bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nonparametric function estimation from inversely sampled record‐breaking data
Authors: Gulati Sneh , Padgett W. J. 
Published: June 2006

AbstractOften, in industrial stress testing, meteorological data analysis, and other similar situations, measurements may be made sequentially and only values smaller than all previous ones are recorded. When the number of records is fixed in advance, the data are referred to as inversely sampled record‐breaking data. This paper is concerned with nonparametric estimation of the distribution and density functions from such data (successive minima). For a single record‐breaking sample, consistent estimation is not possible except in the extreme left tail of the distribution. Hence, replication is required, and formsuch independent record‐breaking samples, the estimators are shown to be strongly consistent and asymptotically normal asm∞ →. Computer simulations are used to investigate the effect of the bandwidth on the mean squared errors and biases of the smooth estimators, and are also used to provide a comparison of their performance with the analogous estimators obtained under random sampling for record values.
Asymptotic distribution of data‐driven smoothers in density and regression estimation under dependence
Authors: Boente Graciela , Fraiman Ricardo 
Published: June 2006

AbstractWe consider automatic data‐driven density, regression and autoregression estimates, based on any random bandwidth selector h/T. We show that in a first‐order asymptotic approximation they behave as well as the related estimates obtained with the “optimal” bandwidthhTas long ashT/hT→ 1 in probability. The results are obtained for dependent observations; some of them are also new for independent observations.
Generalized Laplacian approximations in Bayesian inference
Authors: HSU John S. J. 
Published: June 2006

AbstractThis paper presents a new Laplacian approximation to the posterior density of η = g(θ). It has a simpler analytical form than that described by Leonard et al. (1989). The approximation derived by Leonard et al. requires a conditional information matrix Rη to be positive definite for every fixed η. However, in many cases, not all Rη are positive definite. In such cases, the computations of their approximations fail, since the approximation cannot be normalized. However, the new approximation may be modified so that the corresponding conditional information matrix can be made positive definite for every fixed η. In addition, a Bayesian procedure for contingency‐table model checking is provided. An example of cross‐classification between the educational level of a wife and fertility‐planning status of couples is used for explanation. Various Laplacian approximations are computed and compared in this example and in an example of public school expenditures in the context of Bayesian analysis of the multiparameter Fisher‐Behrens problem.
Uniqueness of the least‐distances estimator in regression models with multivariate response
Authors: Ducharme Gilles R. 
Published: June 2006

AbstractIn a regression model with univariate response, the quantities derived from the least‐absolute‐deviations method need not be unique. In this note, we show that, contrary to the univariate case, in a regression model with multivariate response, the least‐distances method typically yields quantities that exhibit uniqueness properties that are similar to those obtained by the least‐squares method.
Uniform validity of saddlepoint expansion on compact sets
Authors: Routledge Rick , Tsao Min 
Published: June 2006

AbstractThis paper shows that Daniels's (1954) saddlepoint expansion for the density of a sample mean is, for all practical purposes, always uniformly valid on compact subsets in the interior of the domain of the mean. This uniform validity is the key for establishing the relation between the saddlepoint expansion for the density function and Lugannani and Rice's expansion for the tail probability, and for establishing the validity of a high‐order asymptotic expansion for the density of a standardized mean.
Asymptotic normality for chi‐bar‐square distributions
Authors: Dykstra Richard 
Published: June 2006

AbstractChi‐bar‐square distributions, which are mixtures of chi‐square distributions, mixed over their degrees of freedom, often occur when testing hypotheses that involve inequality constraints. Here, necessary and sufficient conditions on the mixing or weighting distribution are found to ensure asymptotic normality of the corresponding chi‐bar‐square distribution. Essentially, asymptotic normality occurs for the chi‐bar‐square distribution if either the ratio of the mean to the variance of the mixing distribution goes to infinity, or the weighting distribution itself is asymptotically normal. Other than a combination of these two phenomena, this is also the only way for asymptotic normality to hold. Several examples of pertinent chi‐bar‐square distributions are shown to be asymptotically normal by the results in this paper.
Multiple‐shrinkage estimators of means in exponential families
Authors: And Fanny Ki , Tsui Kam‐Wah 
Published: June 2006

AbstractShrinkage estimators are often obtained by adjusting the usual estimator towards a target subspace to which the true parameter might belong. However, meaningful reductions in risk below the usual estimator can typically be achieved in a very small part of the parameter space. In the multivariate‐normal mean estimation problem, E. George, in a series of papers, showed how multiple‐shrinkage estimators (data‐weighted averages of several different shrinkage estimators) can attain substantial risk reductions in a large part of the parameter space. This paper extends the multiple‐shrinkage results to the case of simultaneous estimation of the means of several one‐parameter exponential families. Our results are developed by using an identity similar to that of Haff and Johnson (1986). A computer simulation is reported to indicate the magnitude of reductions in risk. Our results are also applied to the problem of how to choose appropriate component variables to combine before a suitable shrinkage estimator is considered.
The power of the circular cone test: A noncentral chi‐bar‐squared distribution
Authors: Conaway Mark , Pillers Carolyn , Robertson Tim , Sconing James 
Published: June 2006

AbstractPincus (1975) derived the null distribution of the likelihood‐ratio test statistic for testing that the mean vector of a multivariate normal distribution is zero against the alternative that the mean vector lies in a circular cone. Under the null hypothesis, the likelihood‐ratio test statistic has a chi‐bar‐squared distribution. We extend the results of Pincus by deriving the distribution of the likelihood‐ratio test statistic under the alternative hypothesis. In a special case, the distribution is a “noncentral chi‐bar‐squared” distribution. To our knowledge, this is the first order‐restricted testing problem for which the relationship between the null and alternative distributions of the test statistic is similar to the relationship in the linear‐model setting. That is, the distribution of the likelihood‐ratio test has a central form of a distribution under the null hypothesis and a noncentral form of the same distribution under the alternative.
Asymptotic behaviour of nonparametric conditional quantile estimates for time series
Authors: Shi Peide 
Published: June 2006

AbstractNonparametric regression quantiles provide informative and powerful alternatives and generalizations to the more traditional mean and median. The use of B‐spline approximation in the conditional quantile estimation has been studied recently by He and Shi (1994). The regression quantile splines are given by minimizing n i = 1 ρα(Yi‐ g(Xi))where ρα(t) = |t| ‐ (2α ‐ 1)t is the Czech function and g is taken from the space spanned by normalized B‐splines basis functions. This paper relaxes the independence assumption on the stationary sequence {Xi, Yi}. If the true conditional quantile function is smooth up to order r and the observed sequence is β‐mixing (or absolutely regular), it is shown, under suitable mixing conditions, that the optimal global convergence rates can be achieved by the B‐spline based estimators and their derivatives.Les fractiles de régression non‐paramétriques donnent d'éclairantes et puissantes alternatives et généralisations aux traditionelles moyenne et médiane. L'utilisation d'approximations par B‐splines dans l'estimation conditionnelle du fractile a été étudiée récemment par He et Shi (1994). Les splines des fractiles de régression sont obtenus en minimisant n i = 1 ρα(Yi‐ g(Xi)), o ù ρα(t) = |t| ‐ (2α ‐ 1)t est la fonction de Czech et g est pris dans l'espace généré par une base de fonctions composé de B‐splines normalisées. Cet article affaiblit l'hypothèse d'indépendance de la suite stationnaire {Xi, Yi,}. Si la véritable fonction fractile est lisse d'ordre r et la suite observée est β‐mixante (ou absolument régulière), il est montré, sous des hypothèses appropriées de mixage, que les taux obtimaux de convergence global peuvent ětre obtenus par des estimateurs basés sur les B‐splines et leurs dérivés.
Approximations for marginal densities of M‐estimators
Authors: Fan Rocky Y.K. , Field Christopher A. 
Published: June 2006

AbstractWe develop a saddle‐point approximation for the marginal density of a real‐valued function p(), where is a general M‐estimator of a p‐dimensional parameter, that is, the solution of the system {n‐1ljl(Yl,) = 0}j=1,…,p. The approximation is applied to several regression problems and yields very good accuracy for small samples. This enables us to compare different classes of estimators according to their finite‐sample properties and to determine when asymptotic approximations are useful in practice.
Bayesian analysis of outlier problems using divergence measures
Authors: Peng Fengchun , Dey Dipak K. 
Published: June 2006

AbstractA Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling‐based approach using a Gibbs or Metropolis‐within‐Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.
A necessary and sufficient condition for the strong consistency of a family of estimators of the common odds ratio
Authors: Yu Kai Fun 
Published: June 2006

AbstractA family of easily computable estimators of the odds ratio of a number of two‐by‐two contingency tables is proposed. It includes the well‐known Mantel‐Haenszel estimator as a special case. A necessary and sufficient condition is given for the strong consistency of the estimators for the case when the tables are sparse and the number of tables becomes large. The condition also ensures the asymptotic normality of this family of estimators. A family of consistent estimators is proposed for the variances of the asymptotic distributions. In the case of the Mantel‐Haenszel estimator, the validity of Breslow's (1981, Biometrika) condition for the consistency and asymptotic normality is questioned. Examples are given to demonstrate that it is neither necessary nor sufficient for the consistency of the Mantel‐Haenszel estimator.Cet article propose une famille d'estimateurs faciles à calculer du rapport‐chance d'un certain nombre de tableaux de contingences deux par deux. Elle comprend le fameux estimateur de Mantel‐Haenszel, comme cas particulier. Une condition nécessaire et suffisante pour la convergence forte des estimateurs est donnée, dans le cas où les tableaux sont clairsemés et le nombre de tableaux devient élevé. Cette condition garantit également la normalité asymptotique de cette famille d'estimateurs. Une famille d'estimateurs convergents est proposée pour les variances des distributions aymptotiques. Dans le cas de l'estimateur de Mantel‐Haenszel, la validité de la condition de Breslow (1981, Biometrika) pour la convergence et la normalité asymptotique est remise en cause. Des examples sont fournis, démontrant qu'elle n'est ni nécessaire ni suffisante pour la convergence de l'estimateur de Mantel‐Haenszel.
Belief functions and statistical inference
Authors: Wasserman Larry A. 
Published: June 2006

AbstractThe Dempster Shafer theory of belief functions is a method of quantifying uncertainty that generalizes probability theory. We review the theory of belief functions in the context of statistical inference. We mainly focus on a particular belief function based on the likelihood function and its application to problems with partial prior information. We also consider connections to upper and lower probabilities and Bayesian robustness.
Gaussian‐based kernels
Authors: Wand Matthew P. , Schucany William R. 
Published: June 2006

AbstractWe derive a class of higher‐order kernels for estimation of densities and their derivatives, which can be viewed as an extension of the second‐order Gaussian kernel. These kernels have some attractive properties such as smoothness, manageable convolution formulae, and Fourier transforms. One important application is the higher‐order extension of exact calculations of the mean integrated squared error. The proposed kernels also have the advantage of simplifying computations of common window‐width selection algorithms such as least‐squares cross‐validation. Efficiency calculations indicate that the Gaussian‐based kernels perform almost as well as the optimal polynomial kernels when die order of the derivative being estimated is low.
Saddlepoint approximations for nonlinear statistics
Authors: Wang Soujin 
Published: June 2006

AbstractIt is well known that saddlepoint expansions lead to accurate approximations to the cumulative distributions and densities of a sample mean and other simple linear statistics. The use of such expansions is explored in a broader situation. The saddlepoint formula for the tail probability of a certain type of nonlinear statistic is derived. The relative error ofO(n–1), as in the linear case, is retained. A simple example is considered, to illustrate the great accuracy of the approximation.
Nonparametric density estimation for censored survival data: Regression‐spline approach
Authors: Abrahamowicz Michal , Clampl Antonio , Ramsay James O. 
Published: June 2006

AbstractA method for nonparametric estimation of density based on a randomly censored sample is presented. The density is expressed as a linear combination of cubicM‐splines, and the coefficients are determined by pseudo‐maximum‐likelihood estimation (likelihood is maximized conditionally on data‐dependent knots). By using regression splines (small number of knots) it is possible to reduce the estimation problem to a space of low dimension while preserving flexibility, thus striking a compromise between parametric approaches and ordinary nonparametric approaches based on spline smoothing. The number of knots is determined by the minimum AIC. Examples of simulated and real data are presented. Asymptotic theory and the bootstrap indicate that the precision and the accuracy of the estimates are satisfactory.
Beyond kappa: A review of interrater agreement measures
Authors: Banerjee Mousumi , Capozzoli Michelle , McSweeney Laura , Sinha Debajyoti 
Published: June 2006

AbstractIn 1960, Cohen introduced the kappa coefficient to measure chance‐corrected nominal scale agreement between two raters. Since then, numerous extensions and generalizations of this interrater agreement measure have been proposed in the literature. This paper reviews and critiques various approaches to the study of interrater agreement, for which the relevant data comprise either nominal or ordinal categorical ratings from multiple raters. It presents a comprehensive compilation of the main statistical approaches to this problem, descriptions and characterizations of the underlying models, and discussions of related statistical methodologies for estimation and confidence‐interval construction. The emphasis is on various practical scenarios and designs that underlie the development of these measures, and the interrelationships between them.
Smoothing in an underdetermined linear model with random explanatory variables
Authors: Sneddon Gary 
Published: June 2006

AbstractIn some physical systems, where the goal is to describe behaviour over an entire field using scattered observations, a multiple regression model can be derived from the discretization of a continuous process. These models often have more parameters than observations. We propose a technique for constructing smoothed estimators in this situation. Our method assumes the model has random explanatory and response variables, and imposes a smoothness penalty based on the signal‐to‐noise ratio of the model. Results are présentés using a known value for the ratio, and a method for estimating the ratio is discussed. The procedure is applied to modelling temperature measurements taken in the California Current.
Bayesian density estimation using bernstein polynomials
Authors: Petrone Sonia 
Published: June 2006

AbstractWe propose a Bayesian nonparametric procedure for density estimation, for data in a closed, bounded interval, say [0,1]. To this aim, we use a prior based on Bemstein polynomials. This corresponds to expressing the density of the data as a mixture of given beta densities, with random weights and a random number of components. The density estimate is then obtained as the corresponding predictive density function. Comparison with classical and Bayesian kernel estimates is provided. The proposed procedure is illustrated in an example; an MCMC algorithm for approximating the estimate is also discussed.
Robust estimation of extremes
Authors: Dupuis D. J. , Field C. A. 
Published: June 2006

AbstractWe consider the problem of making inferences about extreme values from a sample. The underlying model distribution is the generalized extreme‐value (GEV) distribution, and our interest is in estimating the parameters and quantiles of the distribution robustly. In doing this we find estimates for the GEV parameters based on that part of the data which is well fitted by a GEV distribution. The robust procedure will assign weights between 0 and 1 to each data point. A weight near 0 indicates that the data point is not well modelled by the GEV distribution which fits the points with weights at or near 1. On the basis of these weights we are able to assess the validity of a GEV model for our data. It is important that the observations with low weights be carefully assessed to determine whether diey are valid observations or not. If they are, we must examine whether our data could be generated by a mixture of GEV distributions or whether some other process is involved in generating the data. This process will require careful consideration of die subject matter area which led to the data. The robust estimation techniques are based on optimal B‐robust estimates. Their performance is compared to the probability‐weighted moment estimates of Hoskinget al.(1985) in both simulated and real data.
On the trimmed mean and minimax‐variance L‐estimation in Kolmogorov neighbourhoods
Authors: Wiens Douglas P. , Wu Eden K.H. , Zhou Julie 
Published: June 2006

