bluuebunny/crossref_metadata_2025_split huggingface dataset:
Monotonic minimax estimators of a 2×2 covariance matrix
Authors: Perron François 
Published: June 2006

AbstractLet S : 2 × 2 have a nonsingular Wishart distribution with unknown matrix σ and n degrees of freedom. For estimating σ two families of mimmax estimators, with respect to the entropy loss, are presented. These estimators are of the form σ(S) = Rø(L)Rt where R is orthogonal, L and Φ are diagonal, and RLRT = S. Conditions under which the components of Φ and L follow the same order relation [i.e., writing Φ = diag(Φ1,Φ2) and L = diag(l1,/2) with l1 ≥ l2, we have Φ1 ≥ Φ2] are established. Comparisons with Stein's estimators and other orthogonally invariant estimators are discussed.
Prior elicitation in the classification problem
Authors: Cooleyd Craig A. , Maceachern Steven N. 
Published: June 2006

AbstractResults are developed concerning the asymptotic behaviour of the Bayes classification rule as the number of unclassified observations grows without bound. It is shown that unclassified observations serve only to estimate the individual population parameters in an unlabeled sense and do not provide information about the labels that are attached to the populations. Prior construction is approached through investigation of prior odds over regions of the joint parameter space (across all populations) deemed likely to contain the true joint parameter vector. It is shown that consideration of these prior odds can lead to more robust a posteriori classification of individual observations.
Designs for approximately linear regression: Maximizing the minimum coverage probability of confidence ellipsoids
Authors: Wiens Douglas P. 
Published: June 2006

AbstractThe classical D‐optimality principle in regression design may be motivated by a desire to maximize the coverage probability of a fixed‐volume confidence ellipsoid on the regression parameters. When the fitted model is exactly correct, this amounts to minimizing the determinant of the covariance matrix of the estimators. We consider an analogue of this problem, under the approximately linear model E[y|x] = θTz(x) + f(x). The nonlinear disturbance f(x) is essentially unknown, and the experimenter fits only to the linear part of the response. The resulting bias affects the coverage probability of the confidence ellipsoid on θ. We study the construction of designs which maximize the minimum coverage probability as f varies over a certain class. Explicit designs are given in the case that the fitted response surface is a plane.
On priors that match posterior and frequentist distribution functions
Authors: Ghosh J.K. , Mukerjee Rahul 
Published: June 2006

AbstractIn the multiparameter case, this paper characterizes priors so as to match, up to o(n‐1/2), the posterior joint cumulative distribution function (c.d.f.) of a posterior standardized version of the parametric vector with the corresponding frequentist c.d.f.
Improving on truncated linear estimates of exponential and gamma scale parameters
Authors: Shao Peter Yi‐Shi , Strawderman William E. 
Published: June 2006

AbstractWe consider the problem of estimating the scale parameter of an exponential or a gamma distribution under squared error loss when the scale parameter θ is known to be greater than some fixed value θ0. Natural estimators in this setting include truncated linear functions of the sufficient statistic. Such estimators are typically inadmissible, but explicit improvements seem difficult to find. Some are presented here. A particularly interesting finding is that estimators which are admissible in the untruncated problem which take values only in the interior of the truncated parameter space are found to be inadmissible for the truncated problem.
Jackknife inference for heteroscedastic linear regression models
Authors: Shao Jun , Rao J. N. K. 
Published: June 2006

AbstractInference on the regression parameters in a heteroscedastic linear regression model with replication is considered, using either the ordinary least‐squares (OLS) or the weighted least‐squares (WLS) estimator. A delete‐group jackknife method is shown to produce consistent variance estimators irrespective of within‐group correlations, unlike the delete‐one jackknife variance estimators or those based on the customary δ‐method assuming within‐group independence. Finite‐sample properties of the delete‐group variance estimators and associated confidence intervals are also studied through simulation.
Dynamic sampling plans in on‐line control charts
Authors: Wu Yanhong , Srivastava M. S. 
Published: June 2006

