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

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

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

non optimal levels of a reducible mod l modular representation let 3 be a prime and n be a square free integer prime to for each prime p dividing n let ap be either 1 or 1 we give a sufficient criterion for the existence of a newform f of weight 2 for 0 n such that the mod galois representation attached to f is reducible and upf apf for primes p dividing n the main techniques used are level raising methods based on an exact sequence due to ribet

rigidity transition in two dimensional random fiber networks rigidity percolation is analyzed in two dimensional random fibrous networks the model consists of central forces between the adjacent crossing points of the fibers two strategies are used to incorporate rigidity adding extra constraints between second nearest crossing points with a probability p sn and welding individual crossing points by adding there four additional constraints with a probability p weld and thus fixing the angles between the fibers these additional constraints will make the model rigid at a critical probability p sn p sn c and p weld p weld c respectively accurate estimates are given for the transition thresholds and for some of the associated critical exponents the transition is found in both cases to be in the same universality class as that of the two dimensional central force rigidity percolation in diluted lattices

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 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

profile likelihood inference for highly accurate diagnostic tests nous envisageons une inference sur la vraisemblance de profil basee sur la distribution multinomiale pour evaluer la precision d un test diagnostic la methode s applique a des donnees ordinales quand la precision est evaluee au moyen de l aire sous la courbe caracteristique du receveur courbe roc des resultats de simulation suggerent que les intervalles de confiance derives ont vies probabilites de couverture acceptables meme lorsque les tailles d echantillons sont petites et que le test diagnostic a une haute precision les methodes s etendent a des contextes stratifies et a des situations ou les evaluations sont correlees nous illustrons les methodes sur des donnees provenant d un essai clinique sur la detection du cancer de l ovaire

rigidity of random networks of stiff fibers in the low density limit rigidity percolation is analyzed in two dimensional random networks of stiff fibers as fibers are randomly added to the system there exists a density threshold q q min above which a rigid stress bearing percolation cluster appears this threshold is found to be above the connectivity percolation threshold q q c such that q min 1 1698 0 0004 q c the transition is found to be continuous and in the universality class of the two dimensional central force rigidity percolation on lattices at percolation threshold the rigid backbone of the percolating cluster was found to break into rigid clusters whose number diverges in the limit of infinite system size when a critical bond is removed the scaling with system size of the average size of these clusters was found to give a new scaling exponent delta 1 61 0 04

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

on the computation of local components of a newform the problem let f be a cuspidal newform for 1 n with weight k 2 and character e there are well established methods for computing such forms using modular symbols see ste07 let f be the corresponding automorphic representation of the adele group gl2 aq

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

floppy modes and the free energy rigidity and connectivity percolation on bethe lattices we show that the negative of the number of ital floppy modes behaves as a ital free energy for both connectivity and rigidity percolation and we illustrate this result using bethe lattices the rigidity transition on bethe lattices is found to be first order at a bond concentration close to that predicted by maxwell constraint counting we calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster and show how a ital specific heat can be defined as the second derivative of the free energy we demonstrate that the bethe lattice solution is equivalent to that of the random bond model where points are joined randomly with equal probability at all length scales to have a given coordination and then subsequently bonds are randomly removed copyright ital 1999 ital the american physical society

jamming graphs a local approach to global mechanical rigidity we revisit the concept of minimal rigidity as applied to frictionless repulsive soft sphere packings in two dimensions with the introduction of the jamming graph minimal rigidity is a purely combinatorial property encoded via laman s theorem in two dimensions it constrains the global average coordination number of the graph for example however minimal rigidity does not address the geometry of local mechanical stability the jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability we demonstrate how jamming graphs can be constructed using local moves via the henneberg construction such that these graphs fall under the jurisdiction of correlated percolation we then probe how jamming graphs destabilize or become unjammed by deleting a bond and computing the resulting rigid cluster distribution we also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra redundant contacts destabilizes the latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut out or frozen in subsystems

