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This article reviews Albert Einstein's first published paper, submitted for publication in 1900. At that time, Einstein was 21 and a recent college graduate. His paper uses modeling and least squares to analyze data in support of a scientific proposition. Einstein is shown to be well trained, for his day, in using statistics as a tool in his scientific research. This paper also shows his ability to make trivial arithmetic mistakes and some clumsiness in data recording. A major aim of this article is to help provide a better appreciation of Einstein as an active user of statistical arguments in this and other of his important publications. [ABSTRACT FROM AUTHOR]

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p= O( n1 / 2 / log n) and the asymptotic normality for p= o( n1 / 2) are established, where p is the dimension of the predictors and n is sample size. Such asymptotic results improve the rate p= o( n1 / 3) in many existing contexts of semiparametric modeling. In addition, we propose a modified BIC-type criterion to estimate the structural dimension of the central subspace. Its consistency is established when p= o( n1 / 2). Extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The approach can apply readily to many other statistical contexts. Various new penalty functions are proposed. The hard-thresholding and soft-thresholding estimators of Donoho and Johnstone are specific members of nonlinear regularized wavelet estimators. They correspond to the lower and upper envelopes of a class of the penalized least squares estimators. Necessary conditions for penalty functions are given for regularized estimators to possess thresholding properties. Oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions. The sampling properties of nonlinear regularized wavelet estimators are established and are shown to be adaptively minimax. To efficiently solve penalized least squares problems, nonlinear regularized Sobolev interpolators (NRSI) are proposed as initial estimators, which are shown to have good sampling properties. The NRSI is further ameliorated by regularized one-step estimators, which are the one-step estimators of the penalized least squares problems using the NRSI as initial estimators. The graduated nonconvexity algorithm is also introduced to handle penalized least squares problems. They newly introduced approaches are illustrated by a few numerical examples. [ABSTRACT FROM AUTHOR]

This article presents a reply to comments on a paper which proposed an alternative procedure for the estimation of panel-data econometric models with predetermined but not strictly exogenous statistical instruments. In the paper, a specification test for strict exogeneity based on comparison of the fixed-effects and first-difference estimators and a test for individual effects based on comparison of the two-stage least squares and first-difference estimators were proposed. In each case, the covariance matrix of the difference of the estimators were constructed by using the sample residuals. Although under ideal circumstances it is true that the tests the commentators suggested would be both more powerful and simpler than the ones suggested in the paper, there are practical reasons to prefer the tests proposed by the paper. First, since the estimator they propose uses all predetermined instruments available at time t, including those dated all the way back to the first observation in the panel, each of the tests that they propose requires that there are no missing observations for any individual in the sample. Second, even if there were no missing observations, the additional orthogonality conditions they suggest may generate substantial bias in parameter estimates obtained from finite samples. Finally, the tests are based on estimators that are easy to compute using existing econometric software.

Comments on an article by A. C. Harvey and P. H. J. Todd titled "Forecasting Economic Time Series With Structural and Box-Jenkins Models: A Case Study," which appeared in the October 1983 issue of the "Journal of Business & Economic Statistics." Information on the variance components model introduced by Harvey and Todd; Description of the pile-up effect in maximum likelihood estimation of moving average models; Difference between the model and Box-Jenkins forecasting.

Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank) = a − b log(Size), and take b as an estimate of the Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this method. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and propose that, if one wants to use an OLS regression, one should use the Rank −1 / 2, and run log(Rank − 1 / 2) = a − b log(Size). The shift of 1 / 2 is optimal, and reduces the bias to a leading order. The standard error on the Pareto exponent ζ is not the OLS standard error, but is asymptotically (2 / n)1 / 2 ζ. Numerical results demonstrate the advantage of the proposed approach over the standard OLS estimation procedures and indicate that it performs well under dependent heavy-tailed processes exhibiting deviations from power laws. The estimation procedures considered are illustrated using an empirical application to Zipf's law for the United States city size distribution. [ABSTRACT FROM AUTHOR]

