an exact confidence band for one dimensional polynomial regression summary an exact piecewise polynomial simultaneous confidence band is described for onedimensional p i th order polynomial regression the band is constructed by placing intervals around the estimated response at the zeros of the pth order orthogonal polynomial with respect to the design points since under the usual assumptions the response estimates are uncorrelated at these zeros the construction of the exact band in the normal case is made easy

m quantile models for small area estimation small area estimation techniques are employed when sample data are insufficient for acceptably precise direct estimation in domains of interest these techniques typically rely on regression models that use both covariates and random effects to explain variation between domains however such models also depend on strong distributional assumptions require a formal specification of the random part of the model and do not easily allow for outlier robust inference we describe a new approach to small area estimation that is based on modelling quantile like parameters of the conditional distribution of the target variable given the covariates this avoids the problems associated with specification of random effects allowing inter domain differences to be characterized by the variation of area specific m quantile coefficients the proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area specific parameters including that of the quantiles of the distribution of the target variable in the different small areas results from two simulation studies comparing the performance of the m quantile modelling approach with more traditional mixed model approaches are also provided

logistic regression analysis of sample survey data summary standard chi squared x2 or likelihood ratio g2 test statistics for logistic regression analysis involving a binary response variable are adjusted to take account of the survey design these adjustments are based on certain generalized design effects logistic regression diagnostics to detect any outlying cell proportions in the table and influential points in the factor space are also developed taking account of the survey design finally the results are used to analyse some data from the october 1980 canadian labour force survey

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

tweedie s formula and selection bias we suppose that the statistician observes some large number of estimates zi each with its own unobserved expectation parameter i the largest few of the zi s are likely to substantially overestimate their corresponding i s this being an example of selection bias or regression to the mean tweedie s formula first reported by robbins in 1956 offers a simple empirical bayes approach for correcting selection bias this article investigates its merits and limitations in addition to the methodology tweedie s formula raises more general questions concerning empirical bayes theory discussed here as relevance and empirical bayes information there is a close connection between applications of the formula and james stein estimation

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

on measuring the variability of small area estimators under a basic area level model summary in this paper based on a basic area level model we obtain second order accurate approxi mations to the mean squared error of model based small area estimators using the fay herriot 1979 iterative method of estimating the model variance based on weighted residual sum of squares we also obtain mean squared error estimators unbiased to second order based on simulations we compare the finite sample performance of our mean squared error estimators with those based on method of moments maximum likelihood and residual maximum likelihood estimators of the model variance our results suggest that the fay herriot method performs better in terms of relative bias of mean squared error estimators than the other methods across different combinations of number of areas pattern of sampling variances and distribution of small area effects we also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second order unbiased for the mean squared error the posterior variance based on such a prior possesses both bayesian and frequentist interpretations

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

nonparametric estimation of mean squared prediction error in nested error regression models nested error regression models are widely used for analyzing clustered data for example they are often applied to two stage sample surveys and in biology and econometrics prediction is usually the main goal of such analyses and mean squared prediction error is the main way in which prediction performance is measured in this paper we suggest a new approach to estimating mean squared prediction error we introduce a matched moment double bootstrap algorithm enabling the notorious underestimation of the naive mean squared error estimator to be substantially reduced our approach does not require specific assumptions about the distributions of errors additionally it is simple and easy to apply this is achieved through using monte carlo simulation to implicitly develop formulae which in a more conventional approach would be derived laboriously by mathematical arguments

the effect of monte carlo approximation on coverage error of double bootstrap confidence intervals a double bootstrap confidence interval must usually be approximated by a monte carlo simulation consisting of two nested levels of bootstrap sampling we provide an analysis of the coverage accuracy of the interval which takes account of both the inherent bootstrap and monte carlo errors the analysis shows that by a suitable choice of the number of resamples drawn at the inner level of bootstrap sampling we can reduce the order of coverage error we consider also the effects of performing a finite monte carlo simulation on the mean length and variability of length of two sided intervals an adaptive procedure is presented for the choice of the number of inner level resamples the effectiveness of the procedure is illustrated through a small simulation study

