a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

asymptotic equivalence of empirical likelihood and bayesian map in this paper we are interested in empirical likelihood el as a method of estimation and we address the following two problems 1 selecting among various empirical discrepancies in an el framework and 2 demonstrating that el has a well defined probabilistic interpretation that would justify its use in a bayesian context using the large deviations approach a bayesian law of large numbers is developed that implies that el and the bayesian maximum a posteriori probability map estimators are consistent under misspecification and that el can be viewed as an asymptotic form of map estimators based on other empirical discrepancies are in general inconsistent under misspecification

local empirical likelihood inference for varying coefficient density ratio models based on case control data in this article we develop a varying coefficient density ratio model for case control studies the case and control samples come from two different distributions under the model assumption the ratio of the two densities is related to the linear combination of covariates with varying coefficients through a known function a special case is the exponential tilt model where the log ratio of the two densities is a linear function of covariates we propose a local empirical likelihood el approach to estimate the nonparametric coefficient functions under some regularity assumptions the proposed estimators are shown to be consistent and asymptotically normally distributed the sieve empirical likelihood ratio selr test statistic for detecting whether the varying coefficients are really constant and other related hypotheses is constructed and it follows approximately a chi squared distribution we introduce a modified bootstrap procedure to estimate the null distribution of the selr when sample size is s

point estimation with exponentially tilted empirical likelihood parameters defined via general estimating equations gee can be estimated by maximizing the empirical likelihood el newey and smith econometrica 72 2004 219 255 have recently shown that this el estimator exhibits desirable higher order asymptotic properties namely that its o n 1 bias is small and that bias corrected el is higher order efficient although el possesses these properties when the model is correctly specified this paper shows that in the presence of model misspecification el may cease to be root n convergent when the functions defining the moment conditions are unbounded even when their expectations are bounded in contrast the related exponential tilting et estimator avoids this problem this paper shows that the et and el estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood etel exhibiting the same o n 1 bias and the same o n 2 variance as el while maintaining root n convergence under model misspecification

recursive estimation methods for discrete systems in system identification the error evolution is composed of two decoupled parts one is the identifying information on the current estimation residual while the other is past arithmetic errors previous recursive algorithms only considered how to update current prediction errors up to now research has mostly been based on recursive least squares rls methods in this note a general recursive identification method is proposed for discrete systems using this new algorithm a recursive empirical frequency domain optimal parameter refop estimate is established the refop method has the advantage of resisting disturbance noise some simulations are included to illustrate the new method s reliability

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

data driven confidence intervals for diffusion process using double smoothing empirical likelihood abstract in this paper we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it compared with double smoothing local constant estimator double smoothing local linear estimator proposed in this paper is an inventive estimation method moreover we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation since the latter undermines the predictability of the estimator accordingly new algorithm for simulation is proposed through monte carlo simulation and empirical analysis both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate etc

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

empirical likelihood based inference in generalized random coefficient autoregressive model with conditional moment restrictions abstract this paper concentrates on the parameter estimating strategy for the generalized random coefficient autoregressive grca model in the presence of the auxiliary information we propose a weighted least squares estimate for the model parameters and empirical likelihood el based weights are obtained through using these auxiliary information the asymptotic distribution of our proposed estimator is normal distribution and the asymptotic variance is reduced compared to the least square ls estimator therefore our method yields more efficient estimates we also carry out some simulation experiments to assess the performance of the suggested estimator and illustrate the usefulness of this method through the analysis of a real time series data sets

large sample properties of weighted monte carlo estimators a general approach to improving simulation accuracy uses information about auxiliary control variables with known expected values to improve the estimation of unknown quantities we analyze weighted monte carlo estimators that implement this idea by applying weights to independent replications the weights are chosen to constrain the weighted averages of the control variables we distinguish two cases unbiased and biased depending on whether the weighted averages of the controls are constrained to equal their expected values or some other values in both cases the number of constraints is usually smaller than the number of replications so there may be many feasible weights we select maximally uniform weights by minimizing a separable convex function of the weights subject to the control variable constraints estimators of this form arise sometimes implicitly in several settings including at least two in finance calibrating a model to market data as in the work of avellaneda et al 2001 and calculating conditional expectations to price american options we analyze properties of these estimators as the number of replications increases we show that in the unbiased case weighted monte carlo reduces asymptotic variance and that all convex objective functions within a large class produce estimators that are very close to each other in a strong sense in contrast in the biased case the choice of objective function does matter we show explicitly how the choice of objective determines the limit to which the estimator converges

