a consistent estimator for the binomial distribution in the presence of incidental parameters an application to patent data in this paper a consistent estimator for the binomial distribution in the presence of incidental parameters or fixed effects when the underlying probability is a logistic function is derived the consistent estimator is obtained from the maximization of a conditional likelihood function in light of andersen s work monte carlo simulations show its superiority relative to the traditional maximum likelihood estimator with fixed effects also in small samples particularly when the number of observations in each cross section t is small finally this new estimator is applied to an original dataset that allows the estimation of the probability of obtaining a patent

on the finite element least squares approximation to higher order elliptic systems the use of variational methods of the least squares type has been studied by many authors they were first introduced for scalar elliptic equations by bramble schatz 1 this work was extended by baker 2 who also treated the scalar case recent applications have stressed the importance of these ideas for systems these include problems in acoustics involving the helmholtz equation 3 4 transonic flow problems of the mixed elliptic hyperbolic type 5 7 and elasto plastic problems 8 the analysis of these methods for the special case of second order systems is given in 9 10 and the goal of this paper is to extend these results to higher order systems

asymptotic properties of the maximum likelihood estimator in dichotomous logit models abstract the existence and strong consistency of the maximum likelihood estimator are analyzed in the context of dichotomous logit models sufficient conditions are given for the asymptotic normality of this estimator

the incidental parameter problem since 1948 this paper was written to mark the 50th anniversary of neyman and scott s econometrica paper defining the incidental parameter problem it surveys the history both of the paper and of the problem in the statistics and econometrics literature

estimating latent distributions in recurrent choice data this paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data these choice models are derived by specifying elements of the choice process at the individual level probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior due to the explicit consideration of random effect sources the choice models are parsimonious and readily interpretable an easy to implement em algorithm is presented for parameter estimation two applications illustrate the proposed approach

nonparametric identification in nonseparable panel data models with generalized fixed effects abstract this paper extends the familiar notion of fixed effects to nonlinear structures with infinite dimensional unobservables like preferences the main result is that a generalized version of differencing identifies local average responses lars in nonseparable structures in contrast to existing results this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest and it requires only two time periods on the other hand the results are confined to the subpopulation of stayers chamberlain 1982 i e the population for which the explanatory variables do not change over time we extend the basic framework to include time trends and dynamics in the explanatory variables and we show how distributional effects as well as average partial effects are identified our approach also allows endogeneity in the transitory unobservables furthermore we show that this new identification principle can be applied to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects finally we suggest estimators for the local average response and average partial effect and we analyze their large and finite sample behavior

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

mmc techniques for limited dependent variables models implementation by the branch and bound algorithm we propose a finite sample approach to some of the most common limited dependent variables models the method rests on the maximized monte carlo mmc test technique proposed by dufour 1998 monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics journal of econometrics this issue we provide a general way for implementing tests and confidence regions we show that the decision rule associated with a mmc test may be written as a mixed integer programming problem the branch and bound algorithm yields a global maximum in finite time an appropriate choice of the statistic yields a consistent test while fulfilling the level constraint for any sample size the technique is illustrated with numerical data for the logit model c 2005 elsevier b v all rights reserved

semiparametric estimation of panel data models without monotonicity or separability abstract nonseparable panel data models with fixed effects have received a great deal of attention in the literature monotonicity is a common assumption in these settings which may be violated in practice monotonicity based estimators are inconsistent and the associated inference misleading under misspecification in this paper we propose some semiparametric estimators without imposing the monotonicity restriction under regularity conditions our estimators are consistent and asymptotically normal our simulation suggests that our estimators work well in finite samples

root n consistent estimation of fixed effect panel data transformation models with censoring this paper considers semiparametric n consistent estimation of the parameters of the generalized panel data transformation model with fixed effects under various forms of censoring without parametric specification for the transformation function or the error distribution while the approach in abrevaya 1999 is n consistent it is not applicable when censoring is present for the case with fixed censoring existing approaches such as those of manski 1987 and abrevaya 2000 apply but their estimators converge at rates slower than n thus possessing zero efficiency compared with n consistent estimators while the approaches by honore 1992 and ridder and tunali 1999 do produce n consistent estimators under fixed and independent censoring respectively they require either the error distribution or the transformation function to be completely known our n consistent estimator for the fixed censoring case could be extended to the cases with independent and dependent censoring under dependent censoring in contrast to our method the existing approaches e g horowitz and lee 2003 lee 2008 and das and ying 2005 require parametric specification for the transformation function or the error distribution large sample properties of the proposed estimators are presented we also provide a simulation study to illustrate our estimation methods in finite samples