a quasi empirical bayes method for small area estimation abstract this article develops an empirical bayes type approach for small area estimation based only on the specification of a set of conditionally independent hierarchical mean and variance functions describing the first two moments of the process generating the data the objective of the analysis is to draw inference about the intermediate or the random means we combine the quasi likelihood functions to construct the quasi posterior density of the random means conditional on the data and the marginal parameters we describe a method for estimating the marginal parameters that are then substituted in the quasi posterior density of the random means the empirical quasi posterior density so derived is used to obtain the quasi empirical bayes estimates of the random parameters we apply the methodology to estimate the utilization rates of cancer chemotherapy for the selected counties in the state of washington

outlier robust small area estimation recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data this naturally leads down to the idea of an outlier robust bias correction for these estimators in this paper we develop this idea and also propose two different analytical mean squared error estimators for the ensuring bias corrected outlier robust estimators simulations based on realistic outlier contaminated data show that the proposed bias correction often leads to more efficient estimators furthermore the proposed mean squared error estimators appear to perform well with a variety of outlier robust smal area estimators

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

reaction diffusion branching models of stock price fluctuations abstract several models of stock trading bak et al physica a 246 1997 430 are analyzed in analogy with one dimensional two species reaction diffusion branching processes using heuristic and scaling arguments we show that the short time market price variation is subdiffusive with a hurst exponent h 1 4 biased diffusion towards the market price and blind eyed copying lead to crossovers to the empirically observed random walk behavior h 1 2 at long times the calculated crossover forms and diffusion constants are shown to agree well with simulation data

estimation of finite population domain means a model assisted empirical best prediction approach in this article we introduce a general methodology for producing a model assisted empirical best predictor ebp of a finite population domain mean using data from a complex survey our method improves on the commonly used design consistent survey estimator by using a suitable mixed model such a model combines information from related sources such as census and administrative data unlike a purely model based ebp the proposed model assisted ebp converges in probability to the customary design consistent estimator as the domain and sample sizes increase the convergence in probability is shown to hold with respect to the sampling design irrespective of the assumed mixed model a property commonly known as design consistency this property ensures robustness of the proposed predictor against possible model failures in addition the convergence in probability is shown to be valid with respect to the assumed mixed model model consistency a new mean squared prediction error mspe estimator is proposed

exact simultaneous confidence bands for a collection of univariate polynomials in regression analysis we discuss a simple simulation method for construction of exact confidence bands having a pre assigned confidence level simultaneously for several regression functions which are univariate polynomials in the predictors this is accomplished by combining and extending existing results in a manner that permits both finite and infinite ranges for individual predictor variables we illustrate the method for a logistic regression model with both dichotomous and continuous predictors

complex and composite entropy fluctuation behaviors of statistical physics interacting financial model abstract in an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets a novel complex random interacting financial price model is developed by combining voter interacting system with compound poisson process in this model the dissemination of investors investment attitudes can simulate normal and frequent small price fluctuations of financial markets while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets in order to verify the rationality of the model some statistical characteristics of the model returns including fat tail power law scaling complexity and multifractal are compared with real returns by probability density functions composite distance fuzzy entropy c fuzzyen matching energy and multifractal detrended fluctuation analysis the c fuzzyen is a new entropy based approach based on fuzzy entropy and complexity invariant to measure the complexity behaviors of return series the effectiveness analysis of c fuzzyen indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy the empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases

microscopic models for long ranged volatility correlations we propose a general interpretation for long range correlation effects in the activity and volatility of financial markets this interpretation is based on the fact that the choice between active and inactive strategies is subordinated to random walk like processes we numerically demonstrate our scenario in the framework of simplified market models such as the minority game model with an inactive strategy or a more sophisticated version that includes some price dynamics we show that real market data can be surprisingly well accounted for by these simple models