AbstractThree simple dynamic sampling plans for detecting the change point are investigated in the discrete‐time case. The first is a two‐rate sampling CUSUM procedure. The second is a two‐rate sampling Shiryayev‐Roberts procedure. The third is a periodic sequential testing procedure. Two problems are discussed. First, simple design methods are provided for practical use. Second, a comparison between the three plans is made in the continuous‐time case, which shows that by properly choosing the design parameters, the three plans can be made equally efficient in certain senses.
Constrained nonparametric maximum‐likelihood estimation for mixture models
Authors: Susko E. , Kalbfleisch J. D. , Chen J. 
Published: June 2006

AbstractA nonparametric mixture model specifies that observations arise from a mixture distribution, ∫ f(x, θ) dG(θ), where the mixing distribution G is completely unspecified. A number of algorithms have been developed to obtain unconstrained maximum‐likelihood estimates of G, but none of these algorithms lead to estimates when functional constraints are present. In many cases, there is a natural interest in functional ϕ(G), such as the mean and variance, of the mixing distribution, and profile likelihoods and confidence intervals for ϕ(G) are desired. In this paper we develop a penalized generalization of the ISDM algorithm of Kalbfleisch and Lesperance (1992) that can be used to solve the problem of constrained estimation. We also discuss its use in various different applications. Convergence results and numerical examples are given for the generalized ISDM algorithm, and asymptotic results are developed for the likelihood‐ratio test statistics in the multinomial case.
Applications of a simple regression model to acid rain data
Authors: Stein Michael L. , Shen Xiaotong , Styer Patricia E. 
Published: June 2006

AbstractThis paper addresses two vital and seemingly simple questions concerning wet deposition of sulfates, a major contributor to acid rain. The first is to estimate the annual wet deposition of sulfate at a monitoring site under emissions that existed during the 1980s. This problem is complicated by missing data. The second is to estimate accurately the effect of a change in pollution emissions on concentrations of sulfate in precipitation. This problem is made difficult by the substantial natural variations in sulfate concentrations due to weather variations between years. As a tool for addressing both of these problems, we develop a regression model for the sulfate concentration of precipitation on a particular day as a function of amount of precipitation and time of the year. The model is used as a basis for imputing missing sulfate concentrations to handle the missing‐data problem. It is also used to explain some of the variability in annual sulfate concentrations due to meteorology and hence provide more accurate estimates of the effect of changes in emissions.
Transect‐spacing design of ice cores on the Antarctic continent
Authors: Cressie Noel 
Published: June 2006

AbstractChemical analyses of ice cores, drilled deep into an ice sheet, provide a historical record of the earth's atmosphere that dates back as far as 400,000–500,000 years. Although the atmosphere mixes quite well, it is recognized that spatial variability associated with ice‐core locations should be allowed for. In this article, spatial statistical methodology is applied to the design question of finding the best spacing of ice‐core locations on a partial transect of Antarctica.
Efficient estimation in a nonlinear counting‐process regression model
Authors: Greenwood P. E. , Wefelmeyer W. 
Published: June 2006

AbstractSuppose we observe i.i.d. copies of X, C, Y, where X is a counting process, C is a censoring process talcing only values 0 and 1, and Y is a covariate process. Assume that the intensity process of X is of the form C(s)a(s, Y(s)) with a unknown, but that the distribution of X, C, Y is unspecified otherwise. McKeague and Utikal proposed an estimator for the doubly cumulative hazard f f a(s, y) ds dy and determined its asymptotic distribution. We show that the estimator is regular and efficient in the sense of a Hájek‐Inagaki convolution theorem for partially specified models.
Distributions minimizing fisher information for scale in kolmogorov neighbourhoods
Authors: Wiens Douglas P. , Wu K. H. Eden 
Published: June 2006

AbstractWe construct those distributions minimizing Fisher information for scale in Kolmogorov neighbourhoods Kϵ(G) = {F|supx|F(x) ‐ G(x| ⩽ ϵ} of d.f.'s G satisfying certain mild conditions. The theory is sufficiently general to include those cases in which G is normal, Laplace, logistic, Student's t, etc. As well, we consider G(x) = 1 ‐ e‐x, ⩽ 0, and correct some errors in the literature concerning this case.
Mixture models for matched pairs
Authors: Lesperance Mary L. , Kalbfleisch John D. 
Published: June 2006

AbstractMixture models for matched pairs arise when the pair‐specific parameter is assumed to be a random quantity. We explore the use of semiparametric maximum‐likelihood methods for a family of mixture models for matched pairs. The geometry of mixture likelihoods provides insight into the properties of these models.
A modified chi‐square test of independence against a class of ordered alternatives in an r x c contingency table
Authors: Oluyede Broderick O. 
Published: June 2006

AbstractA modified chi‐square test statistic is constructed for testing the hypothesis of independence in a two‐way contingency table against a class of ordered alternatives defined in terms of pooled cross‐product ratios. The test procedure can also be used to test for positive quadrant dependence in a two‐way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of this test.
Practicing safe statistics with the mid‐p
Authors: Routledge R.D. 
Published: June 2006

AbstractThe mid‐p‐value is the standard p‐value for a test minus half the difference between it and the nearest lower possible value. Its smaller size lends it an obvious appeal to users — it provides a more significant‐looking summary of the evidence against the null hypothesis. This paper examines the possibility that the user might overstate the significance of the evidence by using the smaller mid‐p in place of the standard p‐value. Routine use of the mid‐p is shown to control a quantity related to the Type I error rate. This related quantity is appropriate to consider when the decision to accept or reject the null hypothesis is not always firm. The natural, subjective interpretation of a p‐value as the probability that the null hypothesis is true is also examined. The usual asymptotic correspondence between these two probabilities for one‐sided hypotheses is shown to be strengthened when the standard p‐value is replaced by the mid‐p.
Robust weighted likelihood estimators with an application to bivariate extreme value problems
Authors: Dupuis Debbie J. , Morgenthaler Stephan 
Published: June 2006

AbstractThe authors achieve robust estimation of parametric models through the use of weighted maximum likelihood techniques. A new estimator is proposed and its good properties illustrated through examples. Ease of implementation is an attractive property of the new estimator. The new estimator downweights with respect to the model and can be used for complicated likelihoods such as those involved in bivariate extreme value problems. New weight functions, tailored for these problems, are constructed. The increased insight provided by our robust fits to these bivariate extreme value models is exhibited through the analysis of sea levels at two East Coast sites in the United Kingdom.
Bayesian methods for generalized linear models with covariates missing at random
Authors: Ibrahim Joseph G. , Chen Ming‐Hui , Lipsitz Stuart R. 
Published: June 2006

AbstractThe authors propose methods for Bayesian inference for generalized linear models with missing covariate data. They specify a parametric distribution for the covariates that is written as a sequence of one‐dimensional conditional distributions. They propose an informative class of joint prior distributions for the regression coefficients and the parameters arising from the covariate distributions. They examine the properties of the proposed prior and resulting posterior distributions. They also present a Bayesian criterion for comparing various models, and a calibration is derived for it. A detailed simulation is conducted and two real data sets are examined to demonstrate the methodology.
Highs and lows: Some properties of the extremes of a diffusion and applications in finance
Authors: Mcleish Donald L. 
Published: June 2006