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

on site samples regression problems of non negative integers truncation and endogenous stratification abstract the paper corrects an estimation problem that has not yet been recognized in previous estimates of demand functions using on site samples there are three kinds of problems that one faces in on site samples namely non negative integers truncation and endogenous stratification two theoretically correct maximum likelihood methods are developed based on two different assumptions about the variable distribution the normal distribution and the poisson distribution a simulation is performed to compare the two methods using generated data sets of known models we should not use ols and instead should use the maximum likelihood methods developed here to estimate demand functions that use on site samples if forecasting is the purpose of estimation then the simulation indicates that the poisson ml method may be better

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

numerical methods for a volterra integral equation with non smooth solutions we consider the numerical treatment of a singular volterra integral equation with an infinite set of solutions one of which is smooth and all others have infinite gradient at the origin this equation has been the subject of previous works where we have dealt with the approximation of the smooth solution here we present numerical methods which enable us to obtain approximations to any of the infinite class of solutions some numerical examples are given which illustrate the performance of the methods employed

distribution free estimation of some nonlinear panel data models this paper studies distribution free estimation of some multiplicative unobserved components panel data models one class of estimators requires only specification of the conditional mean in particular the multinomial quasi conditional maximum likelihood estimator is shown to be consistent when only the conditional mean in the unobserved effects model is correctly specified additional orthogonality conditions can be used in a method of moments framework a second class of problems specifies the conditional mean conditional variances and conditional covariances using the notion of a conditional linear predictor it is shown that specification of conditional second moments implies further orthogonality conditions in the observable data that can be exploited for efficiency gains this has applications to both count and gamma type panel data regression models

posterior simulation and bayes factors in panel count data models abstract this paper is concerned with the problems of posterior simulation and model choice for poisson panel data models with multiple random effects efficient algorithms based on markov chain monte carlo methods for sampling the posterior distribution are developed a new parameterization of the random effects and fixed effects is proposed and compared with a parameterization in common use and computation of marginal likelihoods and bayes factors via chib s 1995 method is also considered the methods are illustrated with two real data applications involving large samples and multiple random effects

quantiles for counts this article studies the estimation of conditional quantiles of counts given the discreteness of the data some smoothness must be artificially imposed on the problem we show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques the performance and implementation of the estimators are illustrated by simulations and an application

predictive model assessment for count data we discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data our proposals include a nonrandomized version of the probability integral transform marginal calibration diagrams and proper scoring rules such as the predictive deviance in case studies we critique count regression models for patent data and assess the predictive performance of bayesian age period cohort models for larynx cancer counts in germany the toolbox applies in bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes

estimating count data models with endogenous switching sample selection and endogenous treatment effects count data regression models are extended to account for endogenous switching and its two most common incarnations viz endogenous dummy variables treatment effects and sample selection fully parametric and partially parametric versions of the extended model are discussed in the parametric version of the model a full information maximum likelihood fiml approach to estimation is introduced under the correct model specification the fiml estimator is efficient but computationally burdensome for the relatively robust partially parametric version of the model i develop a two stage method of moments tsm estimator the tsm estimator is a nonlinear least squares analog to the popular heckman 1976 1979 estimator and therefore avoids the computational requirements of fiml estimation a nonlinear weighted least squares nwls estimator is offered for the fully parametric case the nwls estimator is computationally efficient relative to fiml estimation and statistically efficient relative to the tsm estimator for illustrative purposes the tsm and nwls estimators are applied to the estimation of a regression model with household trip frequency as the dependent variable and a potentially endogenous dummy variable indicating vehicle ownership among the regressors

mixed inar 1 poisson regression models analyzing heterogeneity and serial dependencies in longitudinal count data this paper presents finite mixture versions of integer valued autoregressive inar poisson regression models for investigating regularity and predictability of purchase behavior over time the approach facilitates the analysis of heterogeneity and serial correlation effects as well as conditional and marginal analyses of the effects of covariates an application to scanner panel data of detergents yields substantive insights into sources of autodependencies in individual category purchases