resampling based empirical prediction an application to small area estimation best linear unbiased prediction is well known for its wide range of applications including small area estimation while the theory is well established for mixed linear models and under normality of the error and mixing distributions the literature is sparse for nonlinear mixed models under nonnormality of the error distribution or of the mixing distributions we develop a resampling based unified approach for predicting mixed effects under a generalized mixed model set up second order accurate nonnegative estimators of mean squared prediction errors are also developed given the parametric model the proposed methodology automatically produces estimators of the small area parameters and their mean squared prediction errors without requiring explicit analytical expressions for the mean squared prediction errors

small area estimation when auxiliary information is measured with error summary small area estimation methods typically combine direct estimates from a survey with pre dictions from a model in order to obtain estimates of population quantities with reduced mean squared error when the auxiliary information used in the model is measured with error using a small area estimator such as the fay herriot estimator while ignoring measurement error may be worse than simply using the direct estimator we propose a new small area estimator that accounts for sampling variability in the auxiliary information and derive its properties in particular show ing that it is approximately unbiased the estimator is applied to predict quantities measured in the u s national health and nutrition examination survey with auxiliary information from the u s national health interview survey

jackknife estimation of mean squared error of small area predictors in nonlinear mixed models empirical bayes predictors of small area parameters of interest are often obtained under a linear mixed model for continuous response data or a generalized linear mixed model for binary responses or count data however estimation of the unconditional mean squared error of prediction is complicated particularly for a nonlinear mixed model jiang et al 2002 proposed a jackknife method for estimating the unconditional mean squared error and showed that the resulting estimator is nearly unbiased the leading term of this estimator does not depend on the area specific responses in the nonlinear case whereas the posterior variance of the small area parameter given the model parameters is area specific rao 2003 proposed an alternative method that leads to a computationally simpler jackknife estimator with an area specific leading term we show that a modification of rao s method leads to a nearly unbiased area specific jackknife estimator which is also nearly unbiased for the conditional mean squared error given the area specific responses we examine the relative performances of the jackknife estimators conditionally as well as unconditionally in a simulation study and apply the proposed method to estimate small area mean squared errors in disease mapping problems

robust empirical bayes estimation of means from stratified samples abstract this article considers simultaneous estimation of means from several strata where each stratum contains a finite number of elements for example quite often estimates of annual incomes unemployment rates and so forth must be made simultaneously for many areas our results find application in small area estimation where very few samples are available from an individual area and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas ghosh and meeden 1986 considered empirical bayes estimation of the finite population mean assuming a normal superpopulation model their estimators generalize automatically when one estimates a vector of stratum means this article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations this is the so called posterior linearity property as described in ericson 1

reml estimation asymptotic behavior and related topics the restricted maximum likelihood reml estimates of dispersion parameters variance components in a general non normal mixed model are defined as solutions of the reml equations in this paper we show the reml estimates are consistent if the model is asymptotically identifiable and infinitely informative under the location invariant class and are asymptotically normal a n if in addition the model is asymptotically nondegenerate the result does not require normality or boundedness of the rank p of design matrix of fixed effects moreover we give a necessary and sufficient condition for asymptotic normality of gaussian maximum likelihood estimates mle in non normal cases as an application we show for all unconfounded balanced mixed models of the analysis of variance the reml anova estimates are consistent and are also a n provided the models are nondegenerate the mle are consistent a n if and only if certain constraints on p are satisfied

small area estimation with uncertain random effects random effects models play an important role in model based small area estimation random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables in a recent article datta hall and mandal showed that if the random effects can be dispensed with via a suitable test then the model parameters and the small area means may be estimated with substantially higher accuracy the work of datta hall and mandal is most useful when the number of small areas m is moderately large for large m the null hypothesis of no random effects will likely be rejected rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator as a flexible alternative to the fay herriot random effects model and the approach in datta hall and mandal in this article we consider a mixture model for random effects it is reasonably expected that small areas wit