asymptotic optimality of empirical likelihood for testing moment restrictions we show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the exponential rate at which the probability of a type i error tends to zero unless the possible distributions for the observed data are restricted appropriately from this it follows that for the optimality claim for empirical likelihood in kitamura 2001 to hold additional assumptions and qualifications are required under stronger assumptions than those in kitamura 2001 we establish the following optimality result i empirical likelihood controls the rate at which the probability of a type i error tends to zero and ii among all procedures for which the probability of a type i error tends to zero at least as fast empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for most alternatives this result further implies that empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their type i error probabilities

time stepping discontinuous galerkin methods for fractional diffusion problems time stepping hp hp versions discontinuous galerkin dg methods for the numerical solution of fractional subdiffusion problems of order alpha with 1 alpha 0 1 0 will be proposed and analyzed generic hp hp version error estimates are derived after proving the stability of the approximate solution for h h version dg approximations on appropriate graded meshes near t 0 t 0 we prove that the error is of order o k max 2 p frac alpha 2 o kmax 2 p 2 where k k is the maximum time step size and p ge 1 p 1 is the uniform degree of the dg solution for hp hp version dg approximations by employing geometrically refined time steps and linearly increasing approximation orders exponential rates of convergence in the number of temporal degrees of freedom are shown finally some numerical tests are given

hamiltonian monte carlo sampling in bayesian empirical likelihood computation summary we consider bayesian empirical likelihood estimation and develop an efficient hamiltonian monte carlo method for sampling from the posterior distribution of the parameters of interest the method proposed uses hitherto unknown properties of the gradient of the underlying log empirical likelihood function we use results from convex analysis to show that these properties hold under minimal assumptions on the parameter space prior density and the functions used in the estimating equations determining the empirical likelihood our method employs a finite number of estimating equations and observations but produces valid semiparametric inference for a large class of statistical models including mixed effects models generalized linear models and hierarchical bayes models we overcome major challenges posed by complex non convex boundaries of the support routinely observed for empirical likelihood which prevent efficient implementation of traditional markov chain monte carlo methods like random walk metropolis hastings sampling etc with or without parallel tempering a simulation study confirms that our method converges quickly and draws samples from the posterior support efficiently we further illustrate its utility through an analysis of a discrete data set in small area estimation

sharp error estimate of the nonuniform l1 formula for linear reaction subdiffusion equations stability and convergence of the l1 formula on nonuniform time grids are studied for solving linear reaction subdiffusion equations with the caputo derivative a discrete fractional gronwall inequality is developed for the nonuniform l1 formula by introducing a discrete convolution kernel of riemann liouville fractional integral to simplify the consistency analysis of the nonuniform l1 formula we bound the local truncation error in a discrete convolution form and consider a global convolution error involving the discrete riemann liouville integral kernel with the help of discrete fractional gronwall inequality and global consistency error analysis a sharp error estimate reflecting the regularity of solution is obtained for a simple l1 scheme numerical examples are provided to verify the sharpness of the error analysis

fractional cable equation models for anomalous electrodiffusion in nerve cells finite domain solutions in recent work we introduced fractional nernst planck equations and related fractional cable equations to model electrodiffusion of ions in nerve cells with anomalous subdiffusion along and across the nerve cells this work was motivated by many computational and experimental studies showing that anomalous diffusion is ubiquitous in biological systems with binding crowding or trapping for example recent experiments have shown that anomalous subdiffusion occurs along the axial direction in spiny dendrites due to trapping by the spines we modeled the subdiffusion in two ways leading to two fractional cable equations and presented fundamental solutions on infinite and semi infinite domains here we present solutions on finite domains for mixed robin boundary conditions the finite domain solutions model passive electrotonic properties of spiny dendritic branch segments with ends that are voltage clamped sealed or killed the behavior of the finite domain solutions is similar for both fractional cable

bayesian estimation and comparison of moment condition models in this article we develop a bayesian semiparametric analysis of moment condition models by casting the problem within the exponentially tilted empirical likelihood etel framework we use this f