nonparametric estimation of regression functions with both categorical and continuous data abstract in this paper we propose a method for nonparametric regression which admits continuous and categorical data in a natural manner using the method of kernels a data driven method of bandwidth selection is proposed and we establish the asymptotic normality of the estimator we also establish the rate of convergence of the cross validated smoothing parameters to their benchmark optimal smoothing parameters simulations suggest that the new estimator performs much better than the conventional nonparametric estimator in the presence of mixed data an empirical application to a widely used and publicly available dynamic panel of patent data demonstrates that the out of sample squared prediction error of our proposed estimator is only 14 20 of that obtained by some popular parametric approaches which have been used to model this data set

finite element methods of least squares type we consider the application of least squares variational principles to the numerical solution of partial differential equations our main focus is on the development of least squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows linear elasticity and convection diffusion for many of these problems least squares principles offer numerous theoretical and computational advantages in the algorithmic design and implementation of corresponding finite element methods that are not present in standard galerkin discretizations most notably the use of least squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf sup condition arising in mixed methods for the stokes and navier stokes equations as a result application of least squares principles has led to the development of robust and efficient finite element methods for a large class of problems of practical importance

a count data model with unobserved heterogeneity abstract a count data model is defined via the distribution of the durations between successive events it is assumed that the durations follow independent exponential distributions conditionally to a set of variables the parameters of these distributions depend not only on observed and unobserved individual specific factors but also on unobserved spell specific factors the count data model is therefore a natural extension of the compound poisson model a local version of the count data model is used to analyse the effects of unobserved spell specific factors in particular it is shown that spell specific heterogeneity can induce not only overdispersion but also underdispersion the local model is also used to construct a score test for spell specific heterogeneity in the poisson model the results are applied on purchase data of a consumption good

specification and testing of some modified count data models abstract this paper explores the specification and testing of some modified count data models these alternatives permit more flexible specification of the data generating process dgp than do familiar count data models e g the poisson and provide a natural means for modeling data that are over or underdispersed by the standards of the basic models in the cases considered the familiar forms of the distributions result as parameter restricted versions of the proposed modified distributions accordingly score tests of the restrictions that use only the easily computed ml estimates of the standard models are proposed the tests proposed by hausman 1978 and white 1982 are also considered the tests are then applied to count data models estimated using survey microdata on beverage consumption

specification testing and quasi maximum likelihood estimation abstract this paper develops robust regression based conditional moment tests for models estimated by quasi maximum likelihood using a density in the linear exponential family the tests are relatively simple to compute while being robust to distributional assumptions other than those being explicitly tested the conditional mean tests assume only that the conditional mean is correctly specified under the null hypothesis but are asymptotically equivalent to standard forms of the tests if the conditional variance is correctly specified tests for conditional variance misspecification assume only that the first two moments are correctly specified under the null hypothesis an empirical application to individual arrest data is included

semiparametric estimation of heterogeneous count data models unobserved heterogeneity in a stochastic model is usually represented by a mixing distribution in this paper a semiparametric estimator is adapted to over dispersed poisson regression models no assumptions are needed about the estimated mixing distribution the parameters of included explanatory variables are estimated at the same time the applicability and promising properties of the method are illustrated empirically the estimator is applied to a coffee purchase model and to a business travel frequency model subject to zero truncation the approach is useful e g in marketing research where socio demographic variables as well as marketing instruments can be included as explanatory variables

issues related to least squares finite element methods for the stokes equations least squares finite element methods have become increasingly popular for the approximate solution of first order systems of partial differential equations here after a brief review of some existing theories a number of issues connected with the use of such methods for the velocity vorticity pressure formulation of the stokes equations in two dimensions in realistic settings are studied through a series of computational experiments finite element spaces that are not covered by existing theories are considered included in these are piecewise linear approximations for the velocity mixed boundary conditions which are also not covered by existing theories are also considered as is enhancing mass conservation next problems in nonconvex polygonal regions and the resulting nonsmooth solutions are considered with a view toward seeing how accuracy can be improved a conclusion that can be drawn from this series of computational experiments is that the use of appropriate mesh dependent weights in the least squares functional almost always improves the accuracy of the approximations concluding remarks concerning three dimensional problems the nonlinear navier stokes equations and the conditioning of the discrete systems are provided

solution of a class of volterra integral equations with singular and weakly singular kernels a class of volterra integral equations are solved in this paper where the involved kernel may be weakly singular singular and hypersingular for various cases existence and uniqueness of such volterra integral equations are established furthermore by reducing such equations to ordinary differential equations analytic solutions have been determined explicitly when restricting the solutions to certain special function classes the number of suitable solutions is given