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

a new class of average moment matching priors summary we derive a new class of priors for the variance component in the fay herriot model a mixed regression model widely used in small area estimation this class includes the well known uniform or superhannonic prior through simulation we illustrate the use of our class of priors

regression analysis of data from a cluster sample abstract for the case of different regression relationships in different subgroups of a finite population only part of which are sampled the extended least squares estimator of any weighted average of the distinct coefficients is derived under assumptions relating only to the first two moments of the distribution of the coefficients under these assumptions the estimator is shown to be the best linear unbiased estimator while under further distributional assumptions it is also the bayesian estimator for a quadratic loss function for the case of unknown variances a method for estimating them from the sample is proposed the empirical estimator thus obtained is shown to perform well by a simulation comparison with the optimal estimator and with other proposed empirical estimators

best predictive small area estimation we derive the best predictive estimator bpe of the fixed parameters under two well known small area models the fay herriot model and the nested error regression model this leads to a new prediction procedure called observed best prediction obp which is different from the empirical best linear unbiased prediction eblup we show that bpe is more reasonable than the traditional estimators derived from estimation considerations such as maximum likelihood ml and restricted maximum likelihood reml if the main interest is estimation of small area means which is a mixed model prediction problem we use both theoretical derivations and empirical studies to demonstrate that the obp can significantly outperform eblup in terms of the mean squared prediction error mspe if the underlying model is misspecified on the other hand when the underlying model is correctly specified the overall predictive performance of the obp is very similar to that of the eblup if the number of small areas is large a

asymptotic theory in generalized ilinear models with nuisance scale parameters this paper establishes the asymptotic normality and the consistencyrobustness of the weighted least squares estimator wlse in the generalized linear models with multiple nuisance scale parameters in addition noting that the asymptotic robust statistical inference in presence of nuisance scale parameters requires a consistency robust estimator of the asymptotic covariance matrix of the wlse this paper derives a class of covariance estimators and proves their consistency robustness

bayesian versus frequentist measures of error in small area estimation summary this paper compares analytically and empirically the frequentist and bayesian measures of error in small area estimation the model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables when the variance components are known then under a uniform prior for the regression coefficients and normality of the error terms the frequentist and the bayesian approaches yield the same predictors and prediction mean squared errors mses defined accordingly when the variance components are unknown it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors so that the resulting empirical predictors remain the same under the two approaches the use of this paradigm requires however modifications to the expressions of the prediction mse to account for the extra variability induced by the need to estimate the variance components the main focus of this paper is to review and compare the modifications to prediction mses proposed in the literature under the two approaches with special emphasis on the orders of the bias of the resulting approximations to the true mses some new approximations based on monte carlo simulation are also proposed and compared with the existing methods the advantage of these approximations is their simplicity and generality finite sample frequentist properties of the various methods are explored by a simulation study the main conclusions of this study are that the use of second order bias corrections generally yields better results in terms of the bias of the mse approximations and the coverage properties of confidence intervals for the small area means the bayesian methods are found to have good frequentist properties but they can be inferior to the frequentist methods the second order approximations under both approaches have however larger variances than the corresponding first order approximations which in most cases result in higher mses of the mse approximations

simultaneous confidence bounds in multiple regression using predictor variable constraints abstract this article presents a method for approximating the coverage probability of simultaneous confidence bounds for multiple regression functions when the vector of predictor variables is constrained to lie in a polyhedral convex set the method is useful because it allows one to construct simultaneous confidence intervals with prescribed coverage probability for the regression function evaluated at various settings of the predictor variables which are narrower than bounds obtained without using the predictor variable constraints for a family of two sided simultaneous confidence bounds that includes scheffe type and constant width bounds the probability of coverage is related to the distribution of the maximum euclidean norm of the projection onto a polyhedral cone for a pair of random vectors with known joint distribution an analogous relation holds for one sided bounds if an algorithm for computing the projection onto the cone is available then these results enable one to use the monte carlo