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

generic rigidity in three dimensional bond bending networks much progress can be made in studying the mechanical stability of frameworks when they are treated as generic which lack any special symmetries this is because testing for rigidity becomes topological in nature rather than geometrical generic rigidity synonymous with graph rigidity depends only on the connectivity of the network making it a simpler problem to deal with in principle a complete combinatorial constraint counting characterization of graph rigidity is given by laman s theorem for two dimensions unfortunately there is no known corresponding theorem for three dimensions herein it is proposed that the theorem of laman generalizes to three dimensions for bar joint networks that have no implied hinge joints particular attention is given to bond bending networks having a truss structure with constraints between nearest and next nearest neighbours that are suitable for modelling many covalent network glasses and macromolecules it is shown that implied hinge joints do not exist in bond bending networks based on the proposition that an all subgraph constraint counting characterization of generic rigidity is recovered in three dimensional bar joint networks having no implied hinge joints an efficient combinatorial algorithm is constructed for bond bending networks complete agreement is found with exact calculations involving diagonalization of dynamical matrices for systems up to degrees of freedom

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

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

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

rigidity percolation by next nearest neighbor bonds on generic and regular isostatic lattices we study rigidity percolation transitions in two dimensional central force isostatic lattices including the square and the kagome lattices as next nearest neighbor bonds braces are randomly added to the system in particular we focus on the differences between regular lattices which are perfectly periodic and generic lattices with the same topology of bonds but whose sites are at random positions in space we find that the regular square and kagome lattices exhibit a rigidity percolation transition when the number of braces is llnl where l is the linear size of the lattice this transition exhibits features of both first order and second order transitions the whole lattice becomes rigid at the transition and a diverging length scale also exists in contrast we find that the rigidity percolation transition in the generic lattices occur when the number of braces is very close to the number obtained from maxwell s law for floppy modes which is l the transition in generic lattices is a very sharp first order like transition at which the addition of one brace connects all small rigid regions in the bulk of the lattice leaving only floppy modes on the edge we characterize these transitions using numerical simulations and develop analytic theories capturing each transition our results relate to other interesting problems including jamming and bootstrap percolation

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

finite temperature mechanical instability in disordered lattices mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities we develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite temperature mechanical stabilities in various disordered systems we use this theory to study two disordered lattices a randomly diluted triangular lattice and a randomly braced square lattice these two lattices belong to two different universality classes as they approach mechanical instability at t 0 we show that thermal fluctuations stabilize both lattices in particular the triangular lattice displays a critical regime in which the shear modulus scales as g t 1 2 whereas the square lattice shows g t 2 3 we discuss generic scaling laws for finite t mechanical instabilities and relate them to experimental systems

empirical likelihood based inference in linear errors in covariables models with validation data summary linear errors in covariables models are considered assuming the availability of independent validation data on the covariables in addition to primary data on the response variable and surrogate covariables we first develop an estimated empirical loglikelihood with the help of validation data and prove that its asymptotic distribution is that of a weighted sum of independent standard z2 random variables with unknown weights by estimating the unknown weights consistently we construct an estimated empirical likelihood confidence region for the regression parameter vector we also suggest an adjusted empirical loglikelihood and prove that its asymptotic distribution is a standard x2 to avoid estimating the unknown weights or the adjustment factor we propose a partially smoothed bootstrap empirical loglikelihood for constructing a confidence region which has asymptotically correct coverage probability a simulation study is conducted to compare the proposed methods with a method based on a normal approximation in terms of coverage accuracy and average length of the confidence interval

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

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

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

self organization with equilibration a model for the intermediate phase in rigidity percolation recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self organization of the glass network resulting from the tendency to minimize its internal stress however the exact nature of this experimentally measured phase remains unclear we modified a previously proposed model of self organization by generating a uniform sampling of stress free networks in our model studied on a diluted triangular lattice an unusual intermediate phase appears in which both rigid and floppy networks have a chance to occur a result also observed in a related model on a bethe lattice by barr e et al phys rev lett 94 208701 2005 our results for the bond configurational entropy of self organized networks which turns out to be only about 2 lower than that of random networks suggest that a self organized intermediate phase could be common in systems near the rigidity percolation threshold

