Two-level search design for main-effect plus two plan

One important class of screening designs is the search design first proposed by Srivastava (1975). A new class of two-level factorial search designs which are capable of estimating all main-effect plus two interactions is provided. We first give a necessary and sufficient condition for the main-effect plus two plan and then show that the proposed search design always satisfies such a condition. Received October 2000     

Finite sample tail behavior of the multivariate trimmed mean based on Tukey-Donoho halfspace depth

Finite sample tail behavior of the Tukey-Donoho halfspace depth based multivariate trimmed mean is investigated with respect to a tail performance measure. It turns out that the tails of the sampling distribution of the α-depth-trimmed mean approach zero at least ⌊αn⌋ times as fast as the tails of the underlying population distribution and could be n−⌊αn⌋+ 1 times as fast. In addition, there is an intimate relationship among the tail behavior, the halfspace depth, and the finite sample breakdown point of the estimator. It is shown that the lower tail performance bound of the depth based trimmed mean is essentially the same as its halfspace depth and the breakdown point. This finding offers a new insight into the notion of the halfspace depth and extends the important role of the tail behavior as a quantitative assessment of robustness in the regression (He, Jurečková, Koenker and Portnoy (1990)) and the univariate location settings (Jurečková (1981)) to the multivariate location setting. Received: 1 July 1999     

Characterizations of the Pareto and related distributions

In this note, a class of Pareto distributions is characterized based on the Shannon entropy of k-record statistics. As a consequence of that characterizations of the uniform and exponential distributions are given. Received: October 1999     

D-optimal weighing designs for six objects

For all integers m≥6, we determine the maximum value of det X ^T X, where X is an m×6 (0, 1)-matrix, and exhibit (D-optimal) matrices X for which the maximum occurs. For D-optimal matrices X, the uniqueness of the Gram matrix X ^T X is discussed. Received: May 2000     

DS-optimal designs in one way ANOVA

Characterization and construction of optimal designs using the familiar optimality criteria, for example A-, D- and E-optimality are well studied in the literature. However the study of the Distance Optimality (DS-) criterion introduced by Sinha (1970) has very recently drawn attention of researchers. In the present article, we consider the singularly estimable full rank problem of estimating the full set of elementary treatment contrasts using the DS optimality criterion in the set up of a one way ANOVA model. Using a limit argument it turns out that a CRD in which difference between any two allocation numbers is at the most unity is uniquely DS-optimal. Acknowledgement. We are thankful to Prof. B. K. Sinha for suggesting the problem to us and many helpful discussions with him. We are also thankful to the referees for drawing our attention to the reference of Bischoff (1995) and many helpful comments.     

On the choice of support of Re-descendingψ-Functions in linear models with asymmetric error distributions

InM-estimation of the regression parameter vector in the linear model, we discuss the choice of the support of certain re-descendingψ-functions for both cases when the distribution of the i.i.d. errors is partially known and when it is completely functionally unknown. Research supported in part by the Natural Sciences and Engineering Research Council of Canada.     

Robustness issues regarding content-corrected tolerance limits

This article reviews the content-corrected method for tolerance limits proposed by Fernholz and Gillespie (2001) and addresses some robustness issues that affect the length of the corresponding interval as well as the corrected content value. The content-corrected method for k-factor tolerance limits consists of obtaining a bootstrap corrected value p ^* that is robust in the sense of preserving the confidence coefficient for a variety of distributions. We propose several location/scale robust alternatives to obtain robust corrected-content k-factor tolerance limits that produce shorter intervals when outlying observations are present. We analyze the Hadamard differentiability to insure bootstrap consistency for large samples. We define the breakdown point for the particular statistic to be bootstrapped, and we obtain the influence function and the value of the breakdown point for the traditional and the robust statistics. Two examples showing the advantage of using these robust alternatives are also included.     

On multivariate higher order von Mises expansions

In this paper we review the von Mises calculations of higher order for statistical functionals of one variable. For the functionals of several variables, the higher order Gateaux differentials are defined leading to the corresponding multivariate higher order von Mises expansions. These expansions are used to analyze the bias of the corresponding statistical functionals. The second and third order derivatives are computed for M-estimates. Applications of these expansions to study the bias of M-estimates of location and to simultaneous M-estimates of location and scale are also given. Received: July 2000     

Characterization of Normal Distribution Related to Two Samples Based on Regression

Characterization of normal distribution related to two samples based on second conditional moments has been obtained. This characterization has been transformed to a characterization based on the UMVU estimators of the density function. These results are generalized to k samples from normal distributions. Finally applications of these characterization results to goodness-of-fit test are discussed.     

Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests

In practice, it is an important problem (especially in quality control) to secure that a known regression function occurs during a certain period in time. In the present paper, we consider the change-point problem that under the null hypothesis this known regression function occurs. As alternative, we consider a certain non-parametric class of functions that is of particular interest in quality control. We analyze this test problem by using partial sums of the data. Asymptotically, we get Brownian motion and Brownian motion with trend (≠0) under the hypothesis and under the alternative, respectively. We prove that tests based on partial sums have a larger power when the partial sums are taken from the time reversed data. This can be quantitatively determined in an asymptotic way by some new results on Kolmogorov type tests for Brownian motion with trend. We illustrate our results by a certain model that is interesting in quality control and by an example with real data.Supported in part by the Deutsche Forschungsgemeinschaft Grant Bi655.Supported in part by the Deutsche Forschungsgemeinschaft Grant Bi655 and by the Swiss National Science Foundation Grant 20-55586.98.     

