bluuebunny/crossref_metadata_2025_split huggingface dataset:
Confidence intervals for parameters lying in a random polygon
Authors: Kolassa John E. 
Published: June 2006

AbstractThis paper presents algorithms for computing confidence intervals and regions for elements of a parameter vector when the signs of linear combinations of unknown parameters are observed, but the coefficients contain experimental error. These methods were proposed in the geochemical literature by Kolassa (1992) as a method specific to petrology. Experimental data are used to give linear constraints, involving quantities measured with error, on unknown free energies and entropies of a chemical reaction. Confidence intervals are given for these parameters, and these are compared with more naïve approaches.
Efficient bias‐Robust M‐Estimators of location in Kolmogorov normal neighbourhoods
Authors: Wu Eden K.H. , Zhou Julie 
Published: June 2006

AbstractWe consider minimax‐bias M‐estimation of a location parameter in a Kolmogorov neighbourhood K() of a normal distribution. The maximum asymptotic bias of M‐estimators for the Kolmogorov normal neighbourhood is derived, and its relation with the gross‐error sensitivity of the estimator at the nominal model (the Gaussian case) is found. In addition, efficient bias‐robust M‐estimators Ti are constructed. Numerical results are also obtained to show the percentage of increase in maximum asymptotic bias and the efficiency we can achieve for some well‐known ‐functions.
Approximating distributions of random functionals of Ferguson‐Dirichlet priors
Authors: Muliere Pietro , Tardella Luca 
Published: June 2006

AbstractWe explore the possibility of approximating the Ferguson‐Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures. The proposed procedure is based on the constructive definition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule. This allows us to set in advance the closeness to the distributions of interest. The distribution of the stopping rule is derived, and the practicability of the simulating procedure is discussed. Sufficient conditions for convergence of random functionals are provided. The numerical applications provided just sketch the idea of the variety of nonparametric procedures that can be easily and safely implemented in a Bayesian setting.
Combined Bayesian estimates for the equicorrelation coefficient
Authors: Viana Marios A.G. 
Published: June 2006

AbstractCombined Bayesian estimates for equicorrelation covariance matrices are considered. The case of a common equicorrelation p and possibly different standard deviations σl,σk among k experimental groups is examined first, and the Bayesian estimation of (σ, σ1,σk) is discussed. Secondly, under the assumption of a common standard deviation and possibly different equicorrelations, the Bayesian estimation of (ρ1,ρk,σ) is considered.
Equivariant estimators of the covariance matrix
Authors: Perron François 
Published: June 2006

AbstractGiven a Wishart matrix S [S ∽ Wp(n, Σ)] and an independent multinomial vector X [X ∽ Np (μ, Σ)], equivariant estimators of Σ are proposed. These estimators dominate the best multiple of S and the Stein‐type truncated estimators.
Gaussian deconvolution via differentiation
Authors: Masry Elias , Rice John A. 
Published: June 2006

AbstractSuppose that ϕ is a Gaussian density and that g = f * ϕ, where * denotes convolution. From observations with density g, one wishes to estimate f. We analyze an estimate which is a linear combination of estimates of derivatives of g and show that this estimate converges in an L2 norm at a rate which is compatible with the pointwise optimal rate established by Fan (1991).
One‐step M‐estimators in the linear model, with dependent errors
Authors: Field Christopher A. , Wiens Douglas P. 
Published: June 2006

AbstractWe consider the problem of robust M‐estimation of a vector of regression parameters, when the errors are dependent. We assume a weakly stationary, but otherwise quite general dependence structure. Our model allows for the representation of the correlations of any time series of finite length.We first construct initial estimates of the regression, scale, and autocorrelation parameters. The initial autocorrelation estimates are used to transform the model to one of approximate independence. In this transformed model, final one‐step M‐estimates are calculated.Under appropriate assumptions, the regression estimates so obtained are asymptotically normal, with a variance‐covariance structure identical to that in the case in which the autocorrelations are known a priori. The results of a simulation study are given. Two versions of our estimator are compared with the L1 ‐estimator and several Huber‐type M‐estimators. In terms of bias and mean squared error, the estimators are generally very close. In terms of the coverage probabilities of confidence intervals, our estimators appear to be quite superior to both the L1‐estimator and the other estimators. The simulations also indicate that the approach to normality is quite fast.
The Lindsay transform of natural exponential families
Authors: Kokonendji C. C. , Seshadri V. 
Published: June 2006

