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

using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys design weights in surveys are often adjusted to accommodate auxiliary information and to meet pre specified range restrictions typically via some ad hoc algorithmic adjustment to a generalised regression estimator in this paper we present a simple solution to this problem using empirical likelihood methods or generalised regression we first develop algorithms for computing empirical likelihood estimators and model calibrated empirical likelihood estimators the first algorithm solves the computational problem of the empirical likelihood method in general both in survey and non survey settings and theoretically guarantees its convergence the second exploits properties of the model calibration method and is particularly simple the algorithms are adapted for handling benchmark constraints and pre specified range restrictions on the weight adjustments

explicit description of irreducible gl2 qp representations over f p let p be an odd prime number the classi cation of irreducible representations of gl2 qp over fp is known thanks to the works of barthel livne and breuil in the present paper we illustrate an exhaustive description of such irreducible representations through the study of certain functions on the bruhat tits tree of gl2 qp in particular we are able to detect the socle ltration for the kz restriction of supersingular representations principal series and special series

adjustment by minimum discriminant information minimum discriminant information adjustment has primarily been used in the analysis of multinomial data however no such restriction is necessary let p be a distribution on ra and let be a convex set of distributions on ra let xi 1 c i c n be independent and identically distributed observations with common distribution p the minimum discriminant information adjustment mdia of p relative to is the element q of that is closest to p in the sense of kullback leibler discriminant information if pn is the empirical distribution of the xi 1 s i c n and qn is the mdia of pn relative to then qn is the maximum likelihood estimate in y let y consist of distributions a on r such that f t da t where t is a measurable transformation from r to rb and t e rb it is shown that under mild regularity conditions qn converges weakly to q the mdia of the true p with probability 1 and that en d f ddqn is an asymptotically normal and asymptotically unbiased estimate of e d f d dq

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

locally solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method abstractaccurate seismic modeling in realistic media serves as the basis of seismic full waveform inversion and imaging recently viscoacoustic seismic modeling incorporating attenuation effects has been performed by solving a fractional laplacian viscoacoustic wave equation in this equation attenuation being spatially heterogeneous is represented partially by the spatially varying power of the fractional laplacian operator previously approximated by the global fourier method we have developed a local spectral approach based on the hermite distributed approximating functional hdaf method to implement the fractional laplacian in the viscoacoustic wave equation our approach combines local methods simplicity and global methods accuracy several numerical examples are developed to evaluate the feasibility and accuracy of using the hdaf method for the frequency independent q fractional laplacian wave equation

estimation of reliability in field performance studies likelihood based methods are developed for the analysis of field performance studies with particular attention centered on the estimation of regression coefficients in parametric models failure record data are those in which the time to failure and the regressor variables are observed only for those items that fail in some prespecified follow up or warranty period 0 t it is noted that for satisfactory inference about baseline failure rates or regression effects it is usually necessary to supplement the failure record data either by incorporating specific prior information about x or by taking a supplementary sample of items that survive t general methods are outlined and specific formulas for various likelihood based methods are obtained when the failure time model is exponential or weibull in these models the methods are compared with respect to asymptotic efftciency of estimation several extensions to more complicated sampling plans are considered

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

a model calibration approach to using complete auxiliary information from survey data suppose that the finite population consists of n identifiable units associated with the ith unit are the study variable yi and a vector of auxiliary variables xi the values x1 x2 xn are known for the entire population i e complete but yi is known only if the ith unit is selected in the sample one of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage in this article a unified model assisted framework has been attempted using a proposed model calibration technique the proposed model calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of deville and sarndal and or the generalized regression estimators in the linear model case the pseudoempirical maximum likelihood estimator of chen and sitter when used in this setting gives an estimator that is asymptotically equivalent to the model calibration estimator but with positive weights some existing estimators

modelling complex survey data with population level information an empirical likelihood approach survey data are often collected with unequal probabilities from a stratified population in many modelling situations the parameter of interest is a subset of a set of parameters with the others treated as nuisance parameters we show that in this situation the empirical likelihood ratio statistic follows a chi squared distribution asymptotically under stratified single and multi stage unequal probability sampling with negligible sampling fractions simulation studies show that the empirical likelihood confidence interval may achieve better coverages and has more balanced tail error rates than standard approaches involving variance estimation linearization or resampling

