage points, because it is unlikely that nature would concentrates the gross errors on a particular region of the x space. Professor Huber's theoretical results apply only to one parameter, through the-origin regression, and it is not clear how they would extend to multivariate regression. The author also presents their ideas for the solution of the problems raised by Huber in his paper.

The article comments on the paper by Murray Aitkin, Nan Laird and Brian Francis which presents an analyses of survival of patients in the Stanford Heart Transplantation Program, published in the June 1983 issue of the "Journal of the American Statistical Association." The author wishes to congratulate Aitkin, Laird and Francis and to elaborate on some of their cautionary remarks, such as "the apparent benefit of transplant is dwarfed by the magnitude of our uncertainty." The author shall discuss the weakness of the evidence, and he shall use the authors' models to highlight this weakness. An ideal experiment to determine whether transplantation is beneficial would be to regard a patient as eligible for study at the time a suitably matched heart became available and then to randomly allocate that patient either to transplantation or to conservative management. A valid comparison of postrandomization survival could be made, even without covariate adjustment. However, regression methods or stratified analyses could be used to adjust for treatment imbalances on known covariates, such as waiting time since entry into the program. Unfortunately, the present data are not protected by randomization. A surgeon might choose to give the heart to that one of a pair of potential recipients who had waited longer. But waiting time is a dominant covariate: the longer you wait, the better is your prognosis on conservative management.

The article presents the author's response to researcher Arnold Zellner's comments on his paper related to Systems Dynamics National Model. Zellner suggests that systems dynamic modeling might benefit from a greater emphasis on statistical techniques. If statistical methods were answering all economic questions, then there would be no need for developing alternative approaches. Neither the theoretical nor the empirical work in economics seems to be settling the economic debates. Zellner wonders why the author associates system dynamics with the case-study approach. The author believes that the case-study approach has had more impact on the actual management of corporations than other educational approaches. Zellner identified several areas in which he said the System Dynamics National Model is based on essentially the same principles and procedures as econometric modeling. Zellner suggests, correctly, that the forecasting of economic variables has been adopted as a primary objective of econometric models.

The Jorgenson and Lovell axiomatizations of the process of seasonal adjustment are contrasted in this paper. It is argued that dummy variables rather than data subject to prior seasonal adjustment should be employed when time series are utilized in estimating the parameters of a linear economic model. [ABSTRACT FROM AUTHOR]

The article offers comment of author on the study on application to causal inference in longitudinal studies which features existing causal approaches into a multiple imputation framework. Topics include approaches and methods include inverse probability-of-treatment weighting, observations are re-weighted to mimic a setting in which covariates are balanced; and concludes that data from covariate-rich observational studies can be useful where randomized trials are unethical or infeasible.