AbstractWe consider the properties of the trimmed mean, as regards minimax‐variance L‐estimation of a location parameter in a Kolmogorov neighbourhood K() of the normal distribution:We first review some results on the search for an L‐minimax estimator in this neighbourhood, i.e. a linear combination of order statistics whose maximum variance in Kt() is a minimum in the class of L‐estimators. The natural candidate – the L‐estimate which is efficient for that member of Kt,() with minimum Fisher information – is known not to be a saddlepoint solution to the minimax problem. We show here that it is not a solution at all. We do this by showing that a smaller maximum variance is attained by an appropriately trimmed mean. We argue that this trimmed mean, as well as being computationally simple – much simpler than the efficient L‐estimate referred to above, and simpler than the minimax M‐ and R‐estimators – is at least “nearly” minimax.
Improved confidence estimators for Fieller's confidence sets
Authors: Tsao C. Andy , Hwang J. T. Gene 
Published: June 2006

AbstractFieller's confidence setCFfor ratios of location parameters, although of great importance in practice, is often cited as an example to criticize frequentist theory. The reason is that the set can consist of the whole parameter space and yet the confidence is γ = 1 – α in any case. In this paper, we study the problem of constructing data‐dependent estimators better than γ+, A reasonable estimator appears to be γ+, which is one ifCFis the whole parameter space and γ otherwise. By using an estimated confidence approach and a squared‐error loss, it is shown that γ+dominates γ. The risk improvement of γ+over γ can be sizable. Also, by numerically comparing γ+with a generalized Bayes estimator γL, which is shown to be admissible when one or two ratios are concerned, it is shown that γ+is nearly admissible. We also conclude that the common practice of reporting 1 – α only whenCFis not the whole parameter space is nearly admissible.
Bayesian analysis for a stress‐strength system under noninformative priors
Authors: Sun Dongchu , Ghosh Malay , Basu Asit P. 
Published: June 2006

AbstractNoninformative priors are used for estimating the reliability of a stress‐strength system. Several reference priors (cf. Berger and Bernardo 1989, 1992) are derived. A class of priors is found by matching the coverage probabilities of one‐sided Bayesian credible intervals with the corresponding frequentist coverage probabilities. It turns out that none of the reference priors is a matching prior. Sufficient conditions for propriety of posteriors under reference priors and matching priors are provided. A simple matching prior is compared with three reference priors when sample sizes are small. The study shows that the matching prior performs better than Jeffreys's prior and reference priors in meeting the target coverage probabilities.
On the explosion rate of maximum‐bias functions
Authors: Berrendero José R. , Mazzi Sonia , Romo Juan , Zamar Ruben H. 
Published: June 2006

AbstractThe maxbias function BT() contains much information about the robustness properties of the estimate T. This function satisfies BT(0)=0 and BT()<for all 0<<whereis the breakdown point of T. Hampel (1974)pioneered the study of the limiting behaviour of BT(ϵ) where ϵ → 0. He computed and optimized the rate γ at which BT(ϵ) approaches 0 when ϵ → 0. This rate is now called the contamination sensitivity of T, and constitutes one of the cornerstones of the theory of robustness. We show that much can also be learned from the study of the limiting behaviour of BT(ϵ) when ϵ → ϵ*. A new robustness measure, called the relative explosion rate, can be obtained by studying the limiting relative maxbias behaviour of two extimates when approaches their common breakdown point ϵ*. Like the contamination sensitivity, the relative explosion rate can be readily derived from the estimate's score function. General formulae are given for M‐estimates of scale and S‐, MM‐ and τ‐estimates of regression. We also show that the maxbias behaviour for large ϵ is largely determined by the curvature of the estimate's score function near zero. This motivates our definition and study of the local order of a score function.