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

sur quelques representations supersingulieres de gl2 qpf abstract fix a prime number p 5 an integer f 1 and let q p f be the unramified extension of q p of degree f by c breuil and v pask nas 2007 5 to a generic semi simple continuous representation gal q p q p f gl 2 f p we can associate a parameterized family of smooth admissible representations of gl 2 q p f with coefficients in f p in this article we prove that there are more parameters than those known

empirical likelihood estimation for finite populations and the effective usage of auxiliary information summary in finite population inference problems auxiliary population information is often available we show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information we prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information a bahadur type representation for empirical likelihood sample quantiles is given simulation results show that the empirical likelihood estimates perform well among a number of competitors and are model robust

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

efficient estimation of quadratic finite population functions in the presence of auxiliary information by viewing quadratic and other second order finite population functions as totals or means over a derived synthetic finite population we show that the recently proposed model calibration and pseudoempirical likelihood methods for effective use of auxiliary information from survey data can be readily extended to obtain efficient estimators of quadratic and other second order finite population functions in particular estimation of a finite population variance covariance or variance of a linear estimator can be greatly improved when auxiliary information is available the proposed methods are model assisted in that the resulting estimators are asymptotically design unbiased irrespective of the correctness of a working model but very efficient if the working model is nearly correct they have a number of attractive features which include applicability to a general sampling design incorporation of information on possibly multivariate auxiliary variables and the ability to entertain linear or nonlinear

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

estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments abstract a well known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments in this paper we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability these unconditional moments depend on the instruments generated from a generically comprehensively revealing function and they are further projected along the exponential fourier series the objective function is based on the resulting fourier coefficients from which an estimator can be easily computed a novel feature of our method is that the full continuum of unconditional moments is incorporated into each fourier coefficient we show that when the number of fourier coefficients in the objective function grows at a proper rate the proposed estimator is consistent and asymptotically normally distributed an efficient estimator is also readily obtained via the conventional two step gmm method our simulations confirm that the proposed estimator compares favorably with that of dominguez and lobato 2004 econometrica in terms of bias standard error and mean squared error

efficient derivative pricing by the extended method of moments in this paper we introduce the extended method of moments xmm estimator this estimator accommodates a more general set of moment restrictions than the standard generalized method of moments gmm estimator more specifically the xmm differs from the gmm in that it can handle not only uniform conditional moment restrictions i e valid for any value of the conditioning variable but also local conditional moment restrictions valid for a given fixed value of the conditioning variable the local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns the estimated derivative prices are consistent for a large time series dimension but a fixed number of cross sectionally observed derivative prices the asymptotic properties of the xmm estimator are nonstandard since the combination of uniform and local conditional moment restrictions induces different rates of convergence parametric and nonparametric for the parameters

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

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

the classification of irreducible admissible mod p representations of a p adic gln let f be a finite extension of p using the mod p satake transform we define what it means for an irreducible admissible smooth representation of an f split p adic reductive group over overline mathbb f p to be supersingular we then give the classification of irreducible admissible smooth gln f representations over overline mathbb f p in terms of supersingular representations as a consequence we deduce that supersingular is the same as supercuspidal these results generalise the work of barthel livne for n 2 for general split reductive groups we obtain similar results under stronger hypotheses

empirical likelihood confidence intervals for complex sampling designs we define an empirical likelihood approach which gives consistent design based confidence intervals which can be calculated without the need of variance estimates design effects resampling joint inclusion probabilities and linearization even when the point estimator is not linear it can be used to construct confidence intervals for a large class of sampling designs and estimators which are solutions of estimating equations it can be used for means regressions coefficients quantiles totals or counts even when the population size is unknown it can be used with large sampling fractions and naturally includes calibration constraints it can be viewed as an extension of the empirical likelihood approach to complex survey data this approach is computationally simpler than the pseudoempirical likelihood and the bootstrap approaches the simulation study shows that the confidence interval proposed may give better coverages than the confidence intervals based on linearization bootstrap and pseudoempirical likelihood our simulation study shows that under complex sampling designs standard confidence intervals based on normality may have poor coverages because point estimators may not follow a normal sampling distribution and their variance estimators may be biased

information recovery in a study with surrogate endpoints recently there has been a lot of interest in statistical methods for analyzing data with surrogate endpoints in this article we consider parameter estimation from a model that relates a variable y to a set of covariates x in the presence of a surrogate s we assume that the data are made up of two random samples from the population a validation set where y x s are observed on every subject and a nonvalidation set where only x s are measured we show how information from the nonvalidation set can be incorporated to improve upon estimation of a parameter using the validation data only the method we suggest does not require knowledge on the joint distribution between y s given x it is based on a two sample empirical likelihood that simultaneously combines the estimating equations from the validation set and the nonvalidation set the proposed nonparametric likelihood formulation brings a few attractive features to the inference in first the maximum empirical likelihood estimate is m

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 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

neglected heterogeneity in moment condition models abstract the central concern of this paper is parameter heterogeneity in models specified by a number of unconditional or conditional moment conditions and thereby the provision of a framework for the development of apposite optimal m tests against its potential presence we initially consider the unconditional moment restrictions framework optimal m tests against moment condition parameter heterogeneity are derived with the relevant jacobian matrix obtained in terms of the second order own derivatives of the moment indicator in a leading case gmm and gel tests of specification based on generalized information matrix equalities appropriate for moment based models are described and their relation to optimal m tests against moment condition parameter heterogeneity examined a fundamental and important difference is noted between gmm and gel constructions the paper is concluded by a generalization of these tests to the conditional moment context and the provision of a limited set of simulation experiments to illustrate the efficacy of the proposed tests

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

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

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

miscellanea combining parametric and empirical likelihoods imbens lancaster 1994 pointed out that census reports can be interpreted as providing nearly exact knowledge of moments of the marginal distribution of economic variables in this paper we show that empirical likelihood can effectively incorporate auxiliary information like this as long as it can be summarised as unbiased estimating equations by combining empirical and parametric likelihoods we show that the combined likelihood can produce valid inferences for the underlying parameters a wilks type theorem is proved for the combined likelihood ratio statistic simulation results demonstrate that the performance of the combined likelihood ratio confidence intervals is better than conventional confidence intervals that use a normal approximation

a bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data with applications to analysis of quality of life outcomes in clinical trials this article is concerned about the test for the difference in the distributions of multigroup proportional data which is motivated by the problem of comparing the distributions of quality of life qol outcomes among different treatment groups in clinical trials the proportional data such as qol outcomes assessed by answers to questions on a questionnaire are bounded in a closed interval such as 0 1 with continuous observations in 0 1 and in addition excess observations taking the boundary values 0 and or 1 common statistical procedures used in practice such as t and rank based tests may not be very powerful since they ignore the specific feature of the proportional data in this article we propose a three component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in 0 1 a semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi squared random variable under null hypothesis a nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test simulation studies are performed to evaluate the empirical type i error and power of the proposed test procedure and compare it with likelihood ratio tests lrts under parametric distribution assumptions rank based kruskal wallis test and wald type test the proposed test procedure is also applied to the analysis of qol outcomes from a clinical trial on colorectal cancer that motivated our study

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

comparison of parametric and empirical likelihood functions summary in this paper parametric and empirical likelihood functions or surfaces are compared in particular first and second order expansions for log likelihood functions are developed in nonparametric and parametric situations where the functional of interest is a smooth function of vector means the two approaches are compared and the precise order of difference between the nonparametric and parametric log likelihood functions is obtained in general the surfaces need not agree to first order however in certain exponential family models the surfaces are quite close in a distributional sense moreover empirical likelihood can be thought of as an approximation to a true parametric likelihood based on a parametric least favourable family

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

penalized high dimensional empirical likelihood we propose penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models by using an appropriate penalty function we showthat penalized empirical likelihood has the oracle property that is with probability tending to 1 penalized empirical likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance the advantage of penalized empirical likelihood as a nonparametric likelihood approach is illustrated by testing hypotheses and constructing confidence regions numerical simulations confirm our theoretical findings