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

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

confidence tubes for multiple quantile plots via empirical likelihood the nonparametric empirical likelihood approach is used to obtain simultaneous confidence tubes for multiple quantile plots based on k independent possibly right censored samples these tubes are asymptotically distribution free except when both k 3 and censoring is present pointwise versions of the confidence tubes however are asymptotically distribution free in all cases the various confidence tubes are valid under minimal conditions the proposed methods are applied in three real data examples 1 introduction the quantile quantile q q plot is a well known and attractive graphical method for comparing two distributions especially when confidence limits are added in this paper we develop q q plot methods for the comparison of two or more distributions from randomly censored data more specifically we consider the problem of finding simultaneous confidence tubes for multiple quantile plots for brevity multi q plots from k independent samples of possibly right censored survival times the multi q plot is defined to be the k dimensional curve q1 p qk p parameterized by 0 p 1 where qj is the quantile function of the jth distribution it specializes to the ordinary q q plot in the two sample case the comparison of quantile functions is particularly useful for the analysis of survival data in biomedical settings frail and strong individuals corresponding to low and high values of p often respond to different treatments in different ways so treatment effects can be hard to determine from comparison of mean or median survival times alone see for example doksum 1974 the approach developed here allows comparison of treatments simultaneously across all frailty levels our approach is based on the nonparametric empirical likelihood method this method was originally developed by thomas and grunkemeier 1975 and owen 1988 1990 as a way of improving upon wald type confidence regions there now exists a substantial literature on empirical likelihood indicating that it is widely viewed as a desirable and natural approach to

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

intentionally biased bootstrap methods summary a class of weighted bootstrap techniques called biased bootstrap or b bootstrap methods is introduced it is motivated by the need to adjust empirical methods such as the uniform bootstrap in a surgical way to alter some of their features while leaving others unchanged depending on the nature of the adjustment the b bootstrap can be used to reduce bias or to reduce variance or to render some characteristic equal to a predetermined quantity examples of the last application include a b bootstrap approach to hypothesis testing in nonparametric contexts where the b bootstrap enables simulation under the null hypothesis even when the hypothesis is false and a b bootstrap competitor to tibshirani s variance stabilization method an example of the bias reduction application is adjustment of nadaraya watson kernel estimators to make them competitive with local linear smoothing other applications include density estimation under constraints outlier trimming sensitivity analysis skewness or kurtosis reduction and shrinkage

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

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

sample size determination for diagnostic accuracy studies involving binormal roc curve indices receiver operating characteristic roc curves and their associated indices are valuable tools for the assessment of the accuracy of diagnostic tests the area under the roc curve is a popular summary measure of the accuracy of a test the full area under the roc curve however has been criticized because it gives equal weight to all false positive error rates alternative indices include the area under the roc curve in a particular range of false positive rates partial area and the sensitivity of the test for a single fixed false positive rate fpr we present a unified approach for computing sample size for binormal roc curves and their indices our method uses taylor series expansions to derive approximate large sample estimates of the variance and covariance of binormal roc curve parameters several examples from diagnostic radiology illustrate the proposed method

an algorithm for two dimensional rigidity percolation many important macroscopic properties of materials depend upon the number of microscopic degrees of freedom the task of counting the number of such degrees of freedom can be computationally very expensive we describe a new approach for this calculation which is appropriate for two dimensional glass like networks building upon recent work in graph rigidity this purely combinatorial algorithm is formulated in terms of a simplepebble game it has allowed for the first studies of the rigidity transition ingenericnetworks which are models of amorphous materials and glasses in the context of generic rigidity percolation we show how to calculate the number of internal degrees of freedom identify all rigid clusters and locate the overconstrained regions for a network ofnsites the pebble game has a worst case performance ofo n2 in our applications its performance scaled asn1 15at the rigidity transition while away from the transition region it grew linearly

