a unified semiparametric framework for quantitative trait loci analyses with application to spike phenotypes this article proposes a general semiparametric model for multiple quantitative trait loci qtl analyses of complex phenotypes in backcross and intercross designs the model provides tests about genetic hypotheses such as additivity dominance and epistasis that do not require specifying the form of the phenotypic distribution this contrasts with previous approaches based on transformations to normality and generalized linear models which require careful consideration of the phenotypic distribution inferences involve extensions of partial and conditional likelihoods developed for single qtl backcross models we demonstrate that conditional likelihood is robust to unobserved selective genotyping whereas partial likelihood and other standard methods are not to facilitate genome screens a novel resampling method is proposed that is similar in spirit to the popular permutation tests its main advantages are that it is broadly applicable to multiple qtls with nonnormal phenotypes and achieves a substa

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

hypothesis testing in a mixture case control model summary we consider a problem of testing mixture proportions using two sample data one from group one and the other from a mixture of groups one and two with unknown proportion for being in group two various statistical applications including microarray study infectious epidemiological studies case control studies with contaminated controls clinical trials allowing nonresponders genetic studies for gene mutation and fishery applications can be formulated in this setup under the assumption that the log ratio of probability density functions from the two groups is linear in the observations we propose a generalized score test statistic to test the mixture proportion under some regularity conditions it is shown that this statistic converges to a weighted chi squared random variable under the null hypothesis of 0 where the weight depends only on the sampling fraction of both groups the permutation method is used to provide more reliable finite sample approximation simulation results and two real data applications are presented

f divergence estimation and two sample homogeneity test under semiparametric density ratio models a density ratio is defined by the ratio of two probability densities we study the inference problem of density ratios and apply a semiparametric density ratio estimator to the two sample homogeneity test in the proposed test procedure the f divergence between two probability densities is estimated using a density ratio estimator the f divergence estimator is then exploited for the two sample homogeneity test we derive an optimal estimator of f divergence in the sense of the asymptotic variance in a semiparametric setting and provide a statistic for two sample homogeneity test based on the optimal estimator we prove that the proposed test dominates the existing empirical likelihood score test through numerical studies we illustrate the adequacy of the asymptotic theory for finite sample inference

censored quantile regression model with time varying covariates under length biased sampling quantile regression is a flexible and effective tool for modeling survival data and its relationship with important covariates which often vary over time informative right censoring of data from the prevalent cohort within the population often results in length biased observations we propose an estimating equation based approach to obtain consistent estimators of the regression coefficients of interest based on length biased observations with time dependent covariates in addition inspired by zeng and lin 2008 we also develop a more numerically stable procedure for variance estimation large sample properties including consistency and asymptotic normality of the proposed estimator are established numerical studies presented demonstrate convincing performance of the proposed estimator under various settings the application of the proposed method is demonstrated using the oscar dataset

on robust estimation in logistic case control studies consider a logistic regression model under case control sampling prentice pyke 1979 showed that the logistic slope estimates with case control sampling may be estimated from a standard prospective logistic regression program and that the resulting standard errors are asymptotically correct since logistic regression estimates are nonrobust we propose and analyze robust estimates of the slope parameters we focus specifically on estimates which downweight observations on one of three factors i leverage ii extreme fitted values and iii likelihood of misclassification

a minimum relative entropy based correlation model between the response and covariates summary a semiparametric model is presented utilizing dependence between a response and several covariates we show that this model is optimum when the marginal distributions of the response and the covariates are known this model extends the generalized linear model and the proportional likelihood ratio model when the marginal distributions are unknown new interpretations of known models such as the logistic regression model density ratio model and selection bias model are obtained in terms of dependence between variables for estimation of parameters a simple algorithm is presented which is guaranteed to converge it is also the same regardless of the choice of the distribution for response and covariates hence it can fit a very wide variety of useful models asymptotic properties of the estimators of model parameters are derived real data examples are discussed to illustrate our approach and simulation experiments are performed to compare with existing procedures