frequency independent and frequency dependent nonlinear models of twt amplifiers simple two parameter formulas are presented for the functions involved in the amplitude phase and the quadrature nonlinear models of a twt amplifier and are shown to fit measured data very well also a closed form expression is derived for the output signal of a twt amplifier excited by two phase modulated carriers and an expression containing a single integral is given when more than two such earriers are involved finally a frequencydependent quadrature model is proposed whose parameters are obtainable from single tone measurements

empirical likelihood semiparametric regression analysis for longitudinal data a semiparametric regression model for longitudinal data is considered the empirical likelihood method is used to estimate the regression coefficients and the baseline function and to construct confidence regions and intervals it is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made two calibrated empirical likelihood approaches to inference for the baseline function are developed we propose a groupwise empirical likelihood procedure to handle the inter series dependence for the longitudinal semiparametric regression model and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest this leads us to prove a nonparametric version of wilks theorem compared with methods based on normal approximations the empirical likelihood does not require consistent estimators for the asymptotic variance and bias a simulation compares the empirical likelihood and normal based methods in terms of coverage accuracies and average areas lengths of confidence regions intervals

empirical type likelihoods allowing posterior credible sets with frequentist validity higher order asymptotics summary with reference to a general class of empirical type likelihoods we develop higher order asymptotics for the frequentist coverage of bayesian credible sets based on posterior quantiles and highest posterior density these asymptotics in turn characterise members of the class that allow approximate frequentist validity of such sets it is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

a partially decoupled rls algorithm for volterra filters in this correspondence we consider a partially decoupled variation of the rls algorithm it is based on a constrained optimization of the cumulative filter error using the higher order sets of filter weights to improve on the performance of the lower order weight sets whose values are already established from this constrained optimization a recursive algorithm is developed whose form closely resembles the standard volterra rls algorithm but with structural differences that arise from eliminating the dependence of the lower order weight sets on the higher order weight sets while retaining the dependence of the higher order weights on the lower order weights the resulting algorithm while suboptimal requires less computational effort than the fully coupled version converges to steady state in the same amount of time and is shown by example not to exhibit a substantial degradation in performance

bayesian averaging prediction and nonnested model selection abstract this paper studies the asymptotic relationship between bayesian model averaging and post selection frequentist predictors in both nested and nonnested models we derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples this result depends crucially on the relation between posterior odds and frequentist model selection criteria weak conditions are given under which consistent model selection is feasible regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not in the sense that they select the best model with the least number of parameters with probability converging to 1 under these conditions bayesian posterior odds and bics are consistent for selecting among nested models but are not consistent for selecting among nonnested models and possibly overlapping models these findings have important bearing for applied researchers who are frequent users of model selection tools for empirical investigation of model predictions

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

fixed smoothing asymptotics in the generalized empirical likelihood estimation framework this paper concerns the fixed smoothing asymptotics for two commonly used estimators in the generalized empirical likelihood estimation framework for time series data namely the continuous updating estimator and the maximum blockwise empirical likelihood estimator for continuously updating generalized method of moments gmm estimator we show that the results for the two step gmm estimator in sun 2014a continue to hold under suitable assumptions for continuous updating estimator obtained through solving a saddle point problem newey and smith 2004 and the maximum blockwise empirical likelihood estimator kitamura 1997 we show that their fixed smoothing asymptotic distributions up to an unknown linear transformation are mixed normal based on these results we derive the asymptotic distributions of the specification tests including the over identification testing and testing on parameters under the fixed smoothing asymptotics where the corresponding limiting distributions are nonstandard yet pivotal simulation studies show that i the fixed smoothing asymptotics provides better approximation to the sampling distributions of the continuous updating estimator and the maximum blockwise empirical likelihood estimator as compared to the standard normal approximation the testing procedures based on the fixed smoothing critical values are more accurate in size than the conventional chi square based tests ii the continuously updating gmm estimator is asymptotically more efficient and the corresponding specification tests are generally more powerful than the other two competitors finite sample results from an empirical data analysis are also reported

error analysis of a finite difference method on graded meshes for a time fractional diffusion equation a reaction diffusion problem with a caputo time derivative of order alpha in 0 1 is considered the solution of such a problem is shown in general to have a weak singularity near the initial time t 0 and sharp pointwise bounds on certain derivatives of this solution are derived a new analysis of a standard finite difference method for the problem is given taking into account this initial singularity this analysis encompasses both uniform meshes and meshes that are graded in time and includes new stability and consistency bounds the final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme so one can choose an optimal mesh grading numerical results are presented that confirm the sharpness of the error analysis

