symbolic model checking for real time systems abstract we describe finite state programs over real numbered time in a guarded command language with real valued clocks or equivalently as finite automata with real valued clocks model checking answers the question which states of a real time program satisfy a branching time specification given in an extension of ctl with clock variables we develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates without constructing the state space for this purpose we introduce a calculus on computation trees over real numbered time unfortunately many standard program properties such as response for all nonzeno execution sequences during which time diverges cannot be characterized by fixpoints we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed ctl fortunately this result does not impair the symbolic verification of implementable real time programs those whose safety constraints are machine closed with respect to diverging time and whose fairness constraints are restricted to finite upper bounds on clock values all timed ctl properties of such programs are shown to be computable as finitely approximable fixpoints in a simple decidable theory

are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

short communication some remarks on the category fuz h of m eytan the aim of this paper is to disprove a result asserted by m eytan in his paper fuzzy sets a topos logical point of view in this journal vol 5 pp 47 67 namely that the category fuz h is a topos for any complete heyting algebra h it is proved that this result can be true only when h is a boolean algebra

estimation of cross sectional and panel data censored regression models with endogeneity it is very difficult to deal with endogeneity in limited dependent variables models unless strong assumptions are made on the exact relationship between the endogenous regressors and the instruments it is generally not possible to apply instrumental variable type techniques this paper derives moment conditions that are useful in estimating censored regression models with endogenous regressors these moment conditions are motivated by panel data censored regression models with predetermined but not strictly exogenous explanatory variables but the main insight is also applicable to cross sectional models with endogenous explanatory variables

symbolic model checking for probabilistic timed automata probabilistic timed automata are timed automata extended with discrete probability distributions and can be used to model timed randomised protocols or fault tolerant systems we present symbolic model checking algorithms for probabilistic timed automata to verify both qualitative temporal logic properties corresponding to satisfaction with probability 0 or 1 and quantitative properties corresponding to satisfaction with arbitrary probability the algorithms operate on zones which represent sets of valuations of the probabilistic timed automaton s clocks our method considers only those system behaviours which guarantee the divergence of time with probability 1 the paper presents a symbolic framework for the verification of probabilistic timed automata against the probabilistic timed temporal logic ptctl we also report on a prototype implementation of the algorithms using difference bound matrices and present the results of its application to the csma cd and firewire root contention protocol case studies

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

short communication the categories set h and fuz h this paper follows up d ponasse s paper some remarks on the category fuz h of m eytan in this journal 4 in particular it gives a new proof that fuz h cannot have a subobject classifier if h is a complete chain with at least three elements

informational content of special regressors in heteroskedastic binary response models we quantify the informational content of special regressors in heteroskedastic binary response models with median independent or conditionally symmetric errors based on lewbel 1998 a special regressor is additively separable in the latent payoff and conditionally independent from the error term we find that with median independent errors a special regressor does not increase the identifying power by a criterion in manski 1988 or lead to positive fisher information for the coefficients even though it does help recover the average structural function with conditionally symmetric errors a special regressor improves the identifying power and the information for coefficients is positive under mild conditions we propose two estimators for binary response models with conditionally symmetric errors and special regressors

simulation based inference a survey with special reference to panel data models abstract in this article we study the recent developments of inference methods based on simulations in particular we discuss the simulated generalized method of moments the simulated maximum likelihood method and the simulated pseudo maximum likelihood methods the asymptotic properties of the estimators are described when the number of observations n goes to infinity and we distinguish the case where the number h of simulations per observation is fixed from the case where this number also goes to infinity in the former case the possible asymptotic bias is evaluated and in the latter case we carefully examine the consequences of the assumptions on the relative divergence rates of n and h we also show how these methods apply to various contexts in particular to the case of panel data models

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

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

simulated moments estimation of markov models of asset prices this paper provides a simulated moments estimator sme of the parameters of dynamic models in which the state vector follows a time homogeneous markov process conditions are provided for both weak and strong consistency as well as asymptotic normality various tradeoffs among the regularity conditions underlying the large sample properties of the sme are discussed in the context of an asset pricing model this paper provides conditions for the consistency and asymptotic normality of a simulated moments estimator sme of the parameters of asset pricing models with time homogeneous markov representations of the stochastic forc ing process sme s for economic models have been proposed by mcfadden 1989 and pakes and pollard 1989 for i i d environments and by lee and ingram 1991 for a time series environment the sