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

a discrete homotopy theory for binary reflexive structures abstract we present a simple combinatorial construction of a sequence of functors k from the category of pointed binary reflexive structures to the category of groups we prove that if the relational structure is a poset p then the groups are naturally isomorphic to the homotopy groups of p when viewed as a topological space with the topology of ideals or equivalently to the homotopy groups of the simplicial complex associated to p we deduce that the group k x x 0 of the pointed structure x x 0 is naturally isomorphic to the k th homotopy group of the simplicial complex of simplices of x i e those subsets of x which are the homomorphic image of a finite totally ordered set

linear equations with random variables a system of linear equations is presented where the unknowns are unobserved values of random variables a maximum likelihood estimator assuming a multivariate normal distribution and a non parametric proportional allotment estimator are proposed for the unobserved values of the random variables and for their means both estimators can be computed by simple iterative procedures and are shown to perform similarly the methods are illustrated with data from a national nutrition survey in japan

a comment on some recent results concerning the reverse order law for 1 3 4 inverses abstract this paper has been motivated by the one of liu and yang d liu h yang the reverse order law for 1 3 4 inverse of the product of two matrices appl math comp 215 12 2010 4293 4303 in which the authors consider separately the cases when ab 1 3 4 b 1 3 4 a 1 3 4 and ab 1 3 4 b 1 3 4 a 1 3 4 where a c n m and b c m n here we prove that ab 1 3 4 b 1 3 4 a 1 3 4 is actually equivalent to ab 1 3 4 b 1 3 4 a 1 3 4 we show that ab 1 3 4 b 1 3 4 a 1 3 4 can only be possible if n m and in this case we present purely algebraic necessary and sufficient conditions for this inclusion to hold also we give some new characterizations of b 1 3 4 a 1 3 4 ab 1 3 4

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

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

identification of the 1pl model with guessing parameter parametric and semi parametric results in this paper we study the identification of a particular case of the 3pl model namely when the discrimination parameters are all constant and equal to 1 we term this model 1pl g model the identification analysis is performed under three different specifications the first specification considers the abilities as unknown parameters it is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero the second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter it is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero the third specification corresponds to a semi parametric 1pl g model where the distribution g generating the abilities is a parameter of interest it is not only shown that after fixing a difficulty parameter and a guessing parameter at zero the item parameters are identified but also that under those restrictions the distribution g is not identified it is finally shown that after introducing two identification restrictions either on the distribution g or on the item parameters the distribution g and the item parameters are identified provided an infinite quantity of items is available

hard constraint satisfaction problems have hard gaps at location 1 an instance of the maximum constraint satisfaction problem max csp is a finite collection of constraints on a set of variables and the goal is to assign values to the variables that maximises the number of satisfied constraints max csp captures many well known problems such as maxk sat and max cut and is consequently np hard thus it is natural to study how restrictions on the allowed constraint types or constraint language affect the complexity and approximability of max csp the pcp theorem is equivalent to the existence of a constraint language for which max csp has a hard gap at location 1 i e it is np hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable all constraint languages for which the csp problem i e the problem of deciding whether all constraints can be satisfied is currently known to be np hard have a certain algebraic property we prove that any constraint language with this algebraic property makes max csp have a hard gap at location 1 which in particular implies that such problems cannot have a ptas unless p np we then apply this result to max csp restricted to a single constraint type this class of problems contains for instance max cut and max dicut assuming p np we show that such problems do not admit ptas except in some trivial cases our results hold even if the number of occurrences of each variable is bounded by a constant finally we give some applications of our results