In multi-criteria decision analysis, the overall performance of decision alternatives is evaluated with respect to several, generally conflicting decision criteria. One approach to perform the multi-criteria decision analysis is to use ratio-scale pairwise comparisons concerning the performance of decision alternatives and the importance of decision criteria. In this approach, a classical problem has been the phenomenon of rank reversals. In particular, when a new decision alternative is added to a decision problem, and while the assessments concerning the original decision alternatives remain unchanged, the new alternative may cause rank reversals between the utility estimates of the original decision alternatives. This paper studies the connections between rank reversals and the potential inconsistency of the utility assessments in the case of ratio-scale pairwise comparisons data. The analysis was carried out by recently developed statistical modelling techniques so that the inconsistency of the assessments was measured according to statistical estimation theory. Several type of decision problems were analysed and the results showed that rank reversals caused by inconsistency are natural and acceptable. On the other hand, rank reversals caused by the traditional arithmetic-mean aggregation rule are not in line with the ratio-scale measurement of utilities, whereas geometric-mean aggregation does not cause undesired rank reversals. [ABSTRACT FROM AUTHOR]

In industry, the run order of experiments is often randomized, but this does not guarantee that all factor levels are reset from one run to the next. When this happens and the levels of factors are the same in successive runs, the assumption of independent observations from run to run may be violated or incorrect. In this case, an ordinary least squares analysis can produce biased estimates of the coefficients in the model, which leads to erroneous test results and inferences. In this paper we describe how not resetting the levels of one or more factors in successive runs can result in less precision in parameter estimates and a larger than expected prediction variance. We present formulas for the prediction variance and the expected prediction variance for this situation. These quantities are important because they allow us to compare the prediction properties of experiments that are completely randomized to experiments where the levels of one or more factors are not reset. We give an analysis of an industrial experiment of this type and recommendations for carrying out factorial experiments where the levels of one or more factors are not reset. [ABSTRACT FROM AUTHOR]

Comments on a paper by Christian P. Robert, J.T. Gene Hwang, and William E. Strawderman published in the "Journal of the American Statistical Association" on the Pitman closeness criterion (PCC). Incompatibility of the criterion with the usual theoretic analysis; Dependency of the criterion's value on the joint distribution of two competing estimators; Role of PCC in decision theory.

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.

Least squares estimation and quadratic openloop optimal control share both algebra and intuition; this paper explores the duality to develop the parallels in each. Estimation results suggest control analogs to correlation measures, significance tests, distributed lags and problems of multicollinearity, tests of compatability between restrictions and data, and a version of the Kalman filter that is sometimes computationally expedient. Conversely, the control literature provides methods of incorporating certain types of inequality restrictions and a development of recursive estimation based on the Kalman filter. A by-product is a method of solving control problems using least squares computer programs. [ABSTRACT FROM AUTHOR]

The problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators that alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators. A numerical study of these estimators is also discussed. [ABSTRACT FROM AUTHOR]

Viewing truth and beauty as a compromise also is appealing because today many data analysts prefer to use an adjustable Ockham's straight or electric razor, that is, digital computer. Conceptualization of the bump or outlier detection problem in terms of the odds that each bump would be present in a sample of infinite size has certain mathematical advantages. Most scientists also feel that it is usually not enough to demonstrate simple existence, but instead they must also explain the nature of the beast causing a bump. For this reason, before directly commenting on Good and Gaskins's excellent paper, it seems appropriate to illustrate the process of associating apparent anomalies with explanatory factors. Field trials with the primitive form of roughness penalty described before indicated that the scientific the expansion was terminated when the first term failed to satisfy the term-inclusion rule.