quantile calculus and censored regression quantile regression has been advocated in survival analysis to assess evolving covariate effects however challenges arise when the censoring time is not always observed and may be covariate dependent particularly in the presence of continuously distributed covariates in spite of several recent advances existing methods either involve algorithmic complications or impose a probability grid the former leads to difficulties in the implementation and asymptotics whereas the latter introduces undesirable grid dependence to resolve these issues we develop fundamental and general quantile calculus on cumulative probability scale in this article upon recognizing that probability and time scales do not always have a one to one mapping given a survival distribution these results give rise to a novel estimation procedure for censored quantile regression based on estimating integral equations a numerically reliable and efficient progressive localized minimization plmin algorithm is proposed for the computation this procedure reduces exactly to the kaplan meier method in the k sample problem and to standard uncensored quantile regression in the absence of censoring under regularity conditions the proposed quantile coefficient estimator is uniformly consistent and converges weakly to a gaussian process simulations show good statistical and algorithmic performance the proposal is illustrated in the application to a clinical study

first order rigidity on cayley trees tree models for rigidity percolation in systems with only central forces are introduced and solved a probability vector describes the propagation of rigidity outward from a rigid border all components of this vector order parameter are singular at the same rigidity threshold mathrm p mathrm c the infinite cluster probability mathrm p mathrm ensuremath infty is usually first order at mathrm p mathrm c except in those cases which are equivalent to connectivity percolation in many cases mathrm p mathrm ensuremath infty ensuremath sim ensuremath delta mathrm p mathrm ensuremath infty p mathrm p mathrm c 1 mathrm 2 indicating critical fluctuations superimposed on the first order jump ensuremath delta mathrm p mathrm ensuremath infty our tree models for rigidity are in qualitative disagreement with constraint counting mean field theories in an important subclass of tree models bootstrap percolation and rigidity percolation are equivalent

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

bayesian bootstrap estimation of roc curve receiver operating characteristic roc curve is widely applied in measuring discriminatory ability of diagnostic or prognostic tests this makes the roc analysis one of the most active research areas in medical statistics many parametric and semiparametric estimation methods have been proposed for estimating the roc curve and its functionals in this paper we propose the bayesian bootstrap bb a fully nonparametric estimation method for the roc curve and its functionals such as the area under the curve auc the bb method offers a bandwidth free smoothing approach to the empirical estimate and gives credible bounds the accuracy of the estimate of the roc curve in the simulation studies is examined by the integrated absolute error in comparison with other existing curve estimation methods the bb method performs well in terms of accuracy robustness and simplicity we also propose a procedure based on the bb approach to test the binormality assumption

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

posterior consistency of nonparametric conditional moment restricted models this paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite dimensional parameter g0 we estimate it in a quasi bayesian way based on the limited information likelihood and investigate the impact of three types of priors on the posterior consistency i truncated prior priors supported on a bounded set ii thin tail prior a prior that has very thin tail outside a growing bounded set and iii normal prior with nonshrinking variance in addition g0 is allowed to be only partially identified in the frequentist sense and the parameter space does not need to be compact the posterior is regularized using a slowly growing sieve dimension and it is shown that the posterior converges to any small neighborhood of the identified region we then apply our results to the nonparametric instrumental regression model finally the posterior consistency using a random sieve dimension parameter is studied

strong modularity of reducible galois representations in this paper we call strongly modular those reducible semi simple odd mod l galois representations for which the conclusion of the strongest form of serre s original modularity conjecture holds under the assumption that the serre weight k satisfies l k 1 we give a precise characterization of strongly modular representations hence generalizing a classical theorem of ribet pertaining to the case of conductor 1 when the representation rho is not strongly modular we give a necessary and sufficient condition on the primes p not dividing nl for which it arises in level np where n denotes the conductor of rho this generalizes a result of mazur on the case n k 1 2