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

the complexity of solving equations over finite groups we study the computational complexity of solving systems of equations over a finite group an equation over a group g is an expression of the form w1 w2 wk 1g where each wi is either a variable an inverted variable or a group constant and 1g is the identity element of g a solution to such an equation is an assignment of the variables to values in g which realizes the equality a system of equations is a collection of such equations a solution is then an assigmnent which simultaneously realizes each equation we show that the problem of determining if a single equation has a solution is np complete for all nonsolvable groups g for nilpotent groups this same problem is shown to be in p the analogous problem for systems of such equations is shown to be np complete if g is non abelian and in p otherwise finally we observe some connections between these problems and the theory of nonuniform automata

fixed effects dynamic panel models a factor analytical method we consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions individual fixed effects and time fixed effects as well as incidental parameters in the variances we adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves in the presence of cross sectional heteroskedasticity the factor method estimates the average of the cross sectional variances instead of the individual variances the method thereby eliminates the incidental parameter problem in the means and in the variances over the cross sectional dimension we further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental parameter bias even when t and n are comparable moreover efficient and robust estimation is obtained by jointly estimating heteroskedasticities

minimum distance approach to inference with many instruments abstract i analyze a linear instrumental variables model with a single endogenous regressor and many instruments i use invariance arguments to construct a new minimum distance objective function with respect to a particular weight matrix the minimum distance estimator is equivalent to the random effects estimator of chamberlain and imbens 2004 and the estimator of the coefficient on the endogenous regressor coincides with the limited information maximum likelihood estimator this weight matrix is inefficient unless the errors are normal and i construct a new more efficient estimator based on the optimal weight matrix finally i show that when the minimum distance objective function does not impose a proportionality restriction on the reduced form coefficients the resulting estimator corresponds to a version of the bias corrected two stage least squares estimator i use the objective function to construct confidence intervals that remain valid when the proportionality restriction is violated

saddlepoint expansions for directional test probabilities an expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value in particular if the score function of a statistical model is chosen as this variable such a conditional probability gives a test for a simple hypothesis which is asymptotically equivalent to the likelihood ratio test the expansion is of the large deviation type and is derived through the use of saddlepoint methods thus the relative error of the test probability is o n1 uniformly in a bounded set for an average of n independent replications the approximation is based on the cumulant transform for the random variable but is otherwise a simple expression in terms of chi squared distributions in the one dimensional case it reduces to the expansion obtained by lugannani and rice numerical examples show an excellent fit comparable with other saddlepoint expansions when the dimension is low even for very small sample sizes but for higher dimensions more replications are required to give a similar approximation

estimating functions and approximate conditional likelihood summary the approximate conditional likelihood method proposed by cox reid 1987 is applied to the estimation of a scalar parameter 0 in the presence of nuisance parameters the estimating function of 0 based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood a sufficient condition for both approaches to be equivalent is given the role of parameter orthogonality is emphasized several examples including bivariate normal means with known coefficient of variation are presented

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

estimation of heterogeneous autoregressive parameters with short panel data abstract this paper presents a maximum likelihood approach to estimation of cross sectional distributions of heterogeneous autoregressive ar parameters with short panel data we construct a panel likelihood by integrating the unknown cross sectional density of heterogeneous ar parameters with respect to a known time series data generating kernel the solution to this extremal criterion recovers the unknown density of heterogeneous ar parameters applying our method to a model of employment dynamics with the firm level data of arellano and bond 1991 we find that adjustment rates of employment are significantly heterogeneous across firms

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

bias corrections for two step fixed effects panel data estimators this paper introduces large t bias corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity these models include systems of equations with limited dependent variables and unobserved individual effects and sample selection models with unobserved individual effects our two step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity selection bias we then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable the fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem this problem is exacerbated by the two step nature of the procedure as these two step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large t bias adjustments to an important class of models simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator

on the choice of prior distribution for the box cox transformed linear model summary the noninformative prior distribution for the parameters of the linear model transformed following box cox 1964 has the non bayesian property of depending to some extent on the data an alternative choice of prior which is not outcome dependent was suggested by pericchi 1981 but it is argued here that this prior has some undesirable features an alternative family of non outcome dependent priors is suggested leading to a noninformative prior which is closer in spirit to that proposed by box cox the posterior consequences of adopting this prior are fully explored and an example discussed