Designs for smoothing spline ANOVA models

Smoothing spline estimation of a function of several variables based on an analysis of variance decomposition (SS-ANOVA) is one modern nonparametric technique. This paper considers the design problem for specific types of SS-ANOVA models. As criteria for choosing the design points, the integrated mean squared error (IMSE) for the SS-ANOVA estimate and its asymptotic approximation are derived based on the correspondence between the SS-ANOVA model and the random effects model with a partially improper prior. Three examples for additive and interaction spline models are provided for illustration. A comparison of the asymptotic designs, the 2^d factorial designs, and the glp designs is given by numerical computation. Received May 2000     

On universal admissibility of scale parameter estimators

A characterization result of Kushary (1998) regarding universal admissibility of equivariant estimators in the one parameter gamma distribution is generalized to a scale family of distributions with monotone likelihood ratio. New examples are given, among them the F-distribution with a scale parameter. In particular, universal admissibility is characterized within the class of location-scale equivariant estimators of the ratio of the variances of two normal distributions with unknown means. In this context the maximum likelihood estimator is shown to be universally inadmissible by virtue of a general sufficient condition for universal inadmissibility of a scale equivariant estimator. Received: January 2000     

A note on theE-optimality of block designs

Summary In this paper we consider the problem of determiningE-optimal block designs for experimental situations in whichv treatments are to be tested onn experimental units arranged inb blocks and where the block sizes and number of replications assigned to the treatments are allowed to vary. Some sufficient conditions are obtained for designs to beE-optimal in these situations and methods for constructing designs which satisfy the sufficient conditions given are also derived.     

A bayesian estimation of reliability based on the extended gamma process as prior over the cumulative hazard function

The Dykstra and Laud's extended gamma process is assumed as prior process over the cumulative hazard function, (t), for a bayesian nonparametric estimation of the reliability functionR(t) from both exact and censored data. Particular cases and interpretative aspects are discussed also in the light of an illustrative example.This research was supported by Ministero della Pubblica Istruzione, grant 40% (Gruppo di ricerca «Modelli probabilistici»).     

The discrepancy distribution of stationary multiplier rules for rounding probabilities

The problem of rounding finitely many (continuous) probabilities to (discrete) proportions N _i/n is considered, for some fixed rounding accuracy n. It is well known that the rounded proportions need not sum to unity, and instead may leave a nonzero discrepancy D=(∑N _i) −n. We determine the distribution of D, assuming that the rounding function used is stationary and that the original probabilities follow a uniform distribution. Received: April 1999     

A minimal complete class theorem for decision problems where the parameter space contains only finitely many points

In this note we show that the class of stepwise Bayes procedures, suitable defined, forms the minimal complete class for decision problems where the parameter contains only finitely many points. Beyond the assumption on the parameter space, the result is quite general and extends some earlier results.Research supported in part by NSF grant DMS-8911548-01     

On bootstrapping the mode in the nonparametric regression model with random design

In the nonparametric regression model with random design and based on i.i.d. pairs of observations (X _i, Y _i), where the regression function m is given by m(x)=?(Y _i|X _i=x), estimation of the location θ (mode) of a unique maximum of m by the location of a maximum of the Nadaraya-Watson kernel estimator for the curve m is considered. In order to obtain asymptotic confidence intervals for θ, the suitably normalized distribution of is bootstrapped in two ways: we present a paired bootstrap (PB) where resampling is done from the empirical distribution of the pairs of observations and a smoothed paired bootstrap (SPB) where the bootstrap variables are generated from a smooth bivariate density based on the pairs of observations. While the PB requires only relatively small computational effort when carried out in practice, it is shown to work only in the case of vanishing asymptotic bias, i.e. of “undersmoothing” when compared to optimal smoothing for mode estimation. On the other hand, the SPB, although causing more intricate computations, is able to capture the correct amount of bias if the pilot estimator for m oversmoothes. Received: May 2000     

Optimality and efficiency of incomplete split-block designs

In this paper, a balanced incomplete split-block design (BISBD) is shown to be universally optimum for the estimation of the interaction effects with respect to each of the intra-plot stratum estimation and the GLSE. Furthermore, the efficiency factor of an optimal design is investigated.     

THE IMPACT OF IMMIGRATION ON THE LABOR MARKET

The literature on the impact of immigration on the labor market is highly controversial. The aim of this paper is to review the existing literature and draw some general conclusions on how wages and employment respond to immigration. Economic studies indicate that the impact of immigration on the average wage and employment of native workers is null or slightly positive. However, because adjustments take time, the immediate labor market effects of unexpected (as opposed to expected) migration episodes can be detrimental. Immigration also can have distributional consequences. In particular, the skill composition of immigrants matters in determining their impact on native labor market outcomes. An inflow of immigrants will tend to reduce the wages of competing native workers (with skills similar to those of the migrants), and increase those of complementary workers (with skills that complement those of immigrants). By affecting the skill composition of the workforce, immigration can create winners and losers among native workers via changes in the wage structure.