AbstractObservations on security prices, currency exchange rates, interest rates, and other financial time series usually include not only an open and close, but also a high and low price for the period. For Brown‐ian motion and certain diffusion processes, the information on high and low prices is of considerable value, particularly for estimating volatility, correlations between processes, and in the pricing of look‐back and barrier options. For pricing more general derivatives, this information is useful to the extent that change in volatility is an important ingredient in the price. The author gives a simple geometric device for generating the extremes of Brownian motion, and geometric Brownian motion; he then uses these extremes in the estimation of the volatility of the processes and to study survivorship bias.
Covariates in multipath change‐point problems: Modelling and consistency of the MLE
Authors: Asgharian Masoud , Wolfson David B. 
Published: June 2006

AbstractAlthough the single‐path change‐point problem has been extensively treated in the statistical literature, its multipath counterpart has largely been ignored. In the multipath change‐point setting, it is often of interest to assess the impact of covariates on the change point itself as well as on the parameters before and after the change point. This paper is concerned only with the inclusion of covariates in the change‐point distribution. This is achieved through the hazard of change. Maximum likelihood estimation is discussed and consistency of the maximum likelihood estimators established.
Improved log‐linear model estimators of abundance in capture‐recapture experiments
Authors: Rivest Louis‐Paul , Lévesque Tina 
Published: June 2006

AbstractThe authors review log‐linear models for estimating the size of a closed population and propose a new log‐linear estimator for experiments having between animal heterogeneity and a behavioral response. They give a general formula for evaluating the asymptotic biases of estimators of abundance derived from log‐linear models. They propose simple frequency modifications for reducing these asymptotic biases and investigate the modifications in a Monte Carlo experiment which reveals that they reduce both the bias and the mean squared error of abundance estimators.
Estimation and selection procedures in regression: An L1 approach
Authors: Hengartner Nicolas , Wegkamp Marten 
Published: June 2006

AbstractThe authors consider the problem of estimating a regression function go involving several variables by the closest functional element of a prescribed class G that is closest to it in the L1 norm. They propose a new estimator ĝ based on independent observations and give explicit finite sample bounds for the L1distance between ĝg and go. They apply their estimation procedure to the problem of selecting the smoothing parameter in nonparametric regression.
A semi‐Markov model for binary longitudinal responses subject to misclassification
Authors: Rosychuk Rhonda J. , Thompson Mary E. 
Published: June 2006

AbstractThe authors propose a two‐state continuous‐time semi‐Markov model for an unobservable alternating binary process. Another process is observed at discrete time points that may misclassify the true state of the process of interest. To estimate the model's parameters, the authors propose a minimum Pearson chi‐square type estimating approach based on approximated joint probabilities when the true process is in equilibrium. Three consecutive observations are required to have sufficient degrees of freedom to perform estimation. The methodology is demonstrated on parasitic infection data with exponential and gamma sojourn time distributions.
Using adaptive weighted least squares to reduce the lengths of confidence intervals
Authors: O'Gorman Thomas W. 
Published: June 2006

AbstractThe author proposes an adaptive method which produces confidence intervals that are often narrower than those obtained by the traditional procedures. The proposed methods use both a weighted least squares approach to reduce the length of the confidence interval and a permutation technique to insure that its coverage probability is near the nominal level. The author reports simulations comparing the adaptive intervals to the traditional ones for the difference between two population means, for the slope in a simple linear regression, and for the slope in a multiple linear regression having two correlated exogenous variables. He is led to recommend adaptive intervals for sample sizes superior to 40 when the error distribution is not known to be Gaussian.
Robust linear discriminant analysis using S‐estimators
Authors: Croux Christophe , Dehon Catherine 
Published: June 2006

AbstractThe authors consider a robust linear discriminant function based on high breakdown location and covariance matrix estimators. They derive influence functions for the estimators of the parameters of the discriminant function and for the associated classification error. The most B‐robust estimator is determined within the class of multivariate S‐estimators. This estimator, which minimizes the maximal influence that an outlier can have on the classification error, is also the most B‐robust location S‐estimator. A comparison of the most B‐robust estimator with the more familiar biweight S‐estimator is made.
Exact short poisson confidence intervals
Authors: Kabaila Paul , Byrne John 
Published: June 2006