bias reduction in nonlinear and dynamic panels in the presence of cross section dependence abstract fixed effects estimation of nonlinear dynamic panel models is subject to the incidental parameter issue leading to a biased asymptotic distribution while this problem has been studied extensively in the literature a general analysis allowing for both serial and cross sectional dependence is missing in this paper we investigate the large n t theory of the profile and integrated likelihood estimators allowing for dependence across both dimensions we show that under stronger dependence types the asymptotic bias disappears but a o p 1 t small sample bias remains we provide bias correction and inference methods and also obtain primitive conditions for asymptotic normality under various dependence settings

maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor augmented regressions abstract this paper reestablishes the main results in bai 2003 and bai and ng 2006 for generalized factor models with slightly stronger conditions on the relative magnitude of n number of subjects and t number of time periods convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear logit probit tobit poisson and some other single index nonlinear models the probability density mass function is allowed to vary across subjects and time thus mixed models are also allowed for for factor augmented regressions this paper establishes the limit distributions of the parameter estimates the conditional mean and the forecast when factors estimated from nonlinear mixed data are used as proxies for the true factors

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

estimation of fixed effects panel regression models with separable and nonseparable space time filters abstract this paper considers a quasi maximum likelihood estimation for a linear panel data model with time and individual fixed effects where the disturbances have dynamic and spatial correlations which might be spatially stable or unstable we first consider both separable and nonseparable space time filters for the stable model the separable space time filter is subject to a parametric restriction which results in relative computational simplicity in contrast to the spatial econometrics literature we expose economic restrictions imposed by the separable space time filter model and explore computational tractability of the nonseparable filter model throughout this paper the effect of initial observations is taken into account which results in an exact likelihood function for estimation this is important when the span of time periods is short we then investigate spatial unstable cases where we propose to apply a spatial differencing to all variables in the regression equation as a data transformation which may eliminate unstable or explosive spatial components in order to achieve a robust estimator for estimates of the parameters in both the regression part and the disturbance process they are n t consistent and asymptotically centered normal regardless of whether t is large or not and whether the process is stable or not

learning expressions and programs over monoids we study the problem of learning an unknown function represented as an expression or a program over a known finite monoid as in other areas of computational complexity where programs over algebras have been used the goal is to relate the computational complexity of the learning problem with the algebraic complexity of the finite monoid indeed our results indicate a close connection between both kinds of complexity we focus on monoids which are either groups or aperiodic and on the learning model of exact learning from queries for a group g we prove that expressions over g are efficiently learnable if g is nilpotent and impossible to learn efficiently under cryptographic assumptions if g is nonsolvable we present some results for restricted classes of solvable groups and point out a connection between their efficient learnability and the existence of lower bounds on their computational power in the program model for aperiodic monoids our results seem to indicate that the monoid class known as da captures exactly learnability of expressions by polynomially many evaluation queries when using programs instead of expressions we show that our results for groups remain true while the situation is quite different for aperiodic monoids

deviance information criterion for latent variable models and misspecified models abstract deviance information criterion dic has been widely used for bayesian model comparison especially after markov chain monte carlo mcmc is used to estimate candidate models this paper first studies the problem of using dic to compare latent variable models when dic is calculated from the conditional likelihood in particular it is shown that the conditional likelihood approach undermines theoretical underpinnings of dic a new version of dic namely dic l is proposed to compare latent variable models the large sample properties of dic l are studied a frequentist justification of dic l is provided like aic dic l provides an asymptotically unbiased estimator to the expected kullback leibler kl divergence between the dgp and a predictive distribution some popular algorithms such as the em kalman and particle filtering algorithms are introduced to compute dic l for latent variable models moreover this paper studies the problem of using dic to compare misspecified models a new version of dic namely dic m is proposed and it can be regarded as a bayesian version of tic a frequentist justification of dic m is provided under misspecification dic l and dic m are illustrated using asset pricing models and stochastic volatility models