geometry the leading parameter for the poisson s ratio of bending dominated cellular solids control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials in particular those with negative poisson s ratio this article sheds light on the old question of the relationship between geometric microstructure and mechanical response by comparison of the deformation properties of bar and joint frameworks with those of their realisation as a cellular solid made from linear elastic material for ordered planar tessellation models we find a classification in terms of the number of degrees of freedom of the framework model first in cases where the geometry uniquely prescribes a single deformation mode of the framework model the mechanical deformation and poisson s ratio of the linearly elastic cellular solid closely follow those of the unique deformation mode the result is a bending dominated deformation with negligible dependence of the effective poisson s ratio on the underlying material s poisson s ratio and small values of the effective young s modulus second in the case of rigid structures or when geometric degeneracy prevents the bending dominated deformation mode the effective poisson s ratio is material dependent and the young s modulus view the mathml sourcee cs large all analysed structures of this type have positive values of the poisson s ratio and large values of view the mathml sourcee cs third in the case where the framework has multiple deformation modes geometry alone does not suffice to determine the mechanical deformation these results clarify the relationship between mechanical properties of a linear elastic cellular solid and its corresponding bar and joint framework abstraction they also raise the question if in essence auxetic behaviour is restricted to the geometry guided class of bending dominated structures corresponding to unique mechanisms with inherently low values of the young s modulus

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

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

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

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

the analysis of placement values for evaluating discriminatory measures summary the idea of using measurements such as biomarkers clinical data or molecular biology assays for classification and prediction is popular in modern medicine the scientific evaluation of such measures includes assessing the accuracy with which they predict the outcome of interest receiver operating characteristic curves are commonly used for evaluating the accuracy of diagnostic tests they can be applied more broadly indeed to any problem involving classification to two states or populations d 0 or 1 we show that the roc curve can be interpreted as a cumulative distribution function for the discriminatory measure y in the affected population d 1 after y has been standardized to the distribution in the reference population d 0 the standardized values are called placement values if the placement values have a uniform 0 1 distribution then y is not discriminatory because its distribution in the affected population is the same as that in the reference population the degree to which the distribution of the standardized measure differs from uniform 0 1 is a natural way to characterize the discriminatory capacity of y and provides a nontraditional interpretation for the roc curve statistical methods for making inference about distribution functions therefore motivate new approaches to making inference about roc curves we demonstrate this by considering the roc glm regression model and observing that it is equivalent to a regression model for the distribution of placement values the likelihood of the placement values provides a new approach to roc parameter estimation that appears to be more efficient than previously proposed methods the method is applied to evaluate a pulmonary function measure in cystic fibrosis patients as a predictor of future occurrence of severe acute pulmonary infection requiring hospitalization finally we note the relationship between regression models for the mean placement value and recently proposed models for the area under the roc curve which is the classic summary index of discrimination

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

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

modularity of residual galois extensions and the eisenstein ideal for a totally real field f a finite extension f of fp and a galois character gf f unramified away from a finite set of places p p consider the bloch kato selmer group h h1 f 1 in an earlier paper of the authors it was proved that the number d of isomorphism classes of non semisimple reducible residual representations giving rise to lines in h which are modular by some f also unramified outside satisfies d n dimfh this was proved under the assumption that the order of a congruence module is greater than or equal to that of a divisible selmer group we show here that if in addition the relevant local eisenstein ideal j is non principal then d n when f q we prove the desired bounds on the congruence module and the selmer group we also formulate a congruence condition implying the non principality of j that can be checked in practice allowing us to furnish an example where d n

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

structural computations with the singular value decomposition of the equilibrium matrix abstract the singular value decomposition of the equilibrium matrix makes it possible to answer any question of a static kinematic or static kinematic nature for any structural assembly within a unified computational framework the paper introduces this decomposition relates it to the physical properties of a given assembly and derives formulae for stresses displacements etc a simple example illustrates the calculations

generic rigidity percolation in two dimensions we study rigidity percolation for random central force networks on the bondand site diluted generic triangular lattice here each site location is randomly displaced from the perfect lattice removing any special symmetries using the pebble game algorithm the total number of floppy modes are counted exactly and exhibit a cusp singularity in the second derivative at the transition from a rigid to a floppy structure the critical thresholds for bond and site dilution are found to be 0 66020 ifmmode pm else textpm fi 0 0003 and 0 69755 ifmmode pm else textpm fi 0 0003 respectively the network is decomposed into unique rigid clusters and we apply the usual percolation scaling theory from finite size scaling we find that the generic rigidity percolation transition is second order but in a different universality class from connectivity percolation with the exponents ensuremath alpha 0 48 ifmmode pm else textpm fi 0 05 ensuremath beta 0 175 ifmmode pm else textpm fi 0 02 and ensuremath nu 1 21 ifmmode pm else textpm fi 0 06 the fractal dimension of the spanning rigid clusters and the spanning stressed regions at the critical threshold are found to be mathit d mathit f 1 86 ifmmode pm else textpm fi 0 02 and mathit d mathit bb 1 80 ifmmode pm else textpm fi 0 03 respectively textcopyright 1996 the american physical society