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

double eigenvalue problems for hemivariational inequalities the aim of the present paper is to study a new type of eigenvalue problem called a double eigenvalue problem which arises in hemivariational inequalities related to nonconvex nonsmooth energy functionals the paper provides existence results as well as some qualitative properties for the solutions to double eigenvalue problems for hemivariational inequalities under the presence of given nonlinear compact operators which are not necessarily of a variational structure it presents three different approaches to such problems minimization minimax methods and sub critical point theory on a sphere applications illustrate the theory

inequalities and bounds for kernel length biased density estimation in this note non parametric estimates of the length biased probability density function and related reliability measures are presented non parametric estimates are also presented under random censoring inequalities and bounds for the error of kernel estimators used for the estimation of length biased probability densities are obtained non asymptotic bounds and stochastic convergence results are established inference for length biased energy functions is developed and implemented

transformations of the explanatory variables in the logistic regression model for binary data summary some results are presented on improving the fit of the logistic regression model for binary data by transforming the vector of explanatory variables the methods are based on consideration of the distributions of these variables conditional on outcome group the transformations required are the functions of the explanatory variables which appear in the log density ratio of the conditional distributions

statistical models for intercepted data abstract consider a population of replaceable items of different ages and suppose that for each item there is a certain measurable attribute that is a monotone function perhaps random of the item s age to fix ideas we refer to this attribute as deterioration and we assume that as items age their level of deterioration increases we further assume that as the level of deterioration hits a certain threshold value perhaps unknown the item dies and disappears from the population so it is not available for sampling any more since items that deteriorate at a slower rate live longer any sample obtained over a short period of time would overrepresent slowly deteriorating items consequently under such circumstances longitudinal studies are often needed to statistically study deterioration as a function of age this article presents a statistical model that enables us to study the deterioration function from a single cross section snapshot of the population or some random parts of it specifically

an information matrix test for logistic regression models based on case control data summary we propose an information matrix based goodness of fit statistic to test the validity of the logistic regression model based on case control data by extending the information matrix test of white 1982 for detecting one sample parametric model misspecification to the semiparametric profile likelihood setting under a two sample semiparamnetric model which is equivalent to the assumed logistic regression model the proposed test statistic requires a high dimensional matrix inversion but is otherwise easily computed and has an asymptotic chi squared distribution this test statistic is an alternative to the kolmogorov smirnov type statistic of qin zhang 1997 and the chi squared type statistic of zhang 1999 and needs neither to employ a bootstrap method to evaluate its critical values nor to group the combined sample data into a finite number of mutually exclusive categories even when the underlying population distribution is continuous we demonstrate that the proposed test statistic and its asymptotic distribution may be obtained by fitting the prospective logistic regression model to case control data we present some results on simulation and on the analysis of three real datasets

non parametric tests for right censored data with biased sampling testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved due to the biased sampling scheme independent censoring assumption is often violated although the issues about biased inference caused by length biased sampling have been widely recognized in statistical epidemiological and economical literature there is no satisfactory solution for efficient two sample testing we propose an asymptotic most efficient nonparametric test by properly adjusting for length biased sampling the test statistic is derived from a full likelihood function and can be generalized from the two sample test to a k sample test the asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation we conduct extensive monte carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right censoring mechanisms for length biased data empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods for general left truncated data the proposed test is robust still maintains accurate control of type i error rate and is also more powerful than the existing methods if the truncation patterns and right censoring patterns are the same between the groups we illustrate the methods using two real data examples

empirical likelihood for right censored lifetime data abstractwhen the empirical likelihood el of a parameter is constructed with right censored data literature shows that 2log empirical likelihood ratio typically has an asymptotic scaled chi squared distribution where the scale parameter is a function of some unknown asymptotic variances therefore the el construction of confidence intervals for requires an additional estimation of the scale parameter additional estimation would reduce the coverage accuracy for by using a special influence function as an estimating function we prove that under very general conditions 2log empirical likelihood ratio has an asymptotic standard chi squared distribution with one degree of freedom this eliminates the need for estimating the scale parameter as well as eases some of the often demanding computations of the el method our estimating function yields a smaller asymptotic variance than those of wang and jing 2001 and qin and zhao 2007 thus it is not surprising that confidence intervals usi

testing for a finite mixture model with two components summary we consider a finite mixture model with k components and a kernel distribution from a general one parameter family the problem of testing the hypothesis k 2 versus k 3 is studied there has been no general statistical testing procedure for this problem we propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function it is shown that estimators of the support points are consistent the asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied simulation studies for the asymptotic modified likelihood ratio test based on finite mixture models with normal binomial and poisson kernels suggest that the test proposed performs well simulation studies are also conducted for a bootstrap method with normal kernels an example involving foetal movement data from a medical study illustrates the testing procedure