panel data discrete choice models with lagged dependent variables in this paper we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables lags of the endogenous dependent variable as well as unobservable individual specific effects for the binary logit model with the dependent variable lagged only once chamberlain 1993 gave conditions under which the model is not identified we present a stronger set of conditions under which the parameters of the model are identified the identification result suggests estimators of the model and we show that these are consistent and asymptotically normal although their rate of convergence is slower than the inverse of the square root of the sample size we also consider identification in the semiparametric case where the logit assumption is relaxed we propose an estimator in the spirit of the conditional maximum score estimator manski 1987 and we show that it is consistent in addition we discuss an extension of the identification result to multinomial discrete choice models and to the case where the dependent variable is lagged twice finally we present some monte carlo evidence on the small sample performance of the proposed estimators for the binary response model

asymptotics for panel quantile regression models with individual effects this paper studies panel quantile regression models with individual fixed effects we formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals n and the number of time periods t jointly go to infinity the estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature nevertheless due to the non smoothness of the objective function we had to impose a more restrictive condition on t to prove asymptotic normality than that usually found in the literature the finite sample performance of the estimator is evaluated by monte carlo simulations

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

reverse order laws in c algebras abstract in this paper we offer purely algebraic necessary and sufficient conditions for reverse order laws for generalized inverses in c algebras extending rank conditions for matrices and range conditions for hilbert space operators

a simple predictive density function abstract an easily computable predictive density is considered although involving a plain maximum likelihood technique it coincides with the posterior predictive density with a noninformative prior for standard situations achievements are comparable with classical inference

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

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

individual and time effects in nonlinear panel models with large n t fixed eects estimators of nonlinear panel data models can be severely biased because of the well known incidental parameter problem we develop analytical and jackknife bias corrections for nonlinear models with both individual and time eects under asymptotic sequences where the time dimension t grows with the cross sectional dimension n the time eects introduce additional incidental parameter bias as the existing bias corrections apply to models with only individual eects we derive the appropriate corrections the basis for the corrections are general asymptotic expansions of xed eects estimators with incidental parameters in multiple dimensions we apply the expansions to m estimators with concave objective functions in parameters for panel models with additive individual and time eects these estimators cover xed eects estimators of the most popular limited dependent variable models such as logit probit ordered probit tobit and poisson models our analysis therefore extends the use of large t bias adjustments to an important class of models we also develop bias corrections for functions of the data parameters and individual and time eects including average partial eects in this case the incidental parameter bias is asymptotically of second order in general but the corrections improve nite sample properties

an invariance property related to the reverse order law abstract it is shown that quite surprisingly all matrices of the form l m where l and m denote generalized inverses of l and m are generalized inverses of ml if and only if the product mll m ml is invariant with respect to the choice of l and m which at the first glance looks to be a weaker condition than the requirement that mll m ml ml for every l and m this statement follows as an immediate corollary to the main result of the present note which provides two criteria for the invariance of expressions of the type kl m n involving four given matrices k l m n with generalized inverses l m of two of them

on the unbiased asymptotic normality of quantile regression with fixed effects abstract nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data in a large class of such models including probit proportional hazard and quantile regression to name just a few it is impossible to difference out the individual effects and inference is usually justified in a large n large t asymptotic framework however there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions such as probit and proportional hazard and quantile regression in the present paper we show that this gap can be bridged and establish unbiased asymptotic normality for fixed effects quantile regression panels under conditions on n t that are very close to what is typically assumed in standard nonlinear panels our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data in terms of n t as other commonly used nonlinear panel data models thorough numerical experiments confirm our theoretical findings

panel binary variables and sufficiency generalizing conditional logit this paper extends the conditional logit approach rasch andersen chamberlain used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors in a two period two state model necessary and sufficient conditions on the joint distribution function of the individual and period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect by extending a result of chamberlain it is shown that root n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds in applied work the estimation method amounts to quasi differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross section model semiparametric approaches can then be readily applied