numerical solution of the time fractional fokker planck equation with general forcing we study two schemes for a time fractional fokker planck equation with space and time dependent forcing in one space dimension the first scheme is continuous in time and discretized in space using a piecewise linear galerkin finite element method the second is continuous in space and employs a time stepping procedure similar to the classical implicit euler method we show that the space discretization is second order accurate in the spatial l 2 norm uniformly in time whereas the corresponding error for the time stepping scheme is o k alpha for a uniform time step k where alpha in 1 2 1 is the fractional diffusion parameter in numerical experiments using a combined fully discrete method we observe convergence behavior consistent with these results

regularity theory for time fractional advection diffusion reaction equations abstract we investigate the behavior of the time derivatives of the solution to a linear time fractional advection diffusion reaction equation allowing space and time dependent coefficients as well as initial data that may have low regularity our focus is on proving estimates that are needed for the error analysis of numerical methods the nonlocal nature of the fractional derivative creates substantial difficulties compared with the case of a classical parabolic pde in our analysis we rely on novel energy methods in combination with a fractional gronwall inequality and certain properties of fractional integrals

on bartlett correction of empirical likelihood in the presence of nuisance parameters summary lazar mykland 1999 showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be bartlett correctable this paper shows that bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest we establish in the broad framework of estimating functions that the empirical likelihood is still bartlett correctable if the nuisance parameter is profiled out given the value of the parameter of interest

improving semiparametric estimation by using surrogate data summary the paper considers estimating a parameter that defines an estimating function u y x for an outcome variable y and its covariate x when the outcome is missing in some of the observations we assume that in addition to the outcome and the covariate a surrogate outcome is available in every observation the efficiency of existing estimators for depends critically on correctly specifying the conditional expectation of u given the surrogate and the covariate when the conditional expectation is not correctly specified which is the most likely scenario in practice the efficiency of estimation can be severely compromised even if the propensity function of missingness is correctly specified we propose an estimator that is robust against the choice of the conditional expectation via an empirical likelihood we demonstrate that the estimator proposed achieves a gain in efficiency whether the conditional score is correctly specified or not when the conditional score is correctly specified the estimator reaches the semiparametric variance bound within the class of estimating functions that are generated by u the practical performance of the estimator is evaluated by using simulation and a data set that is based on the 1996 us presidential election

bayesian and frequentist confidence intervals arising from empirical type likelihoods summary for a general class of empirical type likelihoods for the population mean higher order asymp totics are developed with a view to characterizing its members which allow for any given prior the existence of a confidence interval that has approximately correct posterior as well as fre quentist coverage in particular it is seen that the usual empirical likelihood always allows such a confidence interval while many of its variants proposed in the literature do not enjoy this property an explicit form of the confidence interval is also given

bayesian exponentially tilted empirical likelihood summary while empirical likelihood has been shown to exhibit many of the properties of conven tional parametric likelihoods a formal probabilistic interpretation has so far been lacking we show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric bayesian procedure which places a type of noninformative prior on the space of distributions this prior gives preference to distributions having a small support and among those sharing the same support it favours entropy maximising distributions the resulting nonparametric bayesian procedure admits a computationally convenient representation as an empirical likelihood type likelihood where the probability weights are obtained via exponential tilting the proposed methodology provides an attractive alternative to the bayesian bootstrap as a nonparametric limit of a bayesian procedure for moment condition models

unified empirical likelihood ratio tests for functional concurrent linear models and the phase transition from sparse to dense functional data summary we consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points we propose test procedures based on the empirical likelihood with bias corrected estimating equations to conduct both pointwise and simultaneous inferences the asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses where sparse and dense functional data are considered in a unified framework we find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data specifically the tests proposed can detect alternatives of n order when the number of repeated measurements per curve is of an order larger than n 0 with n being the number of curves the transition points 0 for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem simulation studies and real data analyses are conducted to demonstrate the methods proposed