a note on profile likelihood for exponential tilt mixture models suppose that independent observations are drawn from multiple distributions each of which is a mixture of two component distributions such that their log density ratio satisfies a linear model with a slope parameter and an intercept parameter inference for such models has been studied using empirical likelihood and mixed results have been obtained the profile empirical likelihood of the slope and intercept has an irregularity at the null hypothesis so that the two component distributions are equal we derive a profile empirical likelihood and maximum likelihood estimator of the slope alone and obtain the usual asymptotic properties for the estimator and the likelihood ratio statistic regardless of the null furthermore we show the maximum likelihood estimator of the slope and intercept jointly is consistent and asymptotically normal regardless of the null at the null the joint maximum likelihood estimator falls along a straight line through the origin with perfect correlation asymptotically to the first order

on the morse critical groups for indefinite sublinear elliptic problems we consider the dirichlet problem for the equation u u m x u u q 2 g x u where q 1 2 and m changes sign we prove that the morse critical groups at zero of the energy functional of the problem are trivial as a consequence existence and bifurcation of nontrivial solutions of the problem are established

nonparametric estimation for right censored length biased data a pseudo partial likelihood approach to estimate the lifetime distribution of right censored length biased data we propose a pseudo partial likelihood approach that allows us to derive two nonparametric estimators with its closed form estimators and explicit limiting variances this approach retains the simplicity of conditional analysis and has only a small efficiency loss compared with the unconditional analysis under some regularity conditions we show that the two estimators are uniformly consistent and converge weakly to gaussian processes a simulation study demonstrates that the proposed estimators have satisfactory finite sample performance application to an alzheimer s disease study is reported

semiparametric inference for the dominance index under the density ratio model summary an important and often discussed research problem in statistics is how to compare several populations examples arise in medical science engineering finance and other fields often population means or medians are compared however one population may have a higher mean income for example because of a small number of super rich individuals the mean therefore may not reflect the wealth of the general population instead an index of the degree of stochastic dominance of one population over another would better reflect their relative wealth currently we can estimate such an index under restrictive conditions but there is no generic estimator with a known asymptotic distribution in this paper we suggest linking the populations via the density ratio model under this model we develop an empirical likelihood estimator and establish its asymptotic normality in addition we improve the estimation efficiency by examining the similarities between the populations furthermore we provide a valid bootstrap method for hypothesis testing and the construction of confidence intervals simulation experiments show that the proposed estimator substantially improves the estimation efficiency and power of the test and leads to confidence intervals with satisfactorily precise coverage probabilities it is also robust with respect to mild model misspecification two examples are given to demonstrate the usefulness of both the method and the concept

kernel density estimation for length biased data a new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated it has various advantages over an alternative method suggested by bhattacharyya franklin richardson 1988 it is necessarily a probability density it is particularly better behaved near zero it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems such as density derivative estimation

inferences for case control and semiparametric two sample density ratio models summary we consider inference in general binary response regression models under retrospective sampling plans prentice pyke 1979 discovered that inference for the odds ratio parameter in a logistic model can be based on a prospective likelihood even though the sampling scheme is retrospective we show that the estimating function obtained from the prospective likelihood is optimal in a class of unbiased estimating functions also we link casecontrol sampling with a two sample biased sampling problem where the ratio of two densities is assumed to take a known parametric form connections between this model and the cox proportional hazards model are pointed out large and small sample size behaviour of the proposed estimators is studied

case control studies with contaminated controls abstract this paper considers inference about a parametric binary choice model when the data consist of two distinct samples the first is a random sample from the people who made choice 1 say with all relevant covariates completely observed the second is a random sample from the whole population with only the covariates observed this is called a contaminated sampling scheme an example might be where we have a random sample of female labor force participants and their covariate values and a second random sample of working age women with covariates whose participant status is unknown we consider the cases in which the fraction of the population making choice 1 is known and that in which it is not for both cases we give semiparametrically efficient procedures for estimating the choice model parameters

order restricted semiparametric inference for the power bias model the power bias model a generalization of length biased sampling is introduced and investigated in detail in particular attention is focused on order restricted inference we show that the power bias model is an example of the density ratio model or in other words it is a semiparametric model that is specified by assuming that the ratio of several unknown probability density functions has a parametric form estimation and testing procedures under constraints are developed in detail it is shown that the power bias model can be used for testing for or against the likelihood ratio ordering among multiple populations without resorting to any parametric assumptions examples and real data analysis demonstrate the usefulness of this approach