small area estimation based on natural exponential family quadratic variance function models and survey weights summary we propose pseudo empirical best linear unbiased estimators of small area means based on natural exponential family quadratic variance function models when the basic data consist of survey weighted estimators of these means area specific covariates and certain summary measures involving the weights we also provide explicit approximate mean squared errors of these estimators in the spirit of prasad rao 1990 and these estimators can be readily evaluated a simulation study is undertaken to evaluate the performance of the proposed inferential procedure we estimate also the proportion of poor children in the 5 17 years age group for the different counties in one of the states in the united states

model selection by testing for the presence of small area effects and application to area level data the models used in small area inference often involve unobservable random effects while this can significantly improve the adaptivity and flexibility of a model it also increases the variability of both point and interval estimators if we could test for the existence of the random effects and if the test were to show that they were unlikely to be present then we would arguably not need to incorporate them into the model and thus could significantly improve the precision of the methodology in this article we suggest an approach of this type we develop simple bootstrap methods for testing for the presence of random effects applicable well beyond the conventional context of the natural exponential family if the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small area means such estimators can be substantially more effective for example because they enjoy much fa

exact hurst exponent and crossover behavior in a limit order market model abstract an exclusion particle model is considered as a highly simplified model of a limit order market its price behavior reproduces the well known crossover from over diffusion hurst exponent h 1 2 to diffusion h 1 2 when the time horizon is increased provided that orders are allowed to be canceled for early times a mapping to the totally asymmetric exclusion process yields the exact result h 2 3 which is in good agreement with empirical data the underlying universality class of the exclusion process suggests some robustness of the exponent with respect to changes in the trading rules in the crossover regime the hurst plot has a scaling property where the bulk deposition cancelation rate is the critical parameter analytical results are fully supported by numerical simulations

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

standard errors of prediction in generalized linear mixed models abstract the unconditional mean squared error of prediction umsep is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model but the umsep is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data when the random effects describe variation between independent small domains and domain specific prediction is of interest we propose a conditional mean squared error of prediction cmsep as a general measure of prediction variance the cmsep is shown to be the sum of the conditional variance and a positive correction that accounts for the sampling variability of parameter estimates we derive a second order correct estimate of the cmsep that consists of three components a a plug in estimate of the conditional variance b a plug in estimate of a taylor series approximation to the correction term and c a bootstrap estimate of

scaling approach to related disordered stochastic and free fermion models motivated by mapping from a stochastic system with spatially random rates we consider disordered non conserving free fermion systems using a scaling procedure for the equations of motion this approach demonstrates disorder induced localization acting in competition with the asymmetric driving we discuss the resulting implications for the original stochastic system

mean squared error estimation in transformed fay herriot models summary the problem of accurately estimating the mean squared error of small area estimators within a fay herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable for bias corrected empirical best linear unbiased predictor small area point estimators mean squared error formulae and estimators are provided with biases of smaller order than the reciprocal of the number of small areas the performance of these mean squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the us census bureau s on going small area income and poverty estimation project

robust and efficient estimation by minimising a density power divergence a minimum divergence estimation method is developed for robust parameter estimation the proposed approach uses new density based divergences which unlike existing methods of this type such as minimum hellinger distance estimation avoid the use of nonparametric density estimation and associated complications such as bandwidth selection the proposed class of density power divergences is indexed by a single parameter which controls the trade off between robustness and efficiency the methodology affords a robust extension of maximum likelihood estimation for which 0 choices of near zero afford considerable robustness while retaining efficiency close to that of maximum likelihood

regression analysis with linked data record linkage or exact matching can be used to join together two files that contain information on the same individuals but lack unique personal identification codes the possibility of errors in linkage causes problems for estimating the relationships between variables on the two files the effect is analogous to the impact of measurement error a model of a linear regression relationship between variables in linked files is proposed assuming the probabilities that pairs of records are links are known an unbiased estimator of the regression coefficients is derived methods for estimating the linkage probabilities by using mixture models are discussed a consistent estimator of the covariance matrix of the proposed estimator is proposed a bootstrap estimator is used to reflect the impact of the uncertainty in record linkage model parameters on the estimators of the regression parameters a simulation study compares the performance of the proposed estimator and alternatives