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

numerical analysis of a singular integral equation in this paper we give details of the numerical analysis of an integral equation of the form 1 y t f t email protected 0ts m 1t my s email protected 0 the distinctive feature of the equation is the presence of a singularity at t 0 for all values of m 0 and at s 0 for all values of t 0 for 0 m 1 this means that conventional analytical and numerical theory does not apply in fact for 0 m 1 the equation has an infinite family of solutions as background we give details of the analytical results on existence and uniqueness of solutions to 1 and we give new results on the use of numerical schemes that will yield approximations to any specific solution we conclude with some numerical results that show that our methods enable us to find approximations of any chosen order to any of the infinite class of exact solutions to 1

asymptotics for generalized estimating equations with large cluster sizes generalized estimating equations are used in regression analysis of longitudinal data where observations on each subject are correlated statistical analysis using such methods is based on the asymptotic properties of regression parameter estimators this paper presents asymptotic results when either the number of independent subjects or the cluster sizes the number of observations on each subject or both go to infinity a set of information matrix based general conditions is developed which leads to the weak and strong consistency as well as the asymptotic normality of the estimators most of the results are parallel to the elegant work of fahrmeir and kaufmann on maximum likelihood estimators related to the generalized linear models the conditions for weak consistency and asymptotic normality are verified for several examples of general interest

a poisson mixture model of discrete choice abstract in this paper we introduce a new poisson mixture model for count panel data where the underlying poisson process intensity is determined endogenously by consumer latent utility maximization over a set of choice alternatives this formulation accommodates the choice and count in a single random utility framework with desirable theoretical properties individual heterogeneity is introduced through a random coefficient scheme with a flexible semiparametric distribution we deal with the analytical intractability of the resulting mixture by recasting the model as an embedding of infinite sequences of scaled moments of the mixing distribution and newly derive their cumulant representations along with bounds on their rate of numerical convergence we further develop an efficient recursive algorithm for fast evaluation of the model likelihood within a bayesian gibbs sampling scheme we apply our model to a recent household panel of supermarket visit counts we estimate the nonparametric density of three key variables of interest price driving distance and their interaction while controlling for a range of consumer demographic characteristics we use this econometric framework to assess the opportunity cost of time and analyze the interaction between store choice trip frequency search intensity and household and store characteristics we also conduct a counterfactual welfare experiment and compute the compensating variation for a 10 30 increase in walmart prices

individual effects and dynamics in count data models in this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables use of a linear feedback model is proposed a quasi differenced gmm estimator is consistent for the parameters in the dynamic model but when series are highly persistent there is a problem of weak instrument bias an estimator is proposed that utilises pre sample information of the dependent count variable which is shown in monte carlo simulations to possess desirable small sample properties the models and estimators are applied to data on us patents and r d expenditure

pseudo maximum likelihood methods applications to poisson models pseudo maximum likelihood techniques are applied to basic poisson models and to poisson models with specification errors in the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p d f of the disturbances these estimators are compared both from the finite sample and the asymptotic point of view quasi generalized pml estimators which asymptotically dominate all pml estimators are also proposed finally bivariate and panel data poisson models are discussed the analysis of economic behavior often leads to the study of characteristics taking a small number of positive values the classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables the reasons are similar to those usually given in the case of an endogenous qualitative variable the shape of the observation set does not correspond to a linear model the assumption of normality of the disturbances cannot be made since the endogenous variables take a small number of values with strictly positive probabilities and the prediction formulae which are deduced from a linear model give impossible values in the models considered in the literature to describe discrete variables cox and lewis 2 el sayyad 3 frome kutner and beauchamp 4 gilbert 5 hausman hall and griliches 8 see also lancaster 12 the endogenous variable is assumed to have a poisson distribution conditional upon the exogenous variables the parameter of this distribution is a function of the values of the exogenous variables the choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the poisson process are satisfied for instance the model is adapted to describe daily numbers of oil tankers arrivals in a port the number of accidents at work by factory or the number of patents applied for and received by firms hausman hall and griliches 8

robust priors in nonlinear panel data models many approaches to estimation of panel models are based on an average or integrated likelihood that assigns weights to different values of the individual effects fixed effects random effects and bayesian approaches all fall in this category we provide a characterization of the class of weights or priors that produce estimators that are first order unbiased we show that such bias reducing weights must depend on the data unless an orthogonal reparameterization or an essentially equivalent condition is available two intuitively appealing weighting schemes are discussed we argue that asymptotically valid confidence intervals can be read from the posterior distribution of the common parameters when n and t grow at the same rate finally we show that random effects estimators are not bias reducing in general and discuss important exceptions three examples and some monte carlo experiments illustrate the results

on a simple test for neglected heterogeneity in panel studies summary this paper deals with the performance of a simple test for the detection of unmeasured heterogeneity in regression models for panel data it is assumed that the unmeasured heterogeneity can be modeled by an individual specific random variable that does not vary over time conditionally on the individual specific effects and the regressor variables the distribution of the dependent variable is assumed to belong to a linear exponential family this class of distributions includes linear models for continuous dependent variables as well as nonlinear models for discrete outcomes the proposed test does not assume a special form of the distribution of the heterogeneity and the test statistic can be calculated with available computer programs the performance of the test is investigated in a simulation experiment

rank estimation of a generalized fixed effects regression model abstract this paper considers estimation of a fixed effects version of the generalized regression model of han 1987 journal of econometrics 35 303 316 the model allows for censoring places no parametric assumptions on the error disturbances and allows the fixed effects to be correlated with the covariates we introduce a class of rank estimators that consistently estimate the coefficients in the generalized fixed effects regression model the maximum score estimator for the binary choice fixed effects model is part of this class like the maximum score estimator the class of rank estimators converge at less than the n rate smoothed versions of these estimators however converge at rates approaching the n rate in a version of the model that allows for truncated data a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function

multiplicative error models with sample selection this paper presents a simple approach to deal with sample selection in models with multiplicative errors models for non negative limited dependent variables such as counts fit this framework the approach builds on a specification of the conditional mean of the outcome only and is therefore semiparametric in nature gmm estimators are constructed for both cross section data and for panel data we derive distribution theory and present monte carlo evidence on the finite sample performance of the estimators

analyzing multiple emotions over time by autoregressive negative multinomial regression models abstract this article presents an autoregressive random coefficient model with overdispersed negative multinomial marginal distributions for the analysis of heterogeneity and serial dependencies in multivariate longitudinal count data the model structure consists of four components that take into account a individual difference effects b random time effects c multiple event categories and d autodependencies the last component is based on a stochastic integer valued autoregressive process proposed by mckenzie the model is applied to analyze count data from a panel diary study about the relationship between personality factors and emotion experiences it is shown that there are large and stable individual personality differences in the incidence and duration of self reported emotional experiences theoretical and clinical implications of this result are discussed

likelihood quasi likelihood and pseudolikelihood some comparisons summary there is considerable interest in the fitting of models jointly to the mean and dispersion of a response for the mean parameter the wedderburn estimating equations are widely accepted however there is some controversy about estimating the dispersion parameters finite sampling properties of several dispersion estimators are investigated for three models by simulation we compare the maximum extended quasi likelihood estimator the maximum pseudolikelihood estimator and the maximum likelihood estimator if it exists of these estimators the maximum extended quasi likelihood estimator is usually superior in minimizing the mean squared error

overdispersion tests for truncated poisson regression models abstract score tests of extra poisson variation in left or right truncated poisson regression models are derived for alternatives in the left or right truncated negative binomial family and for arbitrary truncation points using asymptotic expansions of the score function adjustment factors are derived for the tests which are expected to improve their small sample properties overdispersion tests for the untruncated poisson model in the econometric and statistical literature are special cases of the tests derived in this paper a monte carlo investigation of the new tests when data are truncated at zero show that the effect of truncation produces a significant size distortion and power reduction especially in small samples but also that the corrections suggested by asymptotic expansions improve the performance of the tests

generalised structured models summary we present a general class of nonlinear regression and time series models that we call generalised structured models the class is a natural generalisation of generalised additive models and it includes generalised interaction models structured volatility models visual garch generalised autoregressive conditional heteroscedasticity models and varying coefficient models we discuss estimation principles including smoothing splines and a generalisation of the projection approach of mammen et al 1999 we finish the paper with some theoretical considerations about the asymptotic performance of the estimator for the general class of generalised structured models