empirical likelihood based inference under imputation for missing response data inference under kernel regression imputation for missing response data is considered an adjusted empirical likelihood approach to inference for the mean of the response variable is developed a nonparametric version of wilks theorem is proved for the adjusted empirical log likelihood ratio by showing that it has an asymptotic standard chi squared distribution and the corresponding empirical likelihood confidence interval for the mean is constructed with auxiliary information an empirical likelihood based estimator is defined and an adjusted empirical log likelihood ratio is derived asymptotic normality of the estimator is proved also it is shown that the adjusted empirical log likelihood ratio obeys wilks theorem a simulation study is conducted to compare the adjusted empirical likelihood and the normal approximation methods in terms of coverage accuracies and average lengths of confidence intervals based on biases and standard errors a comparision is also made by simulation between the empirical likelihood based estimator and related estimators our simulation indicates that the adjusted empirical likelihood method performs competitively and that the use of auxiliary information provides improved inferences

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

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

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

confidence intervals of the difference between areas under two roc curves in matched pair experiments in a matched pair study when outcomes of two diagnostic tests are ordinal continuous the difference between two correlated areas under roc curves aucs is usually used to compare the overall discriminatory ability of two diagnostic tests this article considers confidence interval ci construction problems of difference between two correlated aucs in a matched pair experiment and proposes 13 hybrid cis based on variance estimates recovery with the maximum likelihood estimation delong s statistic wilson score statistic ws and ws with continuity correction the modified wald statistic mw and mw with continuity correction and agresti coull statistic and three bootstrap resampling based cis for comparison we present traditional parametric and nonparametric cis simulation studies are conducted to assess the performance of the proposed cis in terms of empirical coverage probabilities empirical interval widths and ratios of the mesial noncoverage probabilities to the noncoverage probabilities two examples from clinical studies are illustrated by the proposed methodologies empirical results evidence that the hybrid agresti coull ci with the empirical estimation eac behaved most satisfactorily because its coverage probability was quite close to the prespecified confidence level with short interval width hence we recommend the usage of the eac ci in applications

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

algorithms for three dimensional rigidity analysis and a first order percolation transition a fast computer algorithm the pebble game has been used successfully to analyze the rigidity of two dimensional 2d elastic networks as well as of a special class of 3d networks the bond bending networks and enabled significant progress in studies of rigidity percolation on such networks application of the pebble game approach to general 3d networks has been hindered by the fact that the underlying mathematical theory is strictly speaking invalid in this case we construct an approximate pebble game algorithm for general 3d networks as well as a slower but exact algorithm the relaxation algorithm that we use for testing the new pebble game based on the results of these tests and additional considerations we argue that in the particular case of randomly diluted central force networks on bcc and fcc lattices the pebble game is essentially exact using the pebble game we observe an extremely sharp jump in the largest rigid cluster size in bond diluted central force networks in 3d with the percolating cluster appearing and taking up most of the network after a single bond addition this strongly suggests a first order rigidity percolation transition which is in contrast to the second order transitions found previously for the 2d central force and 3d bond bending networks while a first order rigidity transition has been observed previously for bethe lattices and networks with chemical order here it is in a regular randomly diluted network in the case of site dilution the transition is also first order for bcc lattices but results for fcc lattices suggest a second order transition even in bond diluted lattices while the transition appears massively first order in the order parameter the percolating cluster size it is continuous in the elastic moduli this and the apparent nonuniversality make this phase transition highly unusual

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