empirical likelihood for small area estimation abstract small areaestimation has become a topic of growingimportance inrecent years due to increasing demand for small area statistics fromboth the public and private sectors the current methodologies inthis area with possibly a handful of exceptions are all parametric be it bayesian or frequentist even the so called nonparamet ric procedures based on empirical best linear unbiased predictors eblup assume linearity of the estimators of small area means resampling methods like jacknife and bootstrap are used mostlyfor mean squared error estimation in this paper we propose analternative bayesian approach based on empirical likelihood whichdoes not require the assumption of either a parametric likelihoodor linearity of estimators the proposed method can also handleboth discrete and continuous data in a uni ed manner empiricallikelihood for both area and unit level models are introduced theimproved performance of our estimator is illustrated through twoexamples involving both discrete and continuous data key words and phrases area level exponentially tilted t prior unit level

reaction diffusion front for a b in one dimension we study theoretically and numerically the steady state diffusion controlled reaction a b where currents j of a and b particles are applied at opposite boundaries for a reaction rate and equal diffusion constants d we find that when j 12d 12 1 the reaction front is well described by mean field theory however for j 12d 12 1 the front acquires a gaussian profile a result of noise induced wandering of the reaction front center we make a theoretical prediction for this profile which is in good agreement with simulation finally we investigate the intrinsic nonwandering front width and find results consistent with scaling and field theoretic predictions

price fluctuations from the order book perspective empirical facts and a simple model abstract statistical properties of an order book and the effect they have on price dynamics were studied using the high frequency nasdaq level ii data it was observed that the size distribution of marketable orders transaction sizes has power law tails with an exponent 1 market 2 4 0 1 the distribution of limit order or quote sizes was found to be consistent with a power law with an exponent close to 2 a somewhat better fit to this distribution was obtained by using a log normal distribution which has an effective power law exponent equal to 2 in the middle of the observed range the depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non linear function of its size a large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a predictable short term price change which is in accord with the law of supply and demand

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

decomposition of prediction error abstract the problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y this problem is considered under each of four states of knowledge about the joint distribution of w and y ranging from complete knowledge to no knowledge a point predictor or predictors are presented for each case prediction error is decomposed so that each component reflects an absence of information under certain conditions these components are uncorrelated and have zero means an exact or approximate expression is given for the variance of each component

sumca simple unified monte carlo assisted approach to second order unbiased mean squared prediction error estimation we propose a simple unified monte carlo assisted approach called sumca to second order unbiased estimation of the mean squared prediction error mspe of a small area predictor the mspe estimator proposed is easy to derive has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor empirical best predictor and post model selection empirical best linear unbiased predictor and empirical best predictor as special cases furthermore the leading term of the mspe estimator proposed is guaranteed positive the lower order term corresponds to a bias correction which can be evaluated via a monte carlo method the computational burden for the monte carlo evaluation is much less compared with other monte carlo based methods that have been used for producing second order unbiased mspe estimators such as the double bootstrap and monte carlo jackknife the sumca estimator also has a nice stability feature theoretical and empirical results demonstrate properties and advantages of the sumca estimator

simple stochastic order book model of swarm behavior in continuous double auction abstract in this study we present a simple stochastic order book model for investors swarm behaviors seen in the continuous double auction mechanism which is employed by major global exchanges our study shows a characteristic called fat tail seen in the data obtained from our model that incorporates the investors swarm behaviors our model captures two swarm behaviors one is investors behavior to follow a trend in the historical price movement and another is investors behavior to send orders that contradict a trend in the historical price movement in order to capture the features of influence by the swarm behaviors from price data derived from our simulations using these models we analyzed the price movement range that is how much the price is moved when it is continuously moved in a single direction depending on the type of swarm behavior we saw a difference in the cumulative frequency distribution of this price movement range in particular for the model of investors who followed a trend in the historical price movement we saw the power law in the tail of the cumulative frequency distribution of this price movement range in addition we analyzed the shape of the tail of the cumulative frequency distribution the result demonstrated that one of the reasons the trend following of price occurs is that orders temporarily swarm on the order book in accordance with past price trends

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

bethe ansatz solution for a defect particle in the asymmetric exclusion process the asymmetric exclusion process on a ring in one dimension is considered with a single defect particle the steady state has previously been solved by a matrix product method here we use the bethe ansatz to solve exactly for the long time limit behaviour of the generating function of the distance travelled by the defect particle this allows us to recover steady state properties known from the matrix approach such as the velocity and obtain new results such as the diffusion constant of the defect particle in the case where the defect particle is a second class particle we determine the large deviation function and show that in a certain range the distribution of the distance travelled about the mean is gaussian moreover the variance diffusion constant grows as l1 2 where l is the system size this behaviour can be related to the superdiffusive spreading of excess mass fluctuations on an infinite system in the case where the defect particle produces a shock our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by ferrari and fontes

double bootstrap methods that use a single double bootstrap simulation we show that when the double bootstrap is used to improve performance of bootstrap methods for bias correction techniques based on using a single double bootstrap sample for each single bootstrap sample can be particularly effective in particular they produce third order accuracy for much less computational expense than is required by conventional double bootstrap methods however this improved level of performance is not available for the single double bootstrap methods that have been suggested to construct confidence intervals or distribution estimators

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

the mean squared error of small area predictors constructed with estimated area variances in the small area estimation literature the sampling error variances are customarily assumed to be known or to depend on a finite number of parameters we consider the empirical best linear unbiased predictor eblup obtained by using the individual directly estimated variance for each small area an approximation for the mean squared error mse of the eblup that recognizes the impact on the predictors of estimation of the variance components is derived simulation studies show that the theoretical expressions are good approximations for the mse of the predictors unless the between area variance component is very small relative to the within area variance an improved estimator of the mse is developed that has smaller overestimation than the original estimator when the between area variance component is small the robustness of the mse estimator is studied and predictors for nonnormal sampling errors are proposed an example from the national resources inventory that motivated the development of the t

on symmetric bootstrap confidence intervals on montre que dans des circonstances generales les intervalles de confiance du bootstrap de percentile t symetrique ont une erreur de recouvrement o n 2 ou n denote la taille d echantillon

mean field approximation for a limit order driven market model a mean field variant of the model of limit order driven market introduced recently by maslov is formulated and solved the agents do not have any strategies and the memory of the system is kept within the order book we show that the evolution of the order book is governed by a matrix multiplicative process the resulting stationary distribution of step to step price changes is calculated it exhibits a power law tail with exponent 2 we obtain also the price autocorrelation function which agrees qualitatively with the experimentally observed negative autocorrelation for short times

benchmarked empirical bayes methods in multiplicative area level models with risk evaluation the paper develops empirical bayes and benchmarked empirical bayes estimators of positive small area means under multiplicative models a simple example will be estimation of per capita income for small areas it is now well understood that small area estimation needs explicit or at least implicit use of models one potential difficulty with model based estimators is that the overall estimator for a larger geographical area based on weighted sum of the model based estimators is not necessarily identical to the corresponding direct estimator such as the overall sample mean one way to fix such a problem is the so called benchmarking approach which modifies the model based estimators to match the aggregate direct estimator benchmarked hierarchical and empirical bayes estimators have proved to be particularly useful in this regard however while estimating positive small area parameters the conventional squared error or weighted squared loss subject to the usual benchmark constraint does not necessarily produce positive estimators hence it is necessary to seek other meaningful losses to alleviate this problem in this paper we consider the transformed fay herriot model as a multiplicative model for estimating positive small area means and suggest a weighted kullbackleibler divergence as a loss function we have found out that the resulting bayes estimator is the posterior mean and that the corresponding benchmarked bayes and empirical bayes estimators retain the positivity constraint the prediction errors of the suggested empirical bayes estimators are investigated asymptotically and their second order unbiased estimators are provided in addition bootstrapped estimators of these prediction errors are also provided the

exact confidence bands for linear regression over intervals abstract exact simultaneous confidence intervals and bands for the regression line on a set cx in simple linear regression have been known only when cx is a finite set with one or two points or when cx is a finite or infinite interval otherwise conservative bands have been used in this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points also tables are provided for cases of finite cx with three points and of cx an interval

influence functions and robust bayes and empirical bayes small area estimation we introduce new robust small area estimation procedures based on area level models we first find influence functions corresponding to each individual area level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation next based on these influence functions properly standardized we propose some new robust bayes and empirical bayes small area estimators the mean squared errors and estimated mean squared errors of these estimators are also found a small simulation study compares the performance of the robust and the regular empirical bayes estimators when the model variance is larger than the sample variance the proposed robust empirical bayes estimators are superior

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

weakly coupled antiparallel totally asymmetric simple exclusion processes we study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit by solving the differential equations describing the steady state of the system analytically for vanishing total current and numerically for nonzero total current the system possesses phases with a localized shock in the density profile in one of the lanes similarly to exclusion processes endowed with nonconserving kinetics in the bulk besides the system undergoes a discontinuous phase transition where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk this phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process however as a consequence of the interaction between lanes the density profiles are deformed and in the case of asymmetric lane change the motion of the shocks is confined to a limited domain

more statistical properties of order books and price impact we investigate present some new statistical properties of order books we analyse data from the nasdaq and investigate a the statistics of incoming limit order prices b the shape of the average order book and c the typical life time of a limit order as a function of the distance from the best price we also determine the price impact function using french and british stocks and find a logarithmic rather than a power law dependence of the price response on the volume the weak time dependence of the response function shows that the impact is surprisingly quasi permanent and suggests that trading itself is interpreted by the market as new information

asymptotic confidence bands for generalized nonlinear regression models asymptotic confidence bands for generalized nonlinear regression models are developed these are based on a combination of the s method of scheffe together with the delta method which is used to approximate the mean function by a linear combination of the parameters the approach can be used in any situation where large sample theory can be applied to yield asymptotically normal estimates of the parameters together with a consistent estimate of the large sample covariance matrix alternative formulations for various special cases allow the use of restricted range bands a number of examples are given including a pharmacokinetic model a logit model with a background response rate and a parametric survival model

the horseshoe estimator for sparse signals this paper proposes a new approach to sparsity called the horseshoe estimator the horseshoe is a close cousin of other widely used bayes rules arising from for example double exponential and cauchy priors in that it is a member of the same family of multivariate scale mixtures of normals but the horseshoe enjoys a number of advantages over existing approaches including its robustness its adaptivity to dierent sparsity patterns and its analytical tractability we prove two theorems that formally characterize both the horseshoe s adeptness at large outlying signals and its super ecient rate of convergence to the correct estimate of the sampling density in sparse situations finally using a combination of real and simulated data we show that the horseshoe estimator corresponds quite closely to the answers one would get by pursuing a full bayesian model averaging approach using a discrete mixture prior to model signals and noise

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

weighting for unequal selection probabilities in multilevel models when multilevel models are estimated from survey data derived using multistage sampling unequal selection probabilities at any stage of sampling may induce bias in standard estimators unless the sources of the unequal probabilities are fully controlled for in the covariates this paper proposes alternative ways of weighting the estimation of a two level model by using the reciprocals of the selection probabilities at each stage of sampling consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase scaling of the weights is proposed to improve the properties of the estimators and to simplify computation variance estimators are also proposed in a limited simulation study the scaled weighted estimators are found to perform well although non negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small the variance estimators perform extremely well the procedures are illustrated using data from the survey of psychiatric morbidity

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due