AbstractThe authors propose a new method for constructing a confidence interval for the expectation θ of a Poisson random variable. The interval they obtain cannot be shortened without the infimum over θ of the coverage probability falling below 1 ‐ α. In addition, the endpoints of the interval are strictly increasing functions of the observed variable. An easy‐to‐program algorithm is provided for computing this interval.
Detection of patterns in noisy time series
Authors: Tingley M. A. , Mclean L. 
Published: June 2006

AbstractIn the context of a research project in ergonomy, myoelectric signals monitored over two to three hour periods gave rise to long noisy time series, which were smoothed using running medians. Tests developed by the authors show that the patterns displayed by the smoothed time series are not artifacts of smoothed white noise. Indeed, the smoothed series show amplitude fluctuations and short‐term correlations which are larger than those obtained by applying running medians to independent, identically distributed data. The key idea is that of reduction of data to binary signals.
Robust sequential designs for nonlinear regression
Authors: Sinha Sanjoy , Wiens Douglas P. 
Published: June 2006

AbstractThe authors introduce the formal notion of an approximately specified nonlinear regression model and investigate sequential design methodologies when the fitted model is possibly of an incorrect parametric form. They present small‐sample simulation studies which indicate that their new designs can be very successful, relative to some common competitors, in reducing mean squared error due to model misspecifi‐cation and to heteroscedastic variation. Their simulations also suggest that standard normal‐theory inference procedures remain approximately valid under the sequential sampling schemes. The methods are illustrated both by simulation and in an example using data from an experiment described in the chemical engineering literature.
Penalized likelihood regression: General formulation and efficient approximation
Authors: Gu Chong , Kim Young‐Ju 
Published: June 2006

AbstractThe authors consider a formulation of penalized likelihood regression that is sufficiently general to cover canonical and noncanonical links for exponential families as well as accelerated life models with censored survival data. They present an asymptotic analysis of convergence rates to justify a simple approach to the lower‐dimensional approximation of the estimates. Such an approximation allows for much faster numerical calculation, paving the way to the development of algorithms that scale well with large data sets.
Monte carlo approximation to edgeworth expansions
Authors: Hall Peter , Martin Michael A. , Sun Shan 
Published: June 2006

AbstractSince the 1930s, empirical Edgeworth expansions have been employed to develop techniques for approximate, nonparametric statistical inference. The introduction of bootstrap methods has increased the potential usefulness of Edgeworth approximations. In particular, a recent paper by Lee & Young introduced a novel approach to approximating bootstrap distribution functions, using first an empirical Edgeworth expansion and then a more traditional bootstrap approximation to the remainder. In principle, either direct calculation or computer algebra could be used to compute the Edgeworth component, but both methods would often be difficult to implement in practice, not least because of the sheer algebraic complexity of a general Edgeworth expansion. In the present paper we show that a simple but nonstandard Monte Carlo technique is a competitive alternative. It exploits properties of Edgeworth expansions, in particular their parity and the degrees of their polynomial terms, to develop particularly accurate approximations.
Multiple roots of estimating functions
Authors: Small Christopher G. , Yang Zejiang 
Published: June 2006

AbstractEstimating functions can have multiple roots. In such cases, the statistician must choose among the roots to estimate the parameter. Standard asymptotic theory shows that in a wide variety of cases, there exists a unique consistent root, and that this root will lie asymptotically close to other consistent (possibly inefficient) estimators for the parameter. For this reason, attention has largely focused on the problem of selecting this root and determining its approximate asymptotic distribution. In this paper, however, we concentrate on the exact distribution of the roots as a random set. In particular, we propose the use of higher‐order root intensity functions as a tool for examining the properties of the roots and determining their most problematic features. The use of root intensity functions of first and second order is illustrated by application to the score function for the Cauchy location model.