In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural coefficients and forecasts of endogenous variables, according to parametric and nonparametric measures of bias, dispersion, and dispersion including bias, do not change for any of the four error distributions. Further, least squares is the most biased and maintains the Gauss-Markov property of minimum variance. The large bias of least squares, however, more than offsets the small variance, so that least squares exhibits the largest mean squares of the four estimators. Maximum likelihood is least biased and most efficient, except as an estimator of structural coefficients on the parametric measure of mean squared error. [ABSTRACT FROM AUTHOR]

The papers is concerned primarily with two fundamental issues. The use of multicollinearity measures to determine if the data are sufficiently weak to justify ridge regression, and the selection of a normalization or particular linear transformation to which ridge regression is applied. There are several specific points that the researchers will try to clarify. It is far from certain what measure of data strength is most appropriate for a choice between least squares and ridge regression. Many authors focus on the mean squared errors of the parameter estimates, but there is still the problem of deciding which parameters should receive the most attention. One scalar answer that appeals to these statisticians is mean squared prediction error using the out-of sample values of the variables for which the model will be employed. Those researchers whose objectives cannot be put in a forecasting context may want to look elsewhere for evidence of unsatisfactory estimates. Multicollinearity can cause or explain imprecise estimates but, since it is not the only cause or explanation, measures of multicollinearity are an inadequate gauge of precision. The same cautions that apply to variance inflation factors also apply to Thisted's multicollinearity indexes.

This article is an expository paper to demonstrate the usefulness of Pearson curves in density estimation especially for those unaware of this early development in statistics. It is shown how to fit the curves and how very good approximate percentage points can be obtained for intractable distributions when the first four moments (or three moments and one endpoint) are known exactly (not estimated from sample data). The effectiveness of this method in density estimation is illustrated in three somewhat disparate contexts and reference is given to others. In general, the Pearson curves give an excellent approximation to the long tail of a distribution, the tail-most often needed in practical work. [ABSTRACT FROM AUTHOR]

Loglinear models are classified as direct or indirect depending on whether the maximum likelihood estimates of cell values are explicit functions of the sufficient statistics or not. For saturated (hence, direct) models, Goodman (1970) and Bishop, Fienberg, and Holland (1975) used the delta method to calculate the asymptotic variances of various u terms in the loglinear models. In the present paper, this approach has been generalized to direct unsaturated hierarchical loglinear models. General rules for determining closed form expressions for asymptotic variances in such situations are obtained; bounds for the asymptotic variances of a terms in indirect models are considered; and these rules are compared with other methods of producing asymptotic variances. [ABSTRACT FROM AUTHOR]

Among the unequal probability sampling without replacement procedures applicable for arbitrary sample size, those of Goodman and Kish and of Sampford are relatively simple to operate besides satisfying the criterion that the inclusion probability of each population unit is proportional to its size. Considering the Horvitz-Thompson estimator for estimating the population total, we show in this paper that Sampford's procedure is more efficient than the Goodman and Kish procedure. Our result is a generalization of Rao's result wherein he compared Durbin's procedure with that of Goodman and Kish. [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 study of cointegration in large systems requires a reduction of their dimensionality. To achieve this, we propose to obtain the I(1) common factors in every subsystem and then analyze cointegration among them. In this article, a new way of estimating common long-memory components of a cointegrated system is proposed. The identification of these I(1) common factors is achieved by imposing that they be linear combinations of the original variables Xt, and that the error-correction terms do not cause the common factors at low frequencies. Estimation is done from a fully specified error-correction model, which makes it possible to test hypotheses on the common factors using standard chi-squared tests. Several empirical examples illustrate the procedure. [ABSTRACT FROM AUTHOR]

This article focuses on a paper which proposed an alternative procedure for the estimation of panel-data econometric models with predetermined but not strictly exogenous statistical instruments. It considers the estimation under sequential moment restrictions and calculates the Fisher information. The bound does not depend on the location of the mass points, it only involves various conditional moments. Hence the bound can be shown to apply to a more general class of distributions. In addition, the article shows that there is a sequence of feasible generalized method of moment estimators with asymptotic precision matrices that provide arbitrarily close approximations to the information bound.

