semi parametric single index panel data models with interactive fixed effects theory and practice abstract in this paper we propose a single index panel data model with unobserved multiple interactive fixed effects this model has the advantages of being flexible and of being able to allow for common shocks and their heterogeneous impacts on cross sections thus making it suitable for the investigation of many economic issues the asymptotic theories are established accordingly our monte carlo simulations show that our methodology works well for large n and t cases in our empirical application we illustrate our model by analysing the returns to scale of large commercial banks in the u s

efficient semiparametric estimation via moment restrictions conditional moment restrictions can be combined through gmm estimation to construct more efficient semiparametric estimators this paper is about attainable efficiency for such estimators we define and use a moment tangent set the directions of departure from the truth allowed by the moments to characterize when the semiparametric efficiency bound can be attained the efficiency condition is that the moment tangent set equals the model tangent set we apply these results to transformed censored and truncated regression models e g finding that the conditional moment restrictions from powell s 1986 censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

generalized additive and index models with shape constraints summary we study generalized additive models with shape restrictions e g monotonicity convexity and concavity imposed on each component of the additive prediction function we show that this framework facilitates a non parametric estimator of each additive component obtained by maximizing the likelihood the procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals more generally our methodology can be applied to generalized additive index models here again the procedure can be justified on theoretical grounds and like the original algorithm has highly competitive finite sample performance practical utility is illustrated through the use of these methods in the analysis of two real data sets our algorithms are publicly available in the r package scar short for shape constrained additive regression

breaking the curse of dimensionality in nonparametric testing abstract for tests based on nonparametric methods power crucially depends on the dimension of the conditioning variables and specifically decreases with this dimension this is known as the curse of dimensionality we propose a new general approach to nonparametric testing in high dimensional settings and we show how to implement it when testing for a parametric regression the resulting test behaves against directional local alternatives almost as if the dimension of the regressors was one it is also almost optimal against classes of one dimensional alternatives for a suitable choice of the smoothing parameter the test performs well in small samples compared to several other tests

root n consistent semiparametric estimators of a dynamic panel sample selection model abstract this paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possibly predetermined variables lags of the dependent variables and unobserved individual effects the selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations we derive a set of conditional moment restrictions that are then exploited to construct a three step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term in the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of berkson s minimum chi square sieve method and a first step kernel estimator for the selection probability this second step estimator is of interest in its own right it can be used to semiparametrically estimate a panel data binary response model with a nonparametric individual specific effect without making any other distributional assumptions we show that both estimators second and third stage are n consistent and asymptotically normal

semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables this paper provides estimators of discrete choice models including binary ordered and multinomial response choice models the estimators closely resemble ordinary and two stage least squares the distribution of the model s latent variable error is unknown and may be related to the regressors e g the model could have errors that are heteroscedastic or correlated with regressors the estimator does not require numerical searches even for multinomial choice for ordered and binary choice models the estimator is root n consistent and asymptotically normal a consistent estimator of the conditional error distribution is also provided

estimation of a nonlinear panel data model with semiparametric individual effects abstract this paper investigates identification and estimation of a class of nonlinear panel data single index models the model allows for unknown time specific link functions and semiparametric specification of the individual specific effects we develop an estimator for the parameters of interest and propose a powerful new kernel based modified backfitting algorithm to compute the estimator we derive uniform rates of convergence results for the estimators of the link functions and show the estimators of the finite dimensional parameters are root n consistent with a gaussian limiting distribution we study the small sample properties of the estimator via monte carlo techniques

estimating a generalized correlation coefficient for a generalized bivariate probit model abstract in this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model the generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework our semiparametric estimation procedure consists of two steps combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors the estimator is shown to be consistent and asymptotically normal the estimator performs well in our simulation study

groupwise dimension reduction via envelope method the family of sufficient dimension reduction sdr methods that produce informative combinations of predictors or indices are particularly useful for high dimensional regression analysis in many such analyses it becomes increasingly common that there is available a priori subject knowledge of the predictors for example they belong to different groups while many recent sdr proposals have greatly expanded the scope of the methods applicability how to effectively incorporate the prior predictor structure information remains a challenge in this article we aim at dimension reduction that recovers full regression information while preserving the predictor group structure built upon a new concept of the direct sum envelope we introduce a systematic way to incorporate the group information in most existing sdr estimators as a result the reduction outcomes are much easier to interpret moreover the envelope method provides a principled way to build a variety of prior structures into dimension reduc

a semiparametric single index model with heterogeneous impacts on an unobserved variable this paper proposes a single index semiparametric model in which the unknown function has cross sectional unit specific weights the initial motivation comes from the search for a better measure of liquidity in stock trading which is captured by the unknown function here the model is estimated by semiparametric least squares developed by ichimura 1993 and ichimura and lee 1991 the proposed technique differs from theirs in at least two aspects first i show that the estimator has desirable asymptotic properties under less restrictive assumptions on data second the form of the unknown function is fixed however the coefficients are allowed to differ across the cross sectional units