bayesian pseudo empirical likelihood intervals for complex surveys summary bayesian methods for inference on finite population means and other parameters by using sample survey data face hurdles in all three phases of the inferential procedure the formulation of a likelihood function the choice of a prior distribution and the validity of posterior inferences under the design based frequentist framework in the case of independent and identically distributed observations the profile empirical likelihood function of the mean and a non informative prior on the mean can be used as the basis for inference on the mean and the resulting bayesian empirical likelihood intervals are also asymptotically valid under the frequentist set up for complex survey data we show that a pseudo empirical likelihood approach can be used to construct bayesian pseudo empirical likelihood intervals that are asymptotically valid under the design based set up the approach proposed compares favourably with a full bayesian analysis under simple random sampling without replacement it is also valid under general single stage unequal probability sampling designs unlike a full bayesian analysis moreover the approach is very flexible in using auxiliary population information and can accommodate two scenarios which are practically important incorporation of known auxiliary population information for the construction of intervals by using the basic design weights calculation of intervals by using calibration weights based on known auxiliary population means or totals

bayesian empirical likelihood summary research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods this leads naturally to the possibility of using empirical likelihood as the basis for bayesian inference different ways in which this goal might be accomplished are considered the validity of the resultant posterior inferences is examined as are frequentist properties of the bayesian empirical likelihood intervals

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

asymptotic refinements of a misspecification robust bootstrap for gel estimators abstract i propose a nonparametric iid bootstrap procedure for the empirical likelihood the exponential tilting and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals and wald tests and confidence regions based on such estimators furthermore the proposed bootstrap is robust to model misspecification i e it achieves asymptotic refinements regardless of whether the assumed moment condition model is correctly specified or not this result is new because asymptotic refinements of the bootstrap based on these estimators have not been established in the literature even under correct model specification monte carlo experiments are conducted in dynamic panel data setting to support the theoretical finding as an application bootstrap confidence intervals for the returns to schooling of hellerstein and imbens 1999 are calculated the result suggests that the returns to schooling may be higher

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

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

empirical likelihood inference for the area under the roc curve for a continuous scale diagnostic test the most commonly used summary index of the receiver operating characteristic curve roc is the area under the curve auc that measures the accuracy of the diagnostic test in this article we propose an empirical likelihood el approach for the inference on the auc first we define an el ratio for the auc and show that its limiting distribution is a scaled chi square distribution we then obtain an el based confidence interval for the auc using the scaled chi square distribution this el inference for the auc can be extended to stratified samples and the resulting limiting distribution is a weighted sum of independent chi square distributions additionally we conduct simulation studies to compare the relative performance of the proposed el based interval with the existing normal approximation based intervals and bootstrap intervals for the auc

empirical likelihood as a goodness of fit measure summary the method of empirical likelihood can be viewed as one of allocating probabilities to an n cell contingency table so as to minimise a goodness of fit criterion it is shown that when the cressie read power divergence statistic is used as the criterion confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the cressie read parameter including 1 maximum entropy 0 empirical likelihood and 1 pearson s z2 it is noted that in the power divergence family empirical likelihood is the only member which is bartlettcorrectable however simulation results suggest that for the mean using a scaled f distribution yields more accurate coverage levels for moderate sample sizes

data tilting for time series summary we develop a general methodology for tilting time series data attention is focused on a large class of regression problems where errors are expressed through autoregressive processes the class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression robust statistical inference and estimation subject to constraints the method can be viewed as empirical likelihood with nuisance parameters

bayesian empirical likelihood for quantile regression bayesian inference provides a flexible way of combining data with prior information however quantile regression is not equipped with a parametric likelihood and therefore bayesian inference for quantile regression demands careful investigation this paper considers the bayesian empirical likelihood approach to quantile regression taking the empirical likelihood into a bayesian framework we show that the resultant posterior from any fixed prior is asymptotically normal its mean shrinks toward the true parameter values and its variance approaches that of the maximum empirical likelihood estimator a more interesting case can be made for the bayesian empirical likelihood when informative priors are used to explore commonality across quantiles regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas e g high or low percentile levels through empirical likelihood the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains by using an mcmc algorithm in the computation we avoid the daunting task of directly maximizing empirical likelihood the finite sample performance of the proposed method is investigated empirically where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels a theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method

on empirical likelihood statistical functions abstract we consider the empirical likelihood method for estimation of distribution and quantile functions where side information is incorporated through moment conditions we systematically study the asymptotic properties of the estimators such as the uniform strong laws of large numbers and weak convergence over classes of functions two monte carlo examples are also given to illustrate the practical utility of the method

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

asymptotic equivalence between the cox estimator and the general ml estimators of regression and survival parameters in the cox model the usual approach to estimating regression parameters in the cox regression model uses the partial likelihood if the covariates are not time dependent the model can be stated in terms of the survival function which allows one to derive a generalized likelihood containing both regression and survival curve parameters it is shown that in the absence of ties an estimator results which is asymptotically equivalent to the partial likelihood estimator a joint information matrix leads simply to standard errors for both regression and survival curve parameters which are asymptotically correct

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

constrained empirical likelihood confidence regions in nonignorable covariate missing data problems missing covariates in regression analysis are a pervasive problem in medical social and economic researches we study empirical likelihood confidence regions for unconstrained and constrained regression parameters in a nonignorable covariate missing data problem for an assumed conditional mean regression model we assume that some covariates are fully observed but other covariates are missing for some subjects by exploitation of a probability model of missingness and a working conditional score model from a semiparametric perspective we build a system of unbiased estimating equations where the number of equations exceeds the number of unknown parameters based on the proposed estimating equations we introduce unconstrained and constrained empirical likelihood ratio statistics to construct empirical likelihood confidence regions for the underlying regression parameters without and with constraints we establish the asymptotic distributions of the proposed empirical likelihood ratio statistics simulation results show that the proposed empirical likelihood methods have a better finite sample performance than other competitors in terms of coverage probability and interval length finally we apply the proposed empirical likelihood methods to the analysis of a data set from the us national health and nutrition examination survey

inference of the youden index and associated threshold using empirical likelihood for quantiles the youden index is a widely used measure in the framework of medical diagnostics where the effectiveness of a biomarker screening marker or predictor for classifying a disease status is studied when the biomarker is continuous it is important to determine the threshold or cut off point to be used in practice for the discrimination between diseased and healthy populations we introduce two methods aimed at estimating the youden index and its associated threshold the first one is a modified version of a recent approach based on the delta method and the second one is based on the adjusted empirical likelihood for quantiles in the setting of a two sample problem we also include cis for both of them in the simulation study we compare both methods under different scenarios finally a real example of prostatic cancer well known in the literature is analysed to provide the reader with a better understanding of the new methodology copyright 2011 john wiley sons ltd

jackknife empirical likelihood empirical likelihood has been found very useful in many different occasions however when applied directly to some more complicated statistics such as u statistics it runs into serious computational difficulties in this paper we introduce a so called jackknife empirical likelihood jel method the new method is extremely simple to use in practice in particular the jel is shown to be very effective in handling one and two sample u statistics the jel can be potentially useful for other nonlinear statistics

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

semiparametric approach to a random effects quantile regression model we consider a random effects quantile regression analysis of clustered data and propose a semiparametric approach using empirical likelihood the random regression coefficients are assumed independent with a common mean following parametrically specified distributions the common mean corresponds to the population average effects of explanatory variables on the conditional quantile of interest whereas the random coefficients represent cluster specific deviations in the covariate effects we formulate the estimation of the random coefficients as an estimating equations problem and use empirical likelihood to incorporate the parametric likelihood of the random coefficients a likelihood like statistical criterion function is proposed that which we show is asymptotically concave in a neighborhood of the true parameter value and motivates its maximizer as a natural estimator we use markov chain monte carlo samplers in the bayesian framework and propose the resulting quasi posterior mean as an estimator

semiparametric roc surfaces for continuous diagnostic tests based on two test measurements we propose a semiparametric method for estimating roc surfaces for continuous diagnostic tests based on two test measurements such a three class diagnostic problem based on two test measurements arises naturally from some dna amplification related diagnostic scenarios simulation results show that our proposed semiparametric roc surface estimator is more efficient than the nonparametric counterpart and is quite comparable with the parametric counterpart when model assumption of the data is correctly specified for the parametric method moreover when the parametric model assumption is not true our proposed semiparametric method is superior to both nonparametric and parametric methods some discussions and a simulated example along with r programs for implementation of the proposed method are also provided