Multiple linear regression techniques that are resistant to changes in a small fraction of the data have been proposed and investigated in recent literature. This paper develops a regression procedure based on M-estimators that is adaptive in nature. That is, after a preliminary fit, an attempt is made to assess the nature of the distribution of the errors. Based on this assessment, an appropriate M-estimator is then chosen and the final multiple linear regression equation is computed. The rule's resistance to a few outlying data points is demonstrated with a classical data set on the stack loss of a plant converting ammonia to nitric acid. Thc adaptive procedure's excellent performance characteristics over a broad class of distributions is shown in a Monte Carlo study. [ABSTRACT FROM AUTHOR]

The article presents the author's comments on the paper "Nonparametric Analysis of Randomized Experiments With Missing Covariate and Outcome Data," by Joel L. Horowitz and Charles F. Manski. The problem of missing data is one faced by many analysts. Several approaches for analyzing incomplete data have been and continue to be, developed from various perspectives. All of these approaches, however, make some assumptions about the missing-data mechanism. The most prevalent assumption is that of missing at random (MAR), that is, adjusting for the set of all observed variables, the unobserved residuals are random. If one is not willing to make this MAR assumption, then an explicit modeling of the missing-data mechanism is required through postulating either a selection mechanism or a pattern mixture model. Both these models are empirically unverifiable given only the observed data. These are tough choices an analyst has to make when drawing inferences from incomplete data. Horowitz and Manski propose an alternative, that in the presence of missing data and to avoid making any assumption about the missing-data mechanism, the traditional notion of a point estimate should be abandoned.

Statisticians like Good and Gaskins have given to bump-hunters an inventive approach that uses the special structure of their maximum penalized-likelihood, MPL procedure. This article demonstrates the usefulness of nonparametric density-estimation techniques for unearthing features such as modes in the body of the data without concern for possible tail pathologies. With medical data the estimation and comparison of modes has proved more revealing than simpler tests. For example, the discovery of bimodal bivariate density functions in lipid data has led to clarification of the roles of certain cardiovascular risk factors. Investigators interested in the statistical significance of modes should also find Good and Gaskins's paper useful. The important algorithms presented in this paper deal with optimization of the smoothness or variance-bias trade-off of the density estimate and with removal of potential bumps by surgery.

Comments on a paper by Christian P. Robert, J.T. Gene Hwang, and William E. Strawderman published in the "Journal of the American Statistical Association" on the Pitman closeness criterion. Usefulness of an estimator as a summary of data for purposes of statistical inference; Examination of the performance of an estimator; Need to consider the joint distribution of two estimators.

Responds to the comments on the authors' paper on Pitman's closeness criterion, published in the March 1993 issue of the "Journal of American Statistical Association." Discussion on the central purpose of decision theory; Relation of Pitman closeness with decision theory; Information on the transitivity of the Pitman criterion.

Comments on a paper by Christian P. Robert, J.T. Gene Hwang, and William E. Strawderman published in the "Journal of the American Statistical Association" on the Pitman closeness criterion. Information on the possible intransitivities of the Pitman criterion; Dependence of the criterion on the joint distribution of the two estimators; Comparison of estimators without measuring the closeness of an estimator to the parameter.

Comments on a paper by Christian P. Robert, J.T. Gene Hwang, and William E. Strawderman published in the "Journal of the American Statistical Association" on the Pitman closeness criterion (PCC). Dependency of the average loss criterion on the choice of the loss function; Focus on PCC as an intransitive criterion; Need for exploring statistical properties of the estimator.

Regression analysis, like all statistical procedures, depends on assumptions for its successful implementation. Most data analysts are well aware of the requirements of correct model specification, constant predictor variables, normally distributed errors, and so forth, that underlie classical least squares estimation and inference techniques. Bayesian approaches to a regression analysis incorporate assumptions like these and assumptions about the distribution of the regression coefficients. It is primarily to the debate over assumptions and their reasonableness that Statiscians Gary Smith and Frank Campbell's paper contributes. Two key points on which Smith and Campbell focus throughout much of their article are the necessity, even desirability, of standardizing the predictor variables and the value of using regression estimators that are invariant to linear transformations of the predictor variables. If one's concern is estimating specific parameters or linear combinations of parameters, then transformations to other parametric functions in order to reduce variances are of no avail.