robust logistic discrimination summary logistic discrimination is a well established method for allocating observations to one of two or more populations in this paper we show how the logistic model can be adapted to make it robust against outlying observations from the populations the new model is successfully tested using simulated data against ordinary logistic discrimination and also against logistic discrimination where parameters are fitted using resistant methods the model is then used on data collected from the teeth of rats logistic discrimination is a partially parametric method for discrimination applicable in many situations and under several sampling schemes notable references to the method are day kerridge 1967 anderson 1972 1979 1982 and anderson blair 1982 the appeal of the logistic method for discrimination is that only the ratio of likelihoods has to be modelled and not the full distributional form of the underlying variables press wilson 1978 and byth mclachlan 1980 show that in many circumstances logistic discrimination is preferable to the usual linear discrimination based on either normal populations with equal covariance matrices or fisher s linear discriminant for the two group case suppose x is a vector of observations h1 and h2 are the two groups and a a parameter vector then the log likelihood ratio is modelled as

a proportional likelihood ratio model we propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate this model extends the generalized linear model by leaving the distribution unspecified and has a strong connection with semiparametric models such as the selection bias model gilbert et al 1999 the density ratio model qin 1998 fokianos kaimi 2006 the single index model ichimura 1993 and the exponential tilt regression model rathouz gao 2009 a maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived an example and simulation study illustrate the use of the model copyright 2012 oxford university press

on empirical likelihood for a semiparametric mixture model summary plant and animal studies of quantitative trait loci provide data which arise from mixtures of distributions with known mixing proportions previous approaches to estimation involve modelling the distributions parametrically we propose a semiparametric alternative which assumes that the log ratio of the component densities satisfies a linear model with the baseline density unspecified it is demonstrated that a constrained empirical likelihood has an irregularity under the null hypothesis that the two densities are equal a factorisation of the likelihood suggests a partial empirical likelihood which permits unconstrained estimation of the parameters and which is shown to give consistent and asymptotically normal estimators regardless of the null the asymptotic null distribution of the log partial likelihood ratio is chi squared theoretical calculations show that the procedure may be as efficient as the full empirical likelihood in the regular set up the usefulness of the robust methodology is illustrated with a rat study of breast cancer resistance genes

a note on convergence of an iterative algorithm for semiparametric odds ratio models this paper points out an error in davidov and iliopoulos s biometrika 100 778 80 proof of convergence of an iterative algorithm for the proportional likelihood ratio model it is shown that the iterative algorithm increases the likelihood in each iteration and converges under mild additional conditions when the odds ratio function is bounded

analysing bivariate survival data with interval sampling and application to cancer epidemiology in biomedical studies ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease in cancer studies interest could be focused on bivariate failure times for example time from birth to cancer onset and time from cancer onset to death this paper considers a sampling scheme termed interval sampling in which the first failure event is identified within a calendar time interval the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring in a cancer data application the initiating first and second events could correspond to birth cancer onset and death the fact that the data are collected conditional on the first failure event occurring within a time interval induces bias interval sampling is widely used for collection of disease registry data by governments and medical institutions though the interval sampling bias is frequently overlooked by researchers this paper develops statistical methods for analysing such data semiparametric methods are proposed under semi stationarity and stationarity numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes we apply the proposed methods to ovarian cancer registry data

a theory of statistical models for monte carlo integration summary the task of estimating an integral by monte carlo methods is formulated as a statistical model using simulated observations as data the difficulty in this exercise is that we ordinarily have at our disposal all of the information required to compute integrals exactly by calculus or numerical integration but we choose to ignore some of the information for simplicity or computational feasibility our proposal is to use a semiparametric statistical model that makes explicit what information is ignored and what information is retained the parameter space in this model is a set of measures on the sample space which is ordinarily an infinite dimensional object none the less from simulated data the base line measure can be estimated by maximum likelihood and the required integrals computed by a simple formula previously derived by vardi and by lindsay in a closely related model for biased sampling the same formula was also suggested by geyer and by meng and wong using entirely different arguments by contrast with geyer s retrospective likelihood a correct estimate of simulation error is available directly from the fisher information the principal advantage of the semiparametric model is that variance reduction techniques are associated with submodels in which the maximum likelihood estimator in the submodel may have substantially smaller variance than the traditional estimator the method is applicable to markov chain and more general monte carlo sampling schemes with multiple samplers

a new approach in studying one parameter nonlinear eigenvalue problems with constraints abstract the paper presents a new approach for obtaining existence and location of solutions to nonlinear eigenvalue problems depending on a parameter and subject to constraints the location of eigensolutions and subsequent parameters is achieved by means of the graph of the derivative of a function used also to compensate the lack of coercivity the applications concern one parameter families of semilinear elliptic eigenvalue problems with dirichlet boundary conditions for which various qualitative properties of the solution sets are established