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

conditional inference methods for incomplete poisson data with endogenous time varying covariates we investigate the effect of protease inhibitors pis on the rate of emergency room er visits among hiv infected women from a longitudinal cohort study one strategy for accounting for serial correlation in longitudinal studies is to assume that observations are independent conditional on unit specific nuisance parameters it is possible to estimate these models using unconditional maximum likelihood where the nuisance parameters are assigned a parametric distribution and integrated out of the likelihood alternatively we can proceed using conditional inference where we eliminate the nuisance parameters from the likelihood by conditioning on a sufficient statistic for these parameters an advantage of conditional inference methods over parametric random effects models is that all patient level time invariant factors both measured and unmeasured are accounted for in the analysis a limitation is that standard conditional inference methods assume that missing data are missing completely at random a

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

inapproximability results for equations over infinite groups an equation over a group g is an expression of form w 1 w k 1 g where each w i is either a variable an inverted variable or a group constant and 1 g denotes the identity element such an equation is satisfiable if there is a setting of the variables to values in g such that the equality is realized engebretsen et al 2002 10 in this paper we study the problem of simultaneously satisfying a family of equations over an infinite group g let eq g k denote the problem of determining the maximum number of simultaneously satisfiable equations in which each equation has occurrences of exactly k different variables when g is an infinite cyclic group we show that it is np hard to approximate eq 1 g 3 to within 48 47 e where eq 1 g 3 denotes the special case of eq g 3 in which a variable may only appear once in each equation it is np hard to approximate eq 1 g 2 to within 30 29 e it is np hard to approximate the maximum number of simultaneously satisfiable equations of degree at most d to within d e for any e for any k 4 it is np hard to approximate eq g k within any constant factor these results extend hastad s results hastad 2001 17 and results of engebretsen et al 2002 10 who established the inapproximability results for equations over finite abelian groups and any finite groups respectively

a concave pairwise fusion approach to subgroup analysis abstractan important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup this article considers the problem using samples drawn from a population consisting of subgroups with different mean values along with certain covariates we propose a penalized approach for subgroup analysis based on a regression model in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject specific intercepts we apply concave penalty functions to pairwise differences of the intercepts this procedure automatically divides the observations into subgroups to implement the proposed approach we develop an alternating direction method of multipliers algorithm with concave penalties and demonstrate its convergence we also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between g

approximate predictive likelihood summary a predictive likelihood is given which approximates both bayes and maximum likeli hood predictive inference by expansion of a posterior likelihood this synthesizes and extends previous results and is widely applicable the approximation usually differs from exact bayes posterior predictive density by op n 2 and from exact predictive likelihood by op n 1 but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found the results are applied to the prediction various treatments of the likelihood function form the basis of parametric inference but until recently few non bayesian attempts have been made to define versions of it suitable for prediction however lauritzen 1974 hinkley 1979 and more recently butler 1986 have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic unfortunately they apply only when sufficiency provides a genuine reduction of the data moreover even if for a given problem an exact predictive likelihood exists the calculations needed to derive it can be onerous this paper provides approximations to hinkley lauritzen predictive likelihood accur ate to op n 1 in many cases which are applicable in situations where maximum likelihood estimation is regular they also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data the approximations are derived from a posterior predictive density and may if prior informa tion is available be regarded as bayesian procedures their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum and is fast and accurate using usual numerical maximization methods there is a close connexion with the approximations to posterior moments and marginal densities given by tierney kadane 1986 who suggest the same approxima tion as used here but give no detailed results for prediction section 2 of this paper shows how laplace s method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood section 3 discusses a connection with conditional inference essentially the same approximation

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

an assertion concerning functionally complete algebras and np completeness in a paper published in j acm in 1990 tobias nipkow asserted that the problem of deciding whether or not an equation over a nontrivial functionally complete algebra has a solution is np complete however close examination of the reduction used shows that only a weaker theorem follows from his proof namely that deciding whether or not a system of equations has a solution is np complete over such an algebra nevertheless the statement of nipkow is true as shown here as a corollary of the proof we obtain that it is conp complete to decide whether or not an equation is an identity over a nontrivial functionally complete algebra

consistent estimation of limited dependent variable models despite misspecification of distribution abstract by exploiting conditions on the behavior of regressors estimators are developed which are consistent up to a factor of proportionality for the slope coefficients of the regression function of a imperfectly observed dependent variable limited dependent variables are a special case of interest the consistency is robust to misspecification of the distribution of the latent dependent variable the estimators are weighted pseudo maximum likelihood estimators which can be readily computed using popular methods and software