In this paper we present the asymptotically best linear unbiased estimators for the location and scale parameters of the logistic distribution based on samples where there may be Type 2 censoring in the tails, Given the amount of censoring, the weights of the estimators can be expressed in simple closed forms, Comparisons of these with the best linear unbiased estimators and the Cramer-Rao lower bounds demonstrate that they have good efficiency even for small samples. [ABSTRACT FROM AUTHOR]

Given a family of rules for the three-decision testing problems of locating a scalar parameter theta relative to theta[sub 0], with decisions theta < theta[sub 0], theta = theta[sub 0] and theta > theta[sub 0], and given a sample x, the set S(x) = {theta[sub 0]: decide theta = theta[sub 0]} (usually an interval) is an intuitively appealing set estimate of theta. This paper considers the optimality of S(x) for the case in which the testing rules are Bayes. The main result is that when the losses for the testing problems have a particular structure, S(x) is minimum Bayes risk with respect to a loss function which is the integral (in a certain sense) of the loss functions for testing. [ABSTRACT FROM AUTHOR]

Recently there has been renewed interest in the nonparametric estimate of the innovation variance of a stationary time series. Empirical evidence has shown that some smoothing of the periodogram improves the estimate, This paper attempts to clarify the smoothing question and extends the results to the estimation of the innovation generalized variance of a multivariate stationary time series, [ABSTRACT FROM AUTHOR]

The authors offer a response to the commentaries made on their article on statistical estimation and privacy. They discuss the issues raised by the discussants including the advantages and disadvantages of local notions of privacy as compared to classical differential and approximate differential privacy, the issue of interactivity, and the importance of local differential privacy. The goal of statistical inference is also mentioned.

Electricity load forecasts are an integral part of many decision-making processes in the electricity market. However, most literature on electricity load forecasting concentrates on deterministic forecasts, neglecting possibly important information about uncertainty. A more complete picture of future demand can be obtained by using distributional forecasts, allowing for more efficient decision-making. A predictive density can be fully characterized by tail measures such as quantiles and expectiles. Furthermore, interest often lies in the accurate estimation of tail events rather than in the mean or median. We propose a new methodology to obtain probabilistic forecasts of electricity load that is based on functional data analysis of generalized quantile curves. The core of the methodology is dimension reduction based on functional principal components of tail curves with dependence structure. The approach has several advantages, such as flexible inclusion of explanatory variables like meteorological forecasts and no distributional assumptions. The methodology is applied to load data from a transmission system operator (TSO) and a balancing unit in Germany. Our forecast method is evaluated against other models including the TSO forecast model. It outperforms them in terms of mean absolute percentage error and mean squared error. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Weighting methods that adjust for observed covariates, such as inverse probability weighting, are widely used for causal inference and estimation with incomplete outcome data. Part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes, or a variety of population means for several variables. However, this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings. To address these limitations, this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher. This method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions, such as variances and correlations and also, for example, the quantiles of interactions of pairs and triples of observed covariates, thus, balancing entire two- and three-way marginals. Since the weighting method is based on a well-defined convex optimization problem, duality theory provides insight into the behavior of the variance of the optimal weights in relation to the level of covariate balance adjustment, answering the question, how much does tightening a balance constraint increases the variance of the weights? Also, the weighting method runs in polynomial time so relatively large datasets can be handled quickly. An implementation of the method is provided in the new package sbw for R. This article shows some theoretical properties of the resulting weights and illustrates their use by analyzing both a dataset from the 2010 Chilean earthquake and a simulated example. [ABSTRACT FROM PUBLISHER]

Comments on the characterization and risk analysis of penalized least square estimators in an article by leading mathematician Anestis Antoniadis regarding non-parametric wavelet regression. Characterization of penalized least square estimators; Comment on closely related work in the statistical signal and image processing literature; Risk analysis of penalized least squares.

Comments on a paper by Christian P. Robert, J.T. Gene Hwang, and William E. Strawderman published in the "Journal of the American Statistical Association" on the Pitman closeness criterion. Information on the inherent flaw of the criterion; Focus on the joint distribution of the estimators; Basis of evaluation of a statistical procedure.