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

infinitely many critical points of non differentiable functions and applications to a neumann type problem involving the p laplacian abstract for a family of functionals in a banach space which are possibly non smooth and depend also on a positive real parameter the existence of a sequence of critical points according to motreanu and panagiotopoulos minimax theorems and qualitative properties of the solutions of hemivariational inequalities nonconvex optimization applications vol 29 kluwer dordrecht 1998 chap 3 is established by mainly adapting a new technique due to ricceri 2000 j comput appl math 113 401 410 two applications are then presented both of them treat the neumann problem for an elliptic variational hemivariational inequality with p laplacian

maximum likelihood estimation under a successive sampling discovery model a common problem encountered in the analysis of discovery data is the size bias phenomenon in which the larger units tend to be discovered first one approach to account for this bias is to model the discovery process as sampling successively from a finite population without replacement and with probability proportional to size we consider in this article a generalized version of this model for analyzing multivariate data with any given measure of size we assume a superpopulation framework and develop procedures for maximum likelihood estimation of the parameters of the distribution the use of the em algorithm for computing the maximum likelihood estimates associated computational issues and relationships to regression estimators in survey sampling are discussed oil discovery data from the rimbey meadowbrook reef play are used to illustrate the techniques

estimation of incubation period and generation time based on observed length biased epidemic cohort with censoring for covid 19 outbreak in china the incubation period and generation time are key characteristics in the analysis of infectious diseases the commonly used contact tracing based estimation of incubation distribution is highly influenced by the individuals judgment on the possible date of exposure and might lead to significant errors on the other hand interval censoring based methods are able to utilize a much larger set of traveling data but may encounter biased sampling problems the distribution of generation time is usually approximated by observed serial intervals however it may result in a biased estimation of generation time especially when the disease is infectious during incubation in this paper the theory from renewal process is partially adopted by considering the incubation period as the interarrival time and the duration between departure from wuhan and onset of symptoms as the mixture of forward time and interarrival time with censored intervals in addition a consistent estimator for the distribution of generation time based on incubation period and serial interval is proposed for incubation infectious diseases a real case application to the current outbreak of covid 19 is implemented we find that the incubation period has a median of 8 50 days 95 confidence interval ci 7 22 9 15 the basic reproduction number in the early phase of covid 19 outbreak based on the proposed generation time estimation is estimated to be 2 96 95 ci 2 15 3 86

analyzing length biased data with semiparametric transformation and accelerated failure time models right censored time to event data are often observed from a cohort of prevalent cases that are subject to length biased sampling informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population because the observed failure times are length biased in this paper we consider two classes of flexible semiparametric models the transformation models and the accelerated failure time models to assess covariate effects on the population failure times by modeling the length biased times we develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients large sample properties for the estimators are derived the methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients

prospective analysis of case control data under general multiplicative intercept risk models summary we show that under a general multiplicative intercept model for risk case control data can be analyzed by maximum likelihood as if they had arisen prospectively up to an unidentifiable multiplicative constant which depends on the relative sampling fractions this generalizes earlier work of anderson 1972 1979 by showing that not only the point estimates but also the standard errors based on the observed information matrix are correct when the prospective likelihood is maximized likelihood ratio testing is also valid under this broad class of risk models data on disease status from a much larger cohort are shown to add no information to the estimation of the covariate related parameters

penalized maximum likelihood estimation in logistic regression and discrimination summary maximum likelihood estimation of the parameters of the binary logistic regression model for pr h i x is discussed with separate discussion of sampling from i the conditional distribution of h given x ii the joint distribution of h and x and iii the conditional distribution of x given h difficulties associated with continuous x in the latter sampling scheme are discussed to avoid these penalized maximum likelihood estimates are introduced which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x extensions to multinomial logistic regression are outlined

a least squares approach to direct importance estimation we address the problem of estimating the ratio of two probability density functions which is often referred to as the importance the importance values can be used for various succeeding tasks such as covariate shift adaptation or outlier detection in this paper we propose a new importance estimation method that has a closed form solution the leave one out cross validation score can also be computed analytically therefore the proposed method is computationally highly efficient and simple to implement we also elucidate theoretical properties of the proposed method such as the convergence rate and approximation error bounds numerical experiments show that the proposed method is comparable to the best existing method in accuracy while it is computationally more efficient than competing approaches

low risk population size estimates in the presence of capture heterogeneity summary population estimation methods are used for estimating the size of a population from samples of individuals in many applications the probability of being observed in the sample varies across individuals resulting in sampling bias we show that in this setting estimators of the population size have high and sometimes infinite risk leading to large uncertainty in the population size as an alternative we propose estimating the population of individuals with observation probability exceeding a small threshold we show that estimators of this quantity have lower risk than estimators of the total population size the proposed approach is shown empirically to result in large reductions in mean squared error in a common model for capture recapture population estimation with heterogeneous capture probabilities

joint estimation of the mean and error distribution in generalized linear models this article introduces a semiparametric extension of generalized linear models that is based on a full probability model but does not require specification of an error distribution or variance function for the data the approach involves treating the error distribution as an infinite dimensional parameter which is then estimated simultaneously with the mean model parameters using a maximum empirical likelihood approach the resulting estimators are shown to be consistent and jointly asymptotically normal in distribution when interest lies only in inferences on the mean model parameters we show that maximizing out the error distribution leads to profile empirical log likelihood ratio statistics that have asymptotic 2 distributions under the null simulation studies demonstrate that the proposed method can be more accurate than existing methods that offer the same level of flexibility and generality especially with smaller sample sizes the theoretical and numerical results are complemented by a data

a semiparametric model for vqtl mapping summary quantitative trait locus analysis has been used as an important tool to identify markers where the phenotype or quantitative trait is linked with the genotype most existing tests for single locus association with quantitative traits aim at the detection of the mean differences across genotypic groups however recent research has revealed functional genetic loci that affect the variance of traits known as variability controlling quantitative trait locus in addition it has been suggested that many genotypes have both mean and variance effects while the mean effects or variance effects alone may not be strong enough to be detected the existing methods accounting for unequal variances include the levene s test the lepage test and the d test but suffer from their limitations of lack of robustness or lack of power we propose a semiparametric model and a novel pairwise conditional likelihood ratio test specifically the semiparametric model is designed to identify the combined differences in higher moments among genotypic groups the pairwise likelihood is constructed based on conditioning procedure where the unknown reference distribution is eliminated we show that the proposed pairwise likelihood ratio test has a simple asymptotic chi square distribution which does not require permutation or bootstrap procedures simulation studies show that the proposed test performs well in controlling type i errors and having competitive power in identifying the differences across genotypic groups in addition the proposed test has certain robustness to model mis specifications the proposed test is illustrated by an example of identifying both mean and variances effects in body mass index using the framingham heart study data

multiplicity of the second schrodinger eigenvalue on closed surfaces we improve roughly by a factor 2 the known bound on the multiplicity of the second eigenvalue of schrodinger operators i e laplace plus potential on closed surfaces this gives four new topological types of surfaces for which colin de verdiere s conjecture relating the maximal multiplicity to the chromatic number of the surface is verified the proof goes by defining a space cal p of nodal splittings of the surface equipped with a double covering to which a borsuk ulam type theorem is applied

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

likelihood inferences on semiparametric odds ratio model a flexible semiparametric odds ratio model has been proposed to unify and to extend both the log linear model and the joint normal model for data with a mix of discrete and continuous variables the semiparametric odds ratio model is particularly useful for analyzing biased sampling designs however statistical inference of the model has not been systematically studied when more than one nonparametric component is involved in the model in this article we study the maximum semiparametric likelihood approach to estimation and inference of the semiparametric odds ratio model we show that the maximum semiparametric likelihood estimator of the odds ratio parameter is consistent and asymptotically normally distributed we also establish statistical inference under a misspecified semiparametric odds ratio model which is important when handling weak identifiability in conditionally specified models under biased sampling designs we use simulation studies to demonstrate that the proposed approaches have satis

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