AbstractLet μ be an infinitely divisible positive measure on R. If the measure ρμ is such that x‐2[ρμ(dx)—ρμ({0})δ0(dx)] is the Lévy measure associated with μ and is infinitely divisible, we consider for all positive reals α and β the measure Tα,β(μ) which is the convolution of μ*α and ρμ*β. For example, if μ is the inverse Gaussian law, then ρμ is a gamma law with paramter 3/2. Then Tα,β(μ) is an extension of the Lindsay transform of the first order, restricted to the distributions which are infinitely divisible. The main aim of this paper is to point out that it is possible to apply this transformation to all natural exponential families (NEF) with strictly cubic variance functions P. We then obtain NEF with variance functions of the form □ΔP(□Δ), where A is an affine function of the mean of the NEF. Some of these latter types appear scattered in the literature.
Correction locale de l'estimateur à noyau de la densité d'une loi de probabilité
Authors: Abdous Belkacem , Berlin ÈT Alain 
Published: June 2006

AbstractThe standard Parzen‐Rosenblatt kernel density estimator is known to systematically deviate from the true value near critical points of the density curve. To overcome this difficulty, we extend the Rao‐Blackwell method by using locally sufficient statistics: we define a new estimator and study its asymptotic behaviour. The interest of the method is shown by means of simulations.
On the asymptotic normality of the L1‐ and L2‐errors in histogram density estimation
Authors: Beirlant Jan , Györfi László , Lugosi Gábor 
Published: June 2006

AbstractThe L1 and L2‐errors of the histogram estimate of a density f from a sample X1,X2,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness‐of‐fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).
On the admissibility of the maximum‐likelihood estimator of the binomial variance
Authors: Brown Lawrence D. , Chow Mosuk , Fong Duncan K.H. 
Published: June 2006

AbstractThis paper addresses the admissibility of the maximum‐likelihood estimator (MLE) of the variance of a binomial distribution with parameters n and p under squared‐error loss. We show that the MLE is admissible for n ≤ 5 and inadmissible for n≥ 6.
Consistency of least‐squares estimator and its jackknife variance estimator in nonlinear models
Authors: Shao Jun 
Published: June 2006

AbstractThe purpose of this paper is twofold: (1) We establish the consistency of the least‐squares estimator in a nonlinear modelyi = f(xi,θ) +σiei where the range of the parameter θ is noncompact, the regression function is unbounded, and the σi,'s are not necessarily equal. This extends the results in Jennrich (1969) and Wu (1981). (2) Under the same model, the jackknife estimator of the asymptotic covariance matrix of the least‐squares estimator is shown to be consistent, which provides a theoretical justification of the empirical results in Duncan (1978) and the use of the jackknife method in large‐sample inferences.
M‐Estimates of regression when the scale is unknown and the error distribution is possibly asymmetric: A minimax result
Authors: Li Bing , Zamar Ruben H. 
Published: June 2006

AbstractHuber (1964) found the minimax‐variance M‐estimate of location under the assumption that the scale parameter is known; Li and Zamar (1991) extended this result to the case when the scale is unknown. We consider the robust estimation of the regression coefficients (β1,…,βp) when the scale and the intercept parameters are unknown. The minimax‐variance estimates of (β1,…,βp) with respect to the trace of their asymptotic covariance matrix are derived. The maximum is taken over ϵ‐contamination neighbourhoods of a central regression model with Gaussian errors (asymmetric contamination is allowed), and the minimum is taken over a large class of generalized M‐estimates of regression of the Mallow type. The optimal choice of estimates for the nuisance parameters (scale and intercept) is also considered.
The asymptotic behaviour of a class of L.‐estimators under long‐range dependence
Authors: Mukherjee Kanchan 
Published: June 2006

AbstractThis paper obtains asymptotic representations of a class of L‐estimators in a linear regression model when the errors are a function of long‐range‐dependent Gaussian random variables. These representations are then used to address some of the efficiency robustness properties of L‐estimators compared to the least‐squares estimator. It is observed that under the Gaussian error distribution, each member of the class has the same asymptotic efficiency as that of the least‐squares estimator. The results are obtained as a consequence of the asymptotic uniform linearity of some weighted empirical processes based on long‐range‐dependent random variables.
Quasi‐universal bandwidth selection for kernel density estimators
Authors: Wegkamp Marten H. 
Published: June 2006

AbstractLet f̂n, h denote the kernel density estimate based on a sample of size n drawn from an unknown density f. Using techniques from L2 projection density estimators, the author shows how to construct a data‐driven estimator f̂n, h which satisfies

This paper is inspired by work of Stone (1984), Devroye and Lugosi (1996) and Birge and Massart (1997).
Statistical consequences of an adaptive treatment allocation in a clinical trial
Authors: Farewell V.T. , Viveros R. , Sprott D.A. 
Published: June 2006

AbstractAn examination of the likelihood arising from data in experiments comparing two therapies for neonatal respiratory failure illustrates a difficulty in the use of a design with adaptive treatment allocation as opposed to the use of the classical fixed‐sample‐size design. The requirement of obtaining objective scientific evidence as to which treatment is better for use on future patients conflicts with attempts to give the treatment thought to be the best to the patient at hand.
A characterization of the efficiency of individualized logistic regressions
Authors: Bull Shelley B. , Donner Allan 
Published: June 2006

AbstractThe use of individualized regressions, which reduces the polychotomous logistic regression model to several dichotomous models, has been proposed as a solution to some practical difficulties for binary covariates (Begg and Gray 1984, Biometrika, 71, 11–18). Its disadvantages, however, include loss of efficiency and the complexity of making comparisons among regressions. Using expressions for the large‐sample distribution of the maximum‐likelihood estimates, the efficiency of the individualized procedure relative to the polychotomous procedure is evaluated for the case in which the covariates are assumed to follow a multivariate normal distribution. The relative efficiency when the logistic slope vectors from different regressions are collinear can be substantially lower compared to the efficiency with orthogonal slope vectors. Further evaluations for binary covariates using collinear and orthogonal slope parametrizations lead to a similar characterization.
A modified bootstrap estimator for the mean of an asymmetric distribution
Authors: Swanepoel J.W.H. , BEER C.F. De 
Published: June 2006

AbstractA modified bootstrap estimator of the population mean is proposed which is a convex combination of the sample mean and sample median, where the weights are random quantities. The estimator is shown to be strongly consistent and asymptotically normally distributed. The small‐ and moderate‐sample‐size behavior of the estimator is investigated and compared with that of the sample mean by means of Monte Carlo studies. It is found that the newly proposed estimator has much smaller mean squared errors and also yields significantly shorter confidence intervals for the population mean.
Detecting the interaction of quantity and quality: A study of Fisher's analysis
Authors: Fick Gordon Hilton 
Published: June 2006

AbstractIn Sections 49 and 50 of the Design of Experiments, Fisher discusses an experiment designed to compare the effects of several types of manure on yield. Each type of manure is applied at three dosage levels: zero, single, and double doses. Fisher points out that the usual contrasts constructed for a factorial experiment are unsatisfactory in this setting. In particular, since the response curves necessarily meet at the zero dose, the usual notion of interaction as a lack of parallelism cannot apply. Fisher then gives an appropriate definition for interaction in this setting. This paper is concerned with a class of orthogonal polynomials that can be used as an aid in the detection of this modified definition of interaction.
Robust Bayesian analysis of the binomial empirical Bayes problem
Authors: Sivaganesan S. , Berger James 
Published: June 2006

AbstractEmpirical Bayes estimation is considered for an i.i.d. sequence of binomial parameters θi arising from an unknown prior distribution G(.). This problem typically arises in industrial sampling, where samples from lots are routinely used to estimate the lot fraction defective of each lot. Two related issues are explored. The first concerns the fact that only the first few moments of G are typically estimable from the data. This suggests consideration of the interval of estimates (e.g., posterior means) corresponding to the different possible G with the specified moments. Such intervals can be obtained by application of well‐known moment theory. The second development concerns the need to acknowledge the uncertainty in the estimation of the first few moments of G. Our proposal is to determine a credible set for the moments, and then find the range of estimates (e.g., posterior means) corresponding to the different possible G with moments in the credible set.
A note on the likelihood‐ratio statistic under model misspecification
Authors: Viraswami K. , Reid N. 
Published: June 2006

AbstractFollowing Viraswami and Reid (1996), higher‐order results under model misspecification are obtained for the likelihood‐ratio statistic and the adjusted likelihood‐ratio statistic, for the case of a scalar parameter. An improved version of the adjusted likelihood‐ratio statistic is suggested.
Robust sequential designs for approximately linear models
Authors: Wiens Douglas P. 
Published: June 2006

AbstractWe consider the problem of the sequential choice of design points in an approximately linear model. It is assumed that the fitted linear model is only approximately correct, in that the true response function contains a nonrandom, unknown term orthogonal to the fitted response. We also assume that the parameters are estimated by M‐estimation. The goal is to choose the next design point in such a way as to minimize the resulting integrated squared bias of the estimated response, to order n‐1. Explicit applications to analysis of variance and regression are given. In a simulation study the sequential designs compare favourably with some fixed‐sample‐size designs which are optimal for the true response to which the sequential designs must adapt.
Paradoxes in nonparametric tests
Authors: Haunsperger Deanna B. 
Published: June 2006

AbstractThis paper is a continuation of one (1992) in which the author studied the paradoxes that can arise when a nonparametric statistical test is used to give an ordering of k samples and the subsets of those samples. This article characterizes the projection paradoxes that can occur when using contingency tables, complete block designs, and tests of dichotomous behaviour of several samples. This is done by examining the “dictionaries” of possible orderings of each of these procedures. Specifically, it is shown that contingency tables and complete block designs, like the Kruskal‐Wallis nonparametric test on k samples, minimize the number and kinds of projection paradoxes that can occur; however, using a test of dichotomous behaviour of several samples does not. An analysis is given of two procedures used to determine the ordering of a pair of samples from a set of k samples. It is shown that these two procedures may not have anything in common.
A note on bias reduction in variable‐kernel density estimates
Authors: Mckay Ian 
Published: June 2006

AbstractIt is well known that the inverse‐square‐root rule of Abramson (1982) for the bandwidth h of a variable‐kernel density estimator achieves a reduction in bias from the fixed‐bandwidth estimator, even when a nonnegative kernel is used. Without some form of “clipping” device similar to that of Abramson, the asymptotic bias can be much greater than O(h4) for target densities like the normal (Terrell and Scott 1992) or even compactly supported densities. However, Abramson used a nonsmooth clipping procedure intended for pointwise estimation. Instead, we propose a smoothly clipped estimator and establish a globally valid, uniformly convergent bias expansion for densities with uniformly continuous fourth derivatives. The main result extends Hall's (1990) formula (see also Terrell and Scott 1992) to several dimensions, and actually to a very general class of estimators. By allowing a clipping parameter to vary with the bandwidth, the usual O(h4) bias expression holds uniformly on any set where the target density is bounded away from zero.
Including structural measurement errors in the nonlinear regression analysis of clustered data
Authors: Zidek J. V. , Le N. D. , Wong H. , Burnett R. T. 
Published: June 2006

AbstractThis paper extends methods for nonlinear regression analysis that have developed for the analysis of clustered data. Its novelty lies in its dual incorporation of random cluster effects and structural error in the measurement of the explanatory variables. Moments up to second order are assumed to have been specified for the latter to enable a generalized estimating equations approach to be used for fitting and testing nonlinear models linking response to these explanatory variables and random effects. Taylor expansion methods are used, and a difficulty with earlier approaches overcome. Finally we describe an application of this methodology to indicate how it can be used. That application concerns the degree of association of hospital admissions for acute respiratory health problems and air pollution.
A method for constructing supersaturated designs and its Es2 optimality
Authors: Tang Boxin , Wu C. F. J. 
Published: June 2006

AbstractA lower bound for the Es2 value of an arbitrary supersaturated design is derived. A general method for constructing supersaturated designs is proposed and shown to produce designs with n runs and m = k(n — 1) factors that achieve the lower bound for Es2 and are thus optimal with respect to the Es2 criterion. Within the class of designs given by the construction method, further discrimination can be made by minimizing the pairwise correlations and using the generalized D and A criteria proposed by Wu (1993). Efficient designs of 12, 16, 20 and 24 runs are constructed by following this approach.
Asymptotic properties of a generalized regression‐type predictor of a finite population variance in probability sampling
Authors: Shah D. N. , Patel P. A. 
Published: June 2006

AbstractA system of predictors for estimating a finite population variance is defined and shown to be asymptotically design‐unbiased (ADU) and asymptotically design‐consistent (ADC) under probability sampling. An asymptotic mean squared error (MSE) of a generalized regression‐type predictor, generated from the system, is obtained. The suggested predictor attains the minimum expected variance of any design‐unbiased estimator when the superpopulation model is correct. The generalized regression‐type predictor and the predictor suggested by Mukhopadhyay (1990) are compared.
Un critère de choix de variables en analyse en composantes principales fondé sur des modèles graphiques gaussiens particuliers
Authors: Falguerolles Antoine De , Jmel SaïD 
Published: June 2006

AbstractWe focus on the problem of selection of a subset of the variables so as to preserve the multivariate data structure that a principal‐components analysis of the initial variables would reveal. We propose a new method based on some adapted Gaussian graphical models. This method is then compared with those developed by Bonifas et al. (1984) and Krzanowski (1987a, b). It appears that the criteria for all methods consider the same correlation submatrices and often lead to similar results. The proposed approach offers some guidance as to the number of variables to be selected. In particular, Akaike's information criterion is used.
Mutability of DNA base pairs: A statistical approach based on linear discrimination
Authors: Leong Phaik Mooi , Morgenthaler Stephan 
Published: June 2006

AbstractA mutational spectrum measures the frequency of mutations at particular base pairs along a given DNA sequence under the influence of a particular treatment. Such spectra have been measured for several genes, in various organisms and under different treatments. This article presents a method of analysis based on the statistical discrimination between mutable base pairs and stable base pairs. The coefficients of the discriminant function characterize the mutational spectrum induced by a given treatment on a given sequence. These coefficients can be interpreted by the user without specialized statistical knowledge.
Statistical analysis of right‐censored failure‐time data with partially specified hazard rates
Authors: Qin Jing , Sun Jianguo 
Published: June 2006

AbstractThis paper discusses the analysis of right‐censored failure‐time data in which the failure rate may have different forms in different time intervals. Such data occur naturally, for example, in demography studies and leukemia research, and a number of methods for the analysis have been proposed in the literature. However, most methods are purely parametric or nonparametric. Matthews and Farewell (1982), for example, discussed this problem and proposed a method for testing a constant failure rate against a failure rate involving a change point. To estimate an absolute limit on the attainable human life span, Zelterman (1992) discussed a hazard function that has different parametric forms over different time intervals. We consider a different situation in which the hazard function may follow a parametric form before a change point and is completely unknown after the change point. To test the existence of the change point, a modified maximal‐censored‐likelihood‐ratio test is proposed and its asymptotic properties are studied. A bootstrap method is described for finding critical values of the proposed test. Simulation results indicate that the test performs well.