tailored randomized block mcmc methods with application to dsge models in this paper we develop new markov chain monte carlo schemes for the estimation of bayesian models one key feature of our method which we call the tailored randomized block metropolis hastings tarb mh method is the random clustering of the parameters at every iteration into an arbitrary number of blocks then each block is sequentially updated through an m h step another feature is that the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing following chib and greenberg 1994 1995 and chib and ergashev 2008 we also provide an extended version of our method for sampling multi modal distributions in which at a pre specied mode jumping iteration a single block proposal is generated from one of the modal regions using a mixture proposal density and this proposal is then accepted according to an m h probability of move at the non mode jumping iterations the draws are obtained by applying the tarb mh algorithm we also discuss how the approaches of chib 1995 and chib and jeliazkov 2001 can be adapted to these sampling schemes for estimating the model marginal likelihood the methods are illustrated in several problems in the dsge model of smets and wouters 2007 for example which involves a 36 dimensional posterior distribution we show that the autocorrelations of the sampled draws from the tarb mh algorithm decay to zero within 30 40 lags for most parameters in contrast the sampled draws from the random walk m h method the algorithm that has been used to date in the context of dsge models exhibit signicant autocorrelations even at lags 2500 and beyond additionally the rw mh does not explore the same high density regions of the posterior distribution as the tarb mh algorithm another example concerns the model of an and schorfheide 2007 where the posterior distribution is multi modal while the rw mh algorithm is unable to jump from the low modal region to the high modal region and vice versa we show that the extended tarb mh method explores the posterior distribution globally in an ecient manner

discrete maximal regularity of time stepping schemes for fractional evolution equations in this work we establish the maximal ell p regularity for several time stepping schemes for a fractional evolution model which involves a fractional derivative of order alpha in 0 2 alpha ne 1 in time these schemes include convolution quadratures generated by backward euler method and second order backward difference formula the l1 scheme explicit euler method and a fractional variant of the crank nicolson method the main tools for the analysis include operator valued fourier multiplier theorem due to weis math ann 319 735 758 2001 doi 10 1007 pl00004457 and its discrete analogue due to blunck stud math 146 157 176 2001 doi 10 4064 sm146 2 3 these results generalize the corresponding results for parabolic problems

bayesian empirical likelihood inference with complex survey data we propose a bayesian empirical likelihood approach to survey data analysis on a vector of finite population parameters defined through estimating equations our method allows overidentified estimating equation systems and is applicable to both smooth and non differentiable estimating functions our proposed bayesian estimator is design consistent for general sampling designs and the bayesian credible intervals are calibrated in the sense of having asymptotically valid design based frequentist properties under single stage unequal probability sampling designs with small sampling fractions large sample properties of the bayesian inference proposed are established for both non informative and informative priors under the design based framework we also propose a bayesian model selection procedure with complex survey data and show that it works for general sampling designs an efficient markov chain monte carlo procedure is described for the required computation of the posterior distribution for general vector parameters simulation studies and an application to a real survey data set are included to examine the finite sample performances of the methods proposed as well as the effect of different types of prior and different types of sampling design

partially decoupled volterra filters formulation and lms adaptation the adaptation of volterra filters by one particular method the method of least mean squares lms while easily implemented is complicated by the fact that upper hounds for the values of step sizes employed by a parallel update lms scheme are difficult to obtain in this paper we propose a modification of the volterra filter in which the filter weights of a given order are optimized independently of those weights of higher order using this approach we then solve the minimum mean square error mmse filtering problem as a series of constrained optimization problems which produce a partially decoupled normal equation for the volterra filter from this normal equation we are able to develop an adaptation routine that uses the principles of partial decoupling that is similar in form to the volterra lms algorithm but with important structural differences that allow a straightforward derivation of bounds on the algorithm s step sizes these bounds can be shown to depend on the respective diagonal blocks of the volterra autocorrelation matrix this produces a reliable set of design guidelines that allow more rapid convergence of the lower order weight sets

likelihood ratio based confidence bands for survival functions abstract thomas and grunkemeier introduced a nonparametric likelihood ratio approach to confidence interval estimation of survival probabilities based on right censored data we construct simultaneous confidence bands using this approach the boundaries of the bands are contained within 0 1 a procedure essentially equivalent to a bias correction is developed the resulting increase in coverage accuracy is illustrated by an example and a simulation study we look at various versions of log likelihood ratio based confidence bands and compare them to the hall wellner band and nair s equal precision band we also construct likelihood ratio based bands for cumulative hazard functions

random sieve likelihood and general regression models abstract consider a semiparametric regression model y f x where f is a known function is an unknown vector consists of a random error and possibly of some unobserved variables and the distribution f of x is unspecified this article introduces in a general setting new methodology for estimating and f the proposed method constructs a profile likelihood defined on random level sets a random sieve the proposed method is related to empirical likelihood but is more generally applicable four examples are discussed including a quadratic model high dimensional semiparametric regression a nonparametric random effects model and linear regression with right censored data simulation results and asymptotic analysis support the utility and effectiveness of the proposed method