The article presents the authors' response to the paper written by David W. Scott. Comments on authors' article by Scott, has helped authors' to make substantial changes in their viewpoint since the original version of the article was written. The response is divided into three parts — the first concerning the negative correlation between minimizers of the considered bandwidth selectors and the average squared error, the second dealing with the issue of choice of error criterion, and the third discussing choice among the bandwidth selectors considered in the article as well as boundary effects. Scott's heuristic explanation of the source of this negative correlation in the present context is very suggestive. One of the authors' gave a more graphically oriented explanation. Note that when a number of random samples are generated, some will exhibit positive serial correlation. The notion of robustness considered here is fundamentally different from the classical notions. New results of the type presented in the table are slightly worse than the original.

The original expression for MINQUE estimators of variance components involved the inverse of a matrix whose dimensions equalled the total sample size. Later papers described more practical methods of computing the estimators. In this article a method is described that involves matrices and vectors with dimensions no larger than the number of nonempty cells. [ABSTRACT FROM AUTHOR]

Consider the familiar linear model y = Xβ + e. In an ingenious article by Sielken and Hartley (1973) it was shown how one can construct a computational scheme that will generate unbiased L1 or L∞ estimators even when multiple solutions exist. In a recent paper, Harvey (1978) provides a simple proof of unbiasedness for Lp estimators, 1 < p < ∞, under the assumption that the linear model is of full column rank; this insures that the estimator is unique. In this note it is shown that Sielken and Hartley's computational scheme can be extended to include unbiased Lp estimators, p ≥ 1, without requiring a rank condition. [ABSTRACT FROM AUTHOR]

Transformation has long been a powerful tool in developing parsimonious representations and interpretations of data. In 1964, investigations have been made on the formal estimation of a suitable transformation. In particular, suppose that a response is transformed, where and that it is assumed provisionally that for some unknown vector of transformed observations satisfies a linear model. In a technically impressive paper, a study have been made in particular for a joint estimation, examining consistency and asymptotic variances. They report that the cost of not knowing and having to estimate, can be severe. The performance of all Box-Cox type procedures is unstable and highly dependent on the parameters of the model in structured models with small to moderate error variances. It seems that this general conclusion is qualitatively obvious and at the same time scientifically irrelevant. To illustrate first the obviousness, take as a simple example the comparison of two groups of modest size, the observations in group one being near 995 and those in group two being near 1005, the scatters within the two groups being roughly normal with standard deviations close to unity.

This contribution to the literature on density estimation is a welcome sequel to Good and Gaskins's previous papers on the subject. Certainly the penalized-likelihood approach to curve estimation is of considerable appeal, not least because of its ability to provide a unified approach to various different smoothing problems. Therefore, it would appear that some adjustment should be made to the weight of evidence of a bump to take this fact into account. One possible approach that would deal with this automatically would be to introduce an extra bump-penalty term into the penalized likelihood, either instead of or in addition to the roughness-penalty term. It may be an advantage to avoid direct consideration of the density altogether and instead consider only the second derivative of the density, since the values of the density itself are really of only peripheral interest most of the concern is with points of inflection and senses of curvature. It may be an advantage to avoid direct consideration of the density altogether and instead consider only the second derivative of the density, since the values of the density itself are really of only peripheral interest most of the concern is with points of inflection and senses of curvature.

Focuses on the research papers on additional T-minimax estimations. Technicality of the T-minimax procedures discussed in the literature; Preparation of T-minimax material in presentation in a graduate mathematical statistics; Use of the Bayesian methodology.

We develop new methods for analyzing randomized experiments with noncompliance and, by extension, instrumental variable settings, when the often controversial, but key, exclusion restriction assumption is violated. We show how existing large-sample bounds on intention-to-treat effects for the subpopulations of compliers, never-takers, and always-takers can be tightened by exploiting the joint distribution of the outcome of interest and a secondary outcome, for which the exclusion restriction is satisfied. The derived bounds can be used to detect violations of the exclusion restriction and the magnitude of these violations in instrumental variables settings. It is shown that the reduced width of the bounds depends on the strength of the association of the auxiliary variable with the primary outcome and the compliance status. We also show how the setup we consider offers new identifying assumptions of intention-to-treat effects. The role of the auxiliary information is shown in two examples of a real social job training experiment and a simulated medical randomized encouragement study. We also discuss issues of inference in finite samples and show how to conduct Bayesian analysis in our partial and point identified settings. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a semiparametric conditional covariance (SCC) estimator that combines the first-stage parametric conditional covariance (PCC) estimator with the second-stage nonparametric correction estimator in a multiplicative way. We prove the asymptotic normality of our SCC estimator, propose a nonparametric test for the correct specification of PCC models, and study its asymptotic properties. We evaluate the finite sample performance of our test and SCC estimator and compare the latter with that of the PCC estimator, purely nonparametric estimator, and Hafner, Dijk, and Franses's (2006) estimator in terms of mean squared error and Value-at-Risk losses via simulations and real data analyses. [ABSTRACT FROM AUTHOR]