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

rank estimation of a location parameter in the binary choice model abstract this paper proposes a rank based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition given an initial n consistent estimator for the slope parameter the estimator converges at the usual parametric rate compared with existing estimators no nonparametric smoothing is needed here a small monte carlo study illustrates the usefulness of the estimator we also point out that the location and slope parameters can be jointly estimated

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

identifiability of single index models and additive index models summary we provide a proof for the identifiability for both single index models and partially linear single index models assuming only the continuity of the regression function a condition much weaker than the differentiability conditions assumed in the existing literature our discussion is then extended to the identifiability of the additive index models

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

partial rank estimation of duration models with general forms of censoring abstract in this paper we propose estimators for the regression coefficients in censored duration models which are distribution free impose no parametric specification on the baseline hazard function and can accommodate general forms of censoring the estimators are shown to have desirable asymptotic properties and monte carlo simulations demonstrate good finite sample performance among the data features the new estimators can accommodate are covariate dependent censoring double censoring and fixed individual or group specific effects we also examine the behavior of the estimator in an empirical illustration

merging multiple longitudinal studies with study specific missing covariates a joint estimating function approach merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power this article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics such as different follow up schedules and study specific missing covariates e g covariates observed in some studies but missing in other studies the presence of study specific missing covariates presents great statistical methodology challenge in data merging and analysis we propose a joint estimating function approach to addressing this challenge in which a novel nonparametric estimating function constructed via splines based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates under mild regularity conditions we show that the proposed estimator is consistent and asymptotically normal we evaluate finite sample performances of the proposed method through simulation studies in comparison to the conventional multiple imputation approach our method exhibits smaller estimation bias we provide an illustrative data analysis using longitudinal cohorts collected in mexico city to assess the effect of lead exposures on children s somatic growth

pseudo maximum likelihood estimation in two classes of semiparametric diffusion models abstract two classes of semiparametric diffusion models are considered where either the drift or the diffusion term is parameterized while the other term is left unspecified we propose a pseudo maximum likelihood estimator pmle of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in it is demonstrated how models and estimators can be used in a two step specification testing strategy of semiparametric and fully parametric models and shown that approximate simulated versions of the pmle inherit the properties of the actual but infeasible estimator a simulation study investigates the finite sample performance of the pmle

nonparametric transfer function models in this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between input and output time series the transfer function is smooth with unknown functional forms and the noise is assumed to be a stationary autoregressive moving average arma process the nonparametric transfer function is estimated jointly with the arma parameters by modelling the correlation in the noise the transfer function can be estimated more efficiently the parsimonious arma structure improves the estimation efficiency in finite samples the asymptotic properties of the estimators are investigated the finite sample properties are illustrated through simulations and one empirical example

single index model selections we derive a new model selection criterion for single index models aicc by minimising the expected kullback leibler distance between the true and candidate models the proposed criterion selects not only relevant variables but also the smoothing parameter for an unknown link function thus it is a general selection criterion that provides a unified approach to model selection across both parametric and nonparametric functions monte carlo studies demonstrate that aicc performs satisfactorily in most situations we illustrate the practical use of aicc with an empirical example for modelling the hedonic price function for cars in addition we extend the applicability of aicc to partially linear and additive single index models language en

direct estimation of the index coefficient in a single index model single index modeling is widely applied in for example econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models by such modeling the statistical analysis usually focuses on estimating the index coefficients the average derivative estimator ade of the index vector is based on the fact that the average gradient of a single index function f x t is proportional to the index vector unfortunately a straightforward application of this idea meets the so called curse of dimensionality problem if the dimensionality d of the model is larger than 2 however prior information about the vector can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative the method proposed in this paper consists of such iterative improvements of the original ade the whole procedure requires at most 2 log n iterations and the resulting estimator is n consistent under relatively mild assumptions on the model independently of the dimensionality d