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

the sine gordon equation in the finite line a rather complete numerical study of the perturbed and nonperturbed sine gordon equation in one dimensional cartesian coordinates and finite domains is presented the numerical study is based on five three point linearly implicit finite difference methods of different spatial accuracy for the unperturbed sge the accuracy of these five methods is found to be very sensitive to the implicitness parameter less sensitive to the spatial order of accuracy and almost no sensitive to the time step for second order accurate temporal discretizations the largest errors of the five methods were found to occur at the front of the soliton solution of the unperturbed sge but the techniques were very accurate for long time computations of the unperturbed sge in both infinite domains and in finite domains upon many collisions of the kinks and antikinks with the boundaries despite the fact that they do not preserve a discrete energy it is shown that the largest values of the kinetic and total energies and the smallest values of the strain and potential energies occur when solitons and antisolitons strike on the boundaries subject to homogeneous neumann conditions and the four energies remain constant between collisions with the boundaries for the malomed s perturbation one of the fronts of the soliton soliton doublet and soliton antisoliton doublet is trapped at one boundary and the other one undergoes a change in amplitude and its front describes a curved trajectory the soliton antisoliton breather oscillates in a damped manner and slowly drifts towards one boundary the soliton antisoliton soliton soliton doublet and soliton antisoliton doublet of the unperturbed sge are robust under kivshar and malomed s perturbations whereas the soliton antisoliton breather loses its integrity becomes a kink antikink pair and then yields a chaotic behaviour in both space and time small amplifications proportional to the first order temporal derivative of the amplitude do not alter substantially the initial dynamics of the soliton antisoliton soliton soliton doublet and soliton antisoliton doublet but their amplitudes exhibit oscillatory behaviour of increasing amplitude at large times however small amplifications cause first a transition from the soliton antisoliton breather to the kink antikink solution a linearized stability analysis of the spatially homogeneous solutions of the unperturbed sge is performed and analytical solutions are obtained by means of the method of separation of variables for both homogeneous dirichlet and neumann boundary conditions and the results show that the solution corresponding to a zero amplitude is oscillatory in both space and time whereas that corresponding to an amplitude equal to p may exhibit exponential or linear growth depending on the length of the domain if either of these growths is present it is shown that the evolution of small initial perturbations may result in homoclinic crossings and chaotic behaviour in both space and time in the absence of perturbations in the sge and the existence of an attractor when perturbations of the malomed s type are present in either case the solution may exhibit certain spatial symmetries or antisymmetries at large times finally the results presented in this paper indicate that the accurate computation of homoclinic orbits of the sge is not only controlled by the spatial accuracy of the numerical method but also by its energy preserving characteristics and perhaps by the number of grid points used in the numerical technique

efficient robust regression via two stage generalized empirical likelihood large and finite sample efficiency and resistance to outliers are the key goals of robust statistics although often not simultaneously attainable we develop and study a linear regression estimator that comes close efficiency is obtained from the estimator s close connection to generalized empirical likelihood and its favorable robustness properties are obtained by constraining the associated sum of weighted squared residuals we prove maximum attainable finite sample replacement breakdown point and full asymptotic efficiency for normal errors simulation evidence shows that compared to existing robust regression estimators the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance the estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers

numerical solutions of nonlinear wave equations accurate stable numerical solutions of the nonlinear sine gordon equation are obtained with particular consideration of initial conditions that are exponentially close to the phase space homoclinic manifolds earlier local grid based numerical studies have encountered difficulties including numerically induced chaos for such initial conditions the present results are obtained using the recently reported distributed approximating functional method for calculating spatial derivatives to high accuracy and a simple explicit method for the time evolution the numerical solutions are chaos free for the same conditions employed in previous work that encountered chaos moreover stable results that are free of homoclinic orbit crossing are obtained even when initial conditions are within 10 27 of the phase space separatrix value p it also is found that the present

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

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

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

pseudo likelihood theory for empirical likelihood it is proved that except for a location term empirical likelihood does draw contours which are second order correct for those of a pseudo likelihood however except in the case of one dimension this pseudo likelihood is not that which would commonly be employed when constructing a likelihood based confidence region it is shown that empirical likelihood regions may be adjusted for location so as to render them second order correct furthermore it is proved that location adjusted empirical likelihood regions are bartlett correctable in a certain sense

median estimation in the presence of auxiliary information summary this paper deals with the estimation under simple random sampling of a finite population median in the presence of an auxiliary variable an estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach these estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known on the basis of the asymptotic properties derived and some simulation results the efficiencies of these estimators are compared it is shown that the two estimators proposed unlike that obtained from modifying the ratio estimator always dominate the sample median in mean squared error and that their efficiencies depend directly on the probability of concordance rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable when the linearity assumption is approximately satisfied the three estimators are seen to have comparable efficiencies while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumnption

constrained maximum likelihood estimation for model calibration using summary level information from external big data sources information from various public and private data sources of extremely large sample sizes are now increasingly available for research purposes statistical methods are needed for using information from such big data sources while analyzing data from individual studies that may collect more detailed information required for addressing specific hypotheses of interest in this article we consider the problem of building regression models based on individual level data from an internal study while using summary level information such as information on parameters for reduced models from an external big data source we identify a set of very general constraints that link internal and external models these constraints are used to develop a framework for semiparametric maximum likelihood inference that allows the distribution of covariates to be estimated using either the internal sample or an external reference sample we develop extensions for handling complex stratified sampling designs such as case co

empirical likelihood inference under stratified random sampling using auxiliary population information summary the empirical likelihood method under stratified random sampling is used for making inferences on finite population parameters our results show that it can lead to efficient estimators by making effective use of auxiliary population information in the form of overall population totals or means ascertained from external sources empirical likelihood ratio confidence intervals for the population mean are also studied and adjusted intervals with asymptotically correct coverage rates are obtained

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