disease mapping via negative binomial regression m quantiles we introduce a semi parametric approach to ecological regression for disease mapping based on modelling the regression m quantiles of a negative binomial variable the proposed method is robust to outliers in the model covariates including those due to measurement error and can account for both spatial heterogeneity and spatial clustering a simulation experiment based on the well known scottish lip cancer data set is used to compare the m quantile modelling approach with a disease mapping approach based on a random effects model this suggests that the m quantile approach leads to predicted relative risks with smaller root mean square error the paper concludes with an illustrative application of the m quantile approach mapping low birth weight incidence data for english local authority districts for the years 2005 2010 copyright 2014 john wiley sons ltd

limit theory for panel data models with cross sectional dependence and sequential exogeneity abstract the paper derives a general central limit theorem clt and asymptotic distributions for sample moments related to panel data models with large n the results allow for the data to be cross sectionally dependent while at the same time allowing the regressors to be only sequentially rather than strictly exogenous the setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and or from the presence of common factors the latter leads to the need for random norming the limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied we prove such a central limit theorem by first extending results for stable convergence in hall and heyde 1980 to non nested martingale arrays relevant for our applications we illustrate our result by establishing a generalized estimation theory for gmm estimators of a fixed effect panel model without imposing i i d or strict exogeneity conditions we also discuss a class of maximum likelihood ml estimators that can be analyzed using our clt

an inar 1 negative multinomial regression model for longitudinal count data this paper discusses a regression model for the analysis of longitudinal count data observed in a panel study an integer valued first order autoregressive inar 1 poisson process is adapted to represent time dependent correlations among the counts by combining the inar 1 representation with a random effects approach a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by edwards and gurland 1961 and subrahmaniam 1966 as a special case a detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach

a note on the efficiency of sandwich covariance matrix estimation the sandwich estimator also known as robust covariance matrix estimator heteroscedasticity consistent covariance matrix estimate or empirical covariance matrix estimator has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified surprisingly though there has been little discussion of properties of the sandwich method other than consistency we investigate the sandwich estimator in quasi likelihood models asymptotically and in the linear case analytically we show that under certain circumstances when the quasi likelihood model is correct the sandwich estimate is often far more variable than the usual parametric variance estimate the increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the p

a least squares finite element scheme for transonic flow around harmonically oscillating airfoils abstract a finite element scheme based on a least squares variational principle is used to calculate the transonic flow field around harmonically oscillating airfoils the most important features of this procedure are its insensitivity to equation type and the absence of frequency limitation sample numerical results are reported including transonic flows containing shocks

research and development competition and innovation pseudo maximum likelihood and simulated maximum likelihood methods applied to count data models with heterogeneity abstract this paper focuses on the relationship between the research and development r d expenditures undertaken by firms and the number of patents claimed by them the econometric methods we use incorporate two important features of the data first we introduce a heterogeneity term accounting for the unobservable factors affecting the production of innovations second we allow for a large proportion of the sample not to apply for a patent depending on the specification estimation proceeds by maximum likelihood pseudo maximum likelihood or simulated maximum likelihood methods our main findings are the following i the returns to scale in the innovation technology may be constant on average and ii competitors r d may have a negative impact on own innovation thus revealing a rivalry effect of intellectual property

modelling non stationary multivariate time series of counts via common factors we develop a new parameter driven model for multivariate time series of counts the time series is not necessarily stationary we model the mean process as the product of modulating factors and unobserved stationary processes the former characterizes the long run movement in the data whereas the latter is responsible for rapid fluctuations and other unknown or unavailable covariates the unobserved stationary processes evolve independently of the past observed counts and might interact with each other we express the multivariate unobserved stationary processes as a linear combination of possibly low dimensional factors that govern the contemporaneous and serial correlation within and across the observed counts regression coefficients in the modulating factors are estimated via pseudo maximum likelihood estimation and identification of common factor s is carried out through eigenanalysis on a positive definite matrix that pertains to the autocovariance of the observed counts at non zero lags theoretical validity of the two step estimation procedure is documented in particular we establish consistency and asymptotic normality of the pseudo maximum likelihood estimator in the first step and the convergence rate of the second step estimator we also present an exhaustive simulation study to examine the finite sample performance of the estimators and numerical results corroborate our theoretical findings finally we illustrate the use of the proposed model through an application to the numbers of national science foundation fundings awarded to seven research universities from january 2001 to december 2012

the econometrics of ultra high frequency data ultra high frequency data is defined to be a full record of transactions and their associated characteristics the transaction arrival times and accompanying measures can be analyzed as marked point processes the acd point process developed by engle and russell 1998 is applied to ibm transactions arrival times to develop semiparametric hazard estimates and conditional intensities combining these intensities with a garch model of prices produces ultra high frequency measures of volatility both returns and variances are found to be negatively influenced by long durations as suggested by asymmetric information models of market micro structure

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

regression based tests for overdispersion in the poisson model abstract a property of the poisson regression model is mean variance equality conditional on explanatory variables regression based tests for this property are proposed in a very general setting unlike classical statistical tests these tests require specification of only the mean variance relationship under the alternative rather than the complete distribution whose choice is usually arbitrary the optimal regression based test is easily computed as the t test from an auxiliary regression if a distribution under the alternative hypothesis is in fact specified and is in the katz system of distributions or is cox s local approximation to the poisson the score test for the poisson distribution is equivalent to the optimal regression based test

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

numerical modelling of qualitative behaviour of solutions to convolution integral equations we consider the qualitative behaviour of solutions to linear integral equations of the form 1 y t g t email protected 0 tk t s y s ds where the kernel k is assumed to be either integrable or of exponential type after a brief review of the well known paley wiener theory we give conditions that guarantee that exact and approximate solutions of 1 are of a specific exponential type as an example we provide an analysis of the qualitative behaviour of both exact and approximate solutions of a singular volterra equation with infinitely many solutions we show that the approximations of neighbouring solutions exhibit the correct qualitative behaviour

semiparametric estimation of count regression models this paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity we use the generalized laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a poisson mixture model we establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated censored and zero inflated count regression models monte carlo evidence shows that the finite sample behavior of the estimator is quite good the paper applies the method to a model of individual shopping behavior

numerical solution of a nonuniquely solvable volterra integral equation using extrapolation methods in this work the numerical solution of a volterra integral equation with a certain weakly singular kernel depending on a real parameter is considered although for certain values of this equation possesses an infinite set of solutions we have been able to prove that euler s method converges to a particular solution it is also shown that the error allows an asymptotic expansion in fractional powers of the stepsize so that general extrapolation algorithms like the e algorithm can be applied to improve the numerical results this is illustrated by means of some examples

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

a nystrom interpolant for some weakly singular nonlinear volterra integral equations we consider a second kind weakly singular nonlinear volterra hammerstein integral equation defined by a compact operator and derive a nystrom type interpolant of the solution based on gauss radau nodes we prove the convergence of the interpolant and derive convergence estimates for equations with nonlinearity of algebraic kind we improve the rate of convergence by using a smoothing transformation some numerical examples are given

relative risk risk difference and rate difference models for sparse stratified data a pseudo likelihood approach we consider a relative risk and a risk difference model for binomial data and a rate difference model for poisson person year data it is assumed that the data are stratified in a large number of small strata if each stratum has its own parameter in the model then due to the large number of parameters straightforward maximum likelihood leads to inconsistent estimates of the relevant parameters by contrast to the logistic model conditioning on the number of events per stratum does not help in eliminating the stratum nuisance parameters we propose a pseudo likelihood method to overcome these consistency problems the resulting pseudo maximum likelihood estimates can easily be computed with standard statistical software our approach gives a more general framework for the mantel haenszel type estimators proposed in the literature in the special case of a series of 2 x 2 tables for the risk and rate difference models our approach yields exactly these ad hoc mantel haenszel estimators while for the relative risk model it gives a close approximation of the mantel haenszel relative risk estimator for the regression models corresponding to the association measures relative risk risk difference and rate difference our method provides analogues of conditional logistic regression which were not previously available

the value of water levels in water based recreation a pooled revealed preference contingent behavior model in this paper we present estimated recreation values for preventing a decline in water levels at and even the total loss of a large western lake that is drying up we use a poisson version of the count data travel cost model however in addition to and in combination with revealed preference rp data we employ contingent behavior cb responses to hypothetical questions on alternative water levels and number of trips the pooled model used allows for tests of differences between results using rp and cb data this particular pooled rp cb approach has not to our knowledge previously been applied to examine the values of alternative water quantities in water based recreation