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

characterization of the asymptotic distribution of semiparametric m estimators this paper develops a concrete formula for the asymptotic distribution of two step possibly non smooth semiparametric m estimators under general misspecification our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature the first stage nonparametric estimation may depend on finite dimensional parameters we characterize 1 conditions under which the first stage estimation of nonparametric components do not affect the asymptotic distribution 2 conditions under which the asymptotic distribution is affected by the derivatives of the first stage nonparametric estimator with respect to the finite dimensional parameters and 3 conditions under which one can allow non smooth objective functions our framework is illustrated by applying it to three examples 1 profiled estimation of a single index quantile regression model 2 semiparametric least squares estimation under model misspecification and 3 a smoothed matching estimator 2010 elsevier b v all rights reserved

semiparametric latent variable model estimation with endogenous or mismeasured regressors a simple root n consistent asymptotically normal semiparametric estimator of the coefficient vector b in the latent variable specification y l f b x e is constructed the distribution of e is unknown and may be correlated with x or be conditionally heteroscedastic e g x can contain measurement error the function l can also be unknown the identification assumption is that e is uncorrelated with instruments u and that the conditional distribution of e given x and u does not depend on one of the regressors which has some special properties extensions to more general latent variable specifications are provided

estimation of the binary response model using a mixture of distributions estimator mod abstract in this paper we develop a semiparametric sieve estimator which is termed a mixture of distributions estimator mod to estimate a binary response model when the distribution of the errors is unknown the estimator of the distribution function is composed of a mixture of smooth distributions where the number of mixtures increases with the sample size the model is semiparametric because it is assumed that a parametric index type restriction holds optimal rates of convergence are established for the distribution function under the l 2 norm and conditions are derived under which estimates of the parametric component are asymptotically normal an appealing feature about mod is that it is possible to restrict the estimator of the distribution function a priori to be smooth nonnegative nondecreasing and to integrate to one this has important practical and theoretical implications

generalized varying coefficient models with unknown link function summary we propose a new estimation method for generalized varying coefficient models where the link function is specified up to some smoothness conditions consistency and asymptotic normality of the estimated varying coefficient functions are established simulation results and a real data application demonstrate the usefulness of the new method

adaptive varying coefficient linear models varying coefficient linear models arise from multivariate nonparametric regression nonlinear time series modelling and forecasting functional data analysis longitudinal data analysis and others it has been a common practice to assume that the vary coefficients are functions of a given variable which is often called an index a frequently asked question is which variable should be used as the index in this paper we explore the class of the varying coefficient linear models in which the index is unknown and is estimated as a linear combination of regression and or other variables this will enlarge the modelling capacity substantially we search for the index such that the derived varying coefficient model provides the best approximation to the underlying unknown multi dimensional regression function in the least square sense the search is implemented through the newly proposed hybrid backfitting algorithm the core of the algorithm is the alternative iteration between estimating the index through a one step scheme and estimating coefficient functions through a one dimensional local linear smoothing the generalised cross validation method for choosing bandwidth is efficiently incorporated into the algorithm the locally significant variables are selected in terms of the combined use of t statistic and akaike information criterion we further extend the algorithm for the models with two indices simulation shows that the proposed methodology has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers the methods are further illustrated through the canadian mink muskrat data in 1925 1994 and the pound dollar exchange rates in 1974 1983

gaussian process single index models as emulators for computer experiments a single index model sim provides for parsimonious multidimensional nonlinear regression by combining parametric linear projection with univariate nonparametric nonlinear regression models we show that a particular gaussian process gp formulation is simple to work with and ideal as an emulator for some types of computer experiment as it can outperform the canonical separable gp regression model commonly used in this setting our contribution focuses on drastically simplifying reinterpreting and then generalizing a recently proposed fully bayesian gp sim combination favorable performance is illustrated on synthetic data and a real data computer experiment two r packages both released on cran have been augmented to facilitate inference under our proposed model s

irregular identification support conditions and inverse weight estimation in weighted moment condition models we show a subtle link between identification and estimability that limits the practical usefulness of estimators based on these models in particular if it is necessary for point identification that the weights take arbitrarily large values then the parameter of interest though point identified cannot be estimated at the regular parametric rate and is said to be irregularly identified this rate depends on relative tail conditions and can be as slow in some examples as n 1 4 this nonstandard rate of convergence can lead to numerical instability and or large standard errors we examine two weighted model examples i the binary response model under mean restriction introduced by lewbel 1997 and further generalized to cover endogeneity and selection where the estimator in this class of models is weighted by the density of a special regressor and ii the treatment effect model under exogenous selection rosenbaum and rubin 1983 where the resulting estimator of the average treatment effect is one that is weighted by a variant of the propensity score without strong relative support conditions these models similar to well known identified at infinity models lead to estimators that converge at slower than parametric rate since essentially to ensure point identification one requires some variables to take values on sets with arbitrarily small probabilities or thin sets for the two models above we derive some rates of convergence and propose that one conducts inference using rate adaptive procedures that are analogous to andrews and schafgans 1998 for the sample selection model