This article presents a pseudo-empirical likelihood approach to inference for multiple-frame surveys. We establish a unified framework for point and interval estimation of finite population parameters, and show that inferences on the parameters of interest making effective use of different types of auxiliary population information can be conveniently carried out through the constrained maximization of the pseudo-empirical likelihood function. Confidence intervals are constructed using either the asymptotic χ2 distribution of an adjusted pseudo-empirical likelihood ratio statistic or a bootstrap calibration method. Simulation results based on Statistics Canada's Family Expenditure Survey data show that the proposed methods perform well in finite samples for both point and interval estimation. In particular, a multiplicity-based pseudo-empirical likelihood method is proposed. This method is easily used for multiple-frame surveys with more than two frames and does not require complete frame membership information. The proposed pseudo-empirical likelihood ratio confidence intervals have a clear advantage over the conventional normal approximation-based intervals in estimating population proportions of rare items, a scenario that often motivates the use of multiple-frame surveys. All related computational problems can be handled using existing algorithms for pseudo-empirical likelihood methods with single-frame surveys. [ABSTRACT FROM AUTHOR]

We address the problem of optimally forecasting a binary variable for a heterogeneous group of decision makers facing various (binary) decision problems that are tied together only by the unknown outcome. A typical example is a weather forecaster who needs to estimate the probability of rain tomorrow and then report it to the public. Given a conditional probability model for the outcome of interest (e.g., logit or probit), we introduce the idea of maximum welfare estimation and derive conditions under which traditional estimators, such as maximum likelihood or (nonlinear) least squares, are asymptotically socially optimal even when the underlying model is misspecified. [ABSTRACT FROM AUTHOR]

We propose a new combined semiparametric estimator, which incorporates the parametric and nonparametric estimators of the conditional variance in a multiplicative way. We derive the asymptotic bias, variance, and normality of the combined estimator under general conditions. We show that under correct parametric specification, our estimator can do as well as the parametric estimator in terms of convergence rates; whereas under parametric misspecification our estimator can still be consistent. It also improves over the nonparametric estimator of Ziegelmann (2002) in terms of bias reduction. The superiority of our estimator is verfied by Monte Carlo simulations and empirical data analysis. [ABSTRACT FROM AUTHOR]

The generalized Pareto distribution (GPD) is widely used to model extreme values, for example, exceedences over thresholds, in modeling floods. Existing methods for estimating parameters have theoretical or computational defects. An efficient new estimator is proposed, which is computationally easy, free from the problems observed in traditional approaches, and performs well compared with existing estimators. A numerical example involving heights of waves is used to illustrate the various methods and tests of fit are performed to compare them. [ABSTRACT FROM AUTHOR]

We model 1981-2005 quarterly default frequencies for a panel of U.S. firms in different rating and age classes from the Standard and Poor database. The data are decomposed into systematic and firm-specific risk components, where the systematic component reflects the general economic conditions and the default climate. We need to cope with: the shared exposure of each age cohort, industry, and rating class to the same systematic risk factor; strongly non-Gaussian features of the individual time series; possible dynamics of an unobserved common risk factor; changing default probabilities over the age of the rating; and missing observations. We propose a non-Gaussian multivariate state-space model that deals with all of these issues simultaneously. The model is estimated using importance sampling techniques that have been modified to a multivariate setting. We show in a simulation study that such a multivariate approach improves the performance of the importance sampler. In our empirical work, we find that systematic credit risk may differ substantially in terms of magnitude and timing across industries. [ABSTRACT FROM AUTHOR]