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

approximate inference in location scale regression models abstract it is shown that 2 and multivariate t distributions provide good approximations to posterior distributions arising in location scale regression models in the case of a linear regression model bayesian inferences based on an improper prior have conditional frequency as well as fiducial structural interpretation so the results are also applicable in a non bayesian context numerical support for the approximations is presented for the case of a weibull regression model and a regression with t distributed errors

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

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

on the unidentifiability of the fixed effects 3pl model the paper offers a general review of the basic concepts of both statistical model and parameter identification and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates all these issues are then exemplified for the 1pl 2pl and 1pl g fixed effects models for the 3pl model however we provide a theorem proving that the item parameters are not identified do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them

the score statistic for regression transformation summary the score statistic for regression transformation using a parametric family is developedfurther a simple formula for the approximate variance matrix of score statistics basedon asymptotic theory is applied to yield the score statistic t s for regression transforma tion this is compared to atkinson s t d statistic for the same problem and yields animprovement to its standardization simulations indicate that the significance levels ofthe proposed score statistic t s are very close to their nominal values some key words power transformation regression score statistic simulation tests for normality 1 introduction the work of box cox 1964 has been the basis of many investigations into theuse of transformations in regression analysis and the current state of the topic is wellsummarized in the monographs of cook weisberg 1982 and atkinson 1985 theprincipal aim of the original work was to transform a response or dependent variable sothat it would satisfy the normality and other standard assumptions of regression analysis the authors used a parametric family of transformations to achieve this and placedemphasis on estimating its parameters in subsequent work andrews 1971 was moreconcerned with testing transformation parameters while atkinson 1973 introducedanother statistic for this purpose from consideration of both andrews s statistic and scoreor c a tests the present paper develops a standardized score statistic in the case of ascalar transformation parameter in effect it is found to provide the standardization ofatkinson s statistic an aspect which atkinson 1973 believed to be theoretically intract able and avoided by using an approximate regression argument

when is b a a generalized inverse of ab in practice factorizations of a generalized inverse often arise from factorizations of the matrix which is to be inverted in addition to full rank factorizations normal factorizations and singular value decompositions svd there are other factorizations of particular matrices that are natural to certain problems for instance in statistics answers to questions like when is b a a generalized inverse of ab may thus be a computational tool besides they are of significant interest because they provide us with insights into the g inversion of matrix products

gmm estimation of social interaction models with centrality this paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous contextual correlated and group fixed effects when the network structure in a group is captured by a graph in which the degrees of nodes are not all equal the different positions of group members as measured by the bonacich 1987 centrality provide additional information for identification and estimation in this case the bonacich centrality measure for each group can be used as an instrument for the endogenous social effect but the number of such instruments grows with the number of groups we consider the 2sls and gmm estimation for the model the proposed estimators are asymptotically efficient respectively within the class of iv estimators and the class of gmm estimators based on linear and quadratic moments when the sample size grows fast enough relative to the number of instruments

blind channel estimation for amplify and forward two way relay networks employing m psk modulation we consider the problem of channel estimation for amplify and forward af two way relay networks twrns most works on this problem focus on pilot based approaches which impose a significant training overhead that reduces the spectral efficiency of the system to avoid such losses we propose blind channel estimation algorithms for af twrns that employ constant modulus cm signaling our main algorithm is based on the deterministic maximum likelihood dml approach assuming m psk modulation we show that the resulting estimator is consistent and approaches the true channel with high probability at high snr for modulation orders higher than 2 for bpsk however the dml algorithm performs poorly and we propose an alternative algorithm that yields much better performance by taking into account the bpsk structure of the data symbols for comparative purposes we also investigate the gaussian maximum likelihood gml approach which treats the data symbols as gaussian distributed nuisance parameters we derive the cramer rao bound and use monte carlo simulations to investigate the mean squared error mse performance of the proposed algorithms we also compare the symbol error rate ser performance of the dml algorithm with that of the training based least squares ls algorithm and demonstrate that the dml offers a superior tradeoff between accuracy and spectral efficiency