nonparametric estimation of a generalized additive model with an unknown link function mean of a random scalar y conditional on a random vector x e rd let h x e yix x denote the conditional mean function this paper is concerned with estimating h under weak assumptions about its functional form when x is a multidimensional continuous random variable the paper describes a model that nests single index additive and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model nonparametric estimation of h is usually unattractive when x is multidimensional the rate of convergence of nonparametric estimators decreases rapidly as the dimension of x increases and nonparametric estimates can be very imprecise with samples of practical size when x is multidimensional the curse of dimensionality this problem can be overcome through the use of dimension reduction methods they reduce the effective dimension of the estimation problem by making assumptions about the functional form of h that are stronger than those of a fully nonparametric estimator but weaker than those of a finite dimensional parametric model one method of dimension reduction is semiparametric single index modeling the best known and most easily estimated semiparametric single index model assumes that 1 1 h x g 3 x where 3 is an unknown d x 1 vector and g is an unknown function the vector 3 can be estimated with an n 1 2 rate of convergence in probability which is the rate that would be obtained if g were known han 1987 hardle and stoker 1989 horowitz and hardle 1996 ichimura 1993 klein and spady 1993 newey and stoker 1993 powell stock and stoker 1989 sherman 1993 stoker 1991 g can be estimated with the rate of convergence n r 2r 1 where r is an integer that depends on the smoothness of g but not on d dimension reduction can also be achieved by using a nonparametric generalized additive model in such a model

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

penalized spline estimation for partially linear single index models single index models are potentially important tools for multivariate nonparametric regression they generalize linear regression by replacing the linear combination 0tx with a nonparametric component 0 0tx where 0 is an unknown univariate link function by reducing the dimensionality from that of a general covariate vector x to a univariate index 0tx single index models avoid the so called curse of dimensionality we propose penalized spline p spline estimation of 0 in partially linear single index models where the mean function has the form 0 0tx 0tz the p spline approach offers a number of advantages over other fitting methods for single index models all parameters in the p spline single index model can be estimated simultaneously by penalized nonlinear least squares as a direct least squares fitting method our approach is rapid and computationally stable standard nonlinear least squares software can be used moreover joint inference for 0 0 and 0 is possible by

estimation of marginal effects in semiparametric selection models with binary outcomes this paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting we focus on developing an estimator for the marginal effects this marginal effect estimator uses only observations where the selection probability is above a certain threshold a key innovation is that this high probability set is adaptive to the data we establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends monte carlo studies show that these estimators perform well in finite samples

on single index coefficient regression models abstract in this article we investigate a class of single index coefficient regression models under dependence this includes many existing models such as the smooth transition threshold autoregressive star model of chan and tong the functional coefficient autoregressive far model of chen and tsay and the single index model of ichimura compared to the varying coefficient model of hastie and tibshirani our model can avoid the curse of dimensionality in multivariate nonparametric estimations another advantage of this model is that a threshold variable is chosen automatically an estimation method is proposed and the corresponding estimators are shown to be consistent and asymptotically normal some simulations and applications are also reported

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

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

rates of convergence for estimating regression coefficients in heteroskedastic discrete response models abstract in this paper we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term it is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction the semiparametric information bound is zero even when the homoskedastic error term is parametrically specified hence it is impossible to attain the parametric convergence rate for the parameters of interest however for ordered response models where the response variable can take at least three different values the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption two estimation procedures are proposed the first estimator based on a parametric restriction on the homoskedastic component of the error term is a two step maximum likelihood estimators where the unknown scale function is estimated nonparametrically in the first stage the second procedure which does not require the parametric restriction estimates the parameters by a kernel weighted least squares procedure under regularity conditions which are standard in the literature both estimators are shown to be n consistent and asymptotically normal

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

identification and estimation of nonseparable single index models in panel data with correlated random effects the identification in a nonseparable single index models with correlated random effects is considered in panel data with a fixed number of time periods the identification assumption is based on the correlated random effects structure under this assumption the parameters of interest are identified up to a multiplicative constant and could be estimated by an average difference of derivatives estimator based on the local polynomial smoothing we suggest to linearly combine the estimators obtained for different orders of differences and derive the variance minimizing weighting scheme the asymptotic distribution of the proposed estimators is derived both for stationary and non stationary explanatory variables along with a test of the stationarity finally monte carlo experiments reveal finite sample properties of the proposed estimator

likelihood approaches for proportional likelihood ratio model with right censored data regression methods for survival data with right censoring have been extensively studied under semiparametric transformation models such as the cox regression model and the proportional odds model however their practical application could be limited because of possible violation of model assumption or lack of ready interpretation for the regression coefficients in some cases as an alternative in this paper the proportional likelihood ratio model introduced by luo and tsai is extended to flexibly model the relationship between survival outcome and covariates this model has a natural connection with many important semiparametric models such as generalized linear model and density ratio model and is closely related to biased sampling problems compared with the semiparametric transformation model the proportional likelihood ratio model is appealing and practical in many ways because of its model flexibility and quite direct clinical interpretation we present two likelihood approaches for the estimation and inference on the target regression parameters under independent and dependent censoring assumptions based on a conditional likelihood approach using uncensored failure times a numerically simple estimation procedure is developed by maximizing a pairwise pseudo likelihood we also develop a full likelihood approach and the most efficient maximum likelihood estimator is obtained by a profile likelihood simulation studies are conducted to assess the finite sample properties of the proposed estimators and compare the efficiency of the two likelihood approaches an application to survival data for bone marrow transplantation patients of acute leukemia is provided to illustrate the proposed method and other approaches for handling non proportionality the relative merits of these methods are discussed in concluding remarks

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

generalized partially linear single index model for zero inflated count data count data often arise in biomedical studies while there could be a special feature with excessive zeros in the observed counts the zero inflated poisson model provides a natural approach to accounting for the excessive zero counts in the semiparametric framework we propose a generalized partially linear single index model for the mean of the poisson component the probability of zero or both we develop the estimation and inference procedure via a profile maximum likelihood method under some mild conditions we establish the asymptotic properties of the profile likelihood estimators the finite sample performance of the proposed method is demonstrated by simulation studies and the new model is illustrated with a medical care dataset

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

a model free test for reduced rank in multivariate regression we propose a test of dimension in multivariate regression this test is in the spirit of tests on the rank of the coefficient matrix in a multivariate linear model but it does not require a prespecified model the test may be particularly useful at the outset of an analysis before a multivariate model is posited because it can lead to low dimensional summary plots that are inferred to contain all of the sample information on the multivariate mean function

distribution free estimation of heteroskedastic binary response models using probit logit criterion functions abstract in this paper estimators for distribution free heteroskedastic binary response models are proposed the estimation procedures are based on relationships between distribution free models with a conditional median restriction and parametric models such as probit logit exhibiting multiplicative heteroskedasticity the first proposed estimator is based on the observational equivalence between the two models and is a semiparametric sieve estimator see e g gallant and nychka 1987 ai and chen 2003 and chen et al 2005 for the regression coefficients based on maximizing standard logit probit criterion functions such as nlls and mle this procedure has the advantage that choice probabilities and regression coefficients are estimated simultaneously the second proposed procedure is based on the equivalence between existing semiparametric estimators for the conditional median model manski 1975 manski 1985 horowitz 1992 and the standard parametric probit logit nlls estimator this estimator has the advantage of being implementable with standard software packages such as stata distribution theory is developed for both estimators and a monte carlo study indicates they both perform well in finite samples

semiparametric gee analysis in partially linear single index models for longitudinal data in this article we study a partially linear single index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases a semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations gee is introduced to estimate the two parameter vectors as well as the unknown link function under some mild conditions we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios from which we find that the convergence rates and asymptotic variances of the proposed estimators for sparse longitudinal data would be substantially different from those for dense longitudinal data we also discuss the estimation of the covariance or weight matrices involved in the semiparametric gee method furthermore we provide some numerical studies including monte carlo simulation and an empirical application to illustrate our methodology and theory

parameterization invariant shape comparisons of anatomical surfaces we consider 3 d brain structures as continuous parameterized surfaces and present a metric for their comparisons that is invariant to the way they are parameterized past comparisons of such surfaces involve either volume deformations or non rigid matching under fixed parameterizations of surfaces we propose a new mathematical representation of surfaces called q maps such that l2 distances between such maps are invariant to re parameterizations this property allows for removing the parameterization variability by optimizing over the re parameterization group resulting in a proper parameterization invariant distance between shapes of surfaces we demonstrate this method in shape analysis of multiple brain structures for 34 subjects in the detroit fetal alcohol and drug exposure cohort study which results in a 91 classification rate for attention deficit hyperactivity disorder cases and controls this method outperforms some existing techniques such as spherical harmonic point distribution model spharm pdm or iterative closest point icp