nonparametric likelihood ratio confidence intervals we consider construction of two sided nonparametric confidence intervals in a smooth function model setting a nonparametric likelihood approach based on stein s least favourable family is proposed as an alternative to empirical likelihood the approach enjoys the same asymptotic properties as empirical likelihood but is analytically and computationally less cumbersome the simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as a means of reducing coverage error to levels comparable with those obtained by more computationally intensive techniques such as the iterated bootstrap a simulation study confirms that coverage error may be substantially reduced by simple analytic adjustment of the nonparametric likelihood interval and that bootstrapping the distribution of the nonparametric likelihood ratio results in very desirable coverage accuracy

estimation with survey data under nonignorable nonresponse or informative sampling nonresponse is a very common phenomenon in survey sampling nonignorable nonresponse that is a response mechanism that depends on the values of the variable having nonresponse is the most difficult type of nonresponse to handle this article studies a likelihood based estimation method for data with nonignorable nonresponse the likelihood is semiparametric in the sense that it consists of a parametric component for the response mechanism such as a logistic model and a nonparametric component for the distribution of the variable of interest and the covariates we show how auxiliary information can be augmented to improve the efficiency of estimators asymptotic distributions for the resulting parameter estimates are derived a simulation study shows that the proposed method gives promising results the method can also be applied to problems with two phase sampling in which the second phase sampling is informative

testing conditional moment restrictions let x z be a pair of observable random vectors we construct a new smoothed empirical likelihood based test for the hypothesis e g z x 0 w p 1 where g is a vector of known functions and an unknown finite dimensional parameter we show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives furthermore the test is shown to possess an optimality property in large samples simulation evidence suggests that it also behaves well in small samples

empirical likelihood based inference in missing response problems and its application in observational studies summary the problem of missing response data is ubiquitous in medical and social science studies in the case of responses that are missing at random depending on some covariate information analyses focused only on the complete data may lead to biased results various debias methods have been extensively studied in the literature particularly the weighting method that was motivated by horvitz and thompson s estimators to improve efficiency robins rotnitzky and zhao proposed augmented estimating equations based on corrected complete case analyses a nice feature of the augmented method is its double robustness i e the estimator that is derived from the augmented method is asymptotically unbiased if either the underlying missing data mechanism or the underlying regression function is correctly specified furthermore the augmented estimator can achieve full efficiency if both the missing data mechanism and the regression function are correctly specified in general however it is very difficult to specify the regression function correctly especially when the dimension of covariates is high this is the so called curse of dimensionality problem the augmented estimator has much lower efficiency if the working regression model is not close to the true regression model in this paper the empirical likelihood method is employed to seek a constrained empirical likelihood estimation of mean response with the assumption that responses are missing at random the empirical likelihood based estimators enjoy the double robustness property moreover it is possible that the empirical likelihood based inference can produce asymptotically unbiased and efficient estimators even if the true regression function is not completely known simulation results indicate that the empirical likelihood based estimators are very robust to a misspecification of the propensity score and dominate other competitors in the sense of having smaller mean square errors methods that are developed in this paper have a nice application in observational causal inferences the propensity score is used to adjust for differences in pretreatment variables in the estimation of average treatment effects

on the bootstrap and likelihood based confidence regions summary we describe a method for constructing likelihood based confidence regions for a vector parameter using the bootstrap and nonparametric density estimation the technique is illustrated by application to a numerical example and its theoretical properties are elucidated it is argued that likelihood based regions should not be approximated by ellipses if we are to have any hope of capturing first order departures from normality bootstrap algorithms for constructing simultaneous confidence intervals for the components of a vector parameter are also presented advantages of the percentile t method over the ordinary percentile method are demonstrated in a multivariate setting

merging information for semiparametric density estimation summary the density ratio model specifies that the likelihood ratio of m 1 probability density functions with respect to the mth is of known parametric form without reference to any parametric model we study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood the combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions we adopt variants of well established techniques to choose the smoothing parameter for the density estimators proposed

existence and regularity of solutions to time fractional diffusion equations we investigate some initialboundary value problems for time fractional diffusion equations of order 0 1 such equations model anomalous diffusion on fractals the existence of solution irrelevant to is established only if the external force function f is weighted hlder continuous which is weaker than hlder continuous some interesting versions of maximal and spatial regularity criteria depending on the fractional exponent are also discussed