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

a bayesian approach to transformations to normality summary the analysis of transformation of observations in the linear model with normal errors proposed by box cox 1964 is considered a different choice of noninformative unnormed prior is advocated which is not outcome dependent this new selection of prior leads to a formal identity between likelihood and bayesian inference both for the estimation of the best transformation to normality and for the presence of homoscedasticity and additivity under this transformation extension to a related problem is mentioned

effect of misspecification of regression models in the analysis of survival data the accelerated life and proportional hazards families of models are widely used in the analysis of survival data we examine the question if interest lies in the qualitative effect on failure of various explanatory variables how critical is the choice of model family in assessing the relative importance of the explanatory variables we consider small effects when censoring is independent of the explanatory variables to first order the regression parameters are proportional under the alternative models this is not true when the censoring varies appreciably with the explanatory variables some higherorder theory is examined for the special case of the two sample problem

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

asymptotic analysis of the squared estimation error in misspecified factor models abstract in this paper we obtain asymptotic approximations to the squared error of the least squares estimator of the common component in large approximate factor models with possibly misspecified number of factors the approximations are derived under both strong and weak factors asymptotics assuming that the cross sectional and temporal dimensions of the data are comparable we develop consistent estimators of these approximations and propose to use them for model comparison and for selection of the number of factors we show that the estimators of the number of factors that minimize these loss estimators are asymptotically loss efficient in the sense of shibata 1980 li 1987 and shao 1997

estimation of dynamic models with error components abstract observations on n cross section units at t time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit different assumptions about the initial conditions are a initial state fixed b initial state random c the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed and d the unobserved individual effect independent of the unobserved dynamic process with initial value random asymptotic properties of the maximum likelihood and covariance estimators are obtained when t and when n the relationship between the pseudo and conditional maximum likelihood estimators is clarified a simple consistent estimator that is independent of the initial conditions and the way in which t or n is also suggested

non uniform automata over groups abstract a new model non uniform deterministic finite automata nudfa s over general finite monoids has recently been developed as a strong link between the theory of finite automata and low level parallel complexity achievements of this model include the proof that width 5 branching programs recognize exactly the languages in non uniform nc1 nudfa characterizations of several important subclasses of nc1 and a new proof of the old result that the dot dephth hierarchy is infinite using m sipser s 1983 in proceedings 15th acm symposium on the theory of computing association for computing machinery new york pp 61 69 work on constant depth circuits here we extend this theory to nudfa s over solvable groups nudfa s over non solvable groups have the maximum possible computing power we characterize the power of nudfa s over nilpotent groups and prove some optimal lower bounds for nudfa s over certain groups which are solvable but not nilpotent most of these results appeared in preliminary form in d a barrington and d therien 1987 in automata languages and programming 14th international colloquium springer verlag berlin pp 163 173

the hidden subgroup problem and quantum computation using group representations the hidden subgroup problem is the foundation of many quantum algorithms an efficient solution is known for the problem over abelian groups employed by both simon s algorithm and shor s factoring and discrete log algorithms the nonabelian case however remains open an efficient solution would give rise to an efficient quantum algorithm for graph isomorphism we fully analyze a natural generalization of the algorithm for the abelian case to the nonabelian case and show that the algorithm determines the normal core of a hidden subgroup in particular normal subgroups can be determined we show however that this immediate generalization of the abelian algorithm does not efficiently solve graph isomorphism

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

inference on regressions with interval data on a regressor or outcome this paper examines inference on regressions when interval data are available on one variable the other variables being measured precisely let a population be characterized by a distribution p y x v v 0 v 1 where y r 1 x r k and the real variables v v 0 v 1 satisfy v 0 v v 1 let a random sample be drawn from p and the realizations of y x v 0 v 1 be observed but not those of v the problem of interest may be to infer e y x v or e v x this analysis maintains interval i monotonicity m and mean independence mi assumptions i p v 0 v v 1 1 m e y x v is monotone in v mi e y x v v 0 v 1 e y x v no restrictions are imposed on the distribution of the unobserved values of v within the observed intervals v 0 v 1 it is found that the immi assumptions alone imply simple nonparametric bounds on e y x v and e v x these assumptions invoked when y is binary and combined with a semiparametric binary regression model yield an identification region for the parameters that may be estimated consistently by a modified maximum score mms method the immi assumptions combined with a parametric model for e y x v or e v x yield an identification region that may be estimated consistently by a modified minimum distance mmd method monte carlo methods are used to characterize the finite sample performance of these estimators empirical case studies are performed using interval wealth data in the health and retirement study and interval income data in the current population survey

likelihood and observed geometries a partir du point de vue de la conditionnalite on etablit un parallele observe a la theorie de chentsov efron amari etc en utilisant l information observee et un tenseur d asymetrie observee

efficient estimation of models for dynamic panel data abstract in this paper we consider a dynamic model for panel data we show that under standard assumptions there are more moment conditions than are currently exploited in the literature some of these are linear but others are quadratic so that nonlinear gmm is required we also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model

heteroskedasticity robust standard errors for fixed effects panel data regression the conventional heteroskedasticity robust hr variance matrix estimator for cross sectional regression with or without a degrees of freedom adjustment applied to the fixed effects estimator for panel data with serially uncorrelated errors is inconsistent if the number of time periods t is fixed and greater than 2 as the number of entities n increases we provide a bias adjusted hr estimator that is consistent under any sequences n t in which n and or t increase to this estimator can be extended to handle serial correlation of fixed order

semiparametric estimation of a panel data proportional hazards model with fixed effects this paper considers a panel duration model that has a proportional hazards specification with fixed effects the paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known finite dimensional families of functions existing estimators assume that the baseline hazard function belongs to a known parametric family therefore the estimators presented here are more general than existing ones this paper also presents a method for estimating the parametric part of the proportional hazards model with dependent right censoring under which the partial likelihood estimator is inconsistent the paper presents some monte carlo evidence on the small sample performance of the new estimators

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

unified inference for nonlinear factor models from panels with fixed and large time span abstract we provide unifying inference theory for parametric nonlinear factor models based on a panel of noisy observations the panel has a large cross section and a time span that may be either small or large moreover we incorporate an additional source of information provided by noisy observations on some known functions of the factor realizations the estimation is carried out via penalized least squares i e by minimizing the l 2 distance between observations from the panel and their model implied counterparts augmented by a penalty for the deviation of the extracted factors from the noisy signals of them when the time dimension is fixed the limit distribution of the parameter vector is mixed gaussian with conditional variance depending on the path of the factor realizations on the other hand when the time span is large the convergence rate is faster and the limit distribution is gaussian with a constant variance in this case however we incur an incidental parameter problem since at each point in time we need to recover the concurrent factor realizations this leads to an asymptotic bias that is absent in the setting with a fixed time span in either scenario the limit distribution of the estimates for the factor realizations is mixed gaussian but is related to the limiting distribution of the parameter vector only in the scenario with a fixed time horizon although the limit behavior is very different for the small versus large time span we develop a feasible inference theory that applies without modification in either case hence the user need not take a stand on the relative size of the time dimension of the panel similarly we propose a time varying data driven weighting of the penalty in the objective function which enhances efficiency by adapting to the relative quality of the signal for the factor realizations

trimmed lad and least squares estimation of truncated and censored regression models with fixed effects this paper considers estimation of truncated and censored regression models with fixed effects up until now no estimator has been shown to be consistent as the cross section dimension increases with the time dimension fixed trimmed least absolute deviations and trimmed least squares estimators are proposed for the case where the panel is of length two and it is proven that they are consistent and asymptotically normal it is not necessary to maintain parametric assumptions on the error terms to obtain this result a small scale monte carlo study demonstrates that these estimators can perform well in small samples copyright 1992 by the econometric society