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

variance function partially linear single index models we consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model we do not insist that the variance function depend only upon the mean function as happens in the classical generalized partially linear single index model we develop efficient and practical estimation methods for the variance function and for the mean function asymptotic theory for the parametric and nonparametric parts of the model is developed simulations illustrate the results an empirical example involving ozone levels is used to further illustrate the results and is shown to be a case where the variance function does not depend upon the mean function

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

an output feedback precompensator for nonlinear dae systems with control dependent state space this note considers singular systems of nonlinear differential and algebraic equations daes whose constrained state space depends on the control inputs a state space realization of such systems cannot be derived independently of the controller design an output feedback precompensator is derived which results in a modified dae system whose state space is invariant under any feedback control law and can be used for output feedback controller synthesis its application is illustrated by a nonlinear electrical circuit example

robust response transformations based on optimal prediction nonlinear regression problems can often be reduced to linearity by transforming the response variable e g using the box cox family of transformations the classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion assuming homoscedastic normal errors for the transformed response these estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic this article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution for this purpose a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an m scale this concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients a finite sample estimate of this criterion based on a robust version of s

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

on efficient estimation of the ordered response model in this paper we derive efficiency bounds for the ordered response model when the distribution of the errors is unknown furthermore we develop an estimator that is efficient under suitable conditions interestingly neither the bounds nor the estimator are trivial extensions of what has been proposed in the literature for the binary response model the estimator is composed of quadratic b splines and estimation is performed by the method of sieves in addition the estimator of the distribution function is restricted to be a proper distribution function an empirical example on the effect of fees on attendance rates at universities and community colleges is also included we get substantively different results by relaxing the assumption that the distribution of the errors is normal

rate optimal estimation for a general class of nonparametric regression models with unknown link functions this paper discusses a nonparametric regression model that naturally generalizes neural network models the model is based on a finite number of one dimensional transformations and can be estimated with a one dimensional rate of convergence the model contains the generalized additive model with unknown link function as a special case for this case it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion

a multiple index model and dimension reduction dimension reduction can be used as an initial step in statistical modeling further specification of model structure is imminent and important when the reduced dimension is still greater than 1 in this article we investigate one method of specification that involves separating the linear component from the nonlinear components leading to further dimension reduction in the unknown link function and thus better estimation and easier interpretation of the model the specified model includes the popular econometric multiple index model and the partially linear single index model as its special cases a criterion is developed to validate the model specification an algorithm is proposed to estimate the model directly asymptotic distributions for the estimators of the parameters and the nonparametric link function are derived air pollution data in chicago are used to illustrate the modeling procedure and to demonstrate its advantages over the existing dimension reduction approaches

some comments on copula based regression in a recent article noh el ghouch and bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula this comment investigates the effect which occurs under misspecification of the parametric model we demonstrate by means of several examples that even for a one or two dimensional predictor the error caused by a wrong specification of the parametric family is rather severe if the regression is not monotone in one of the components of the predictor moreover we also show that these problems occur for all of the commonly used copula families and we illustrate in several examples that the copula based regression may lead to invalid results even when flexible copula models such as vine copulas with the common parametric families are used in the estimation procedure

nuisance parameter elimination for proportional likelihood ratio models with nonignorable missingness and random truncation we show that the proportional likelihood ratio model proposed recently by luo tsai 2012 enjoys model invariant properties under certain forms of nonignorable missing mechanisms and randomly double truncated data so that target parameters in the population can be estimated consistently from those biased samples we also construct an alternative estimator for the target parameters by maximizing a pseudo likelihood that eliminates a functional nuisance parameter in the model the corresponding estimating equation has a u statistic structure as an added advantage of the proposed method a simple score type test is developed to test a null hypothesis on the regression coefficients simulations show that the proposed estimator has a small sample efficiency similar to that of the nonparametric likelihood estimator and performs well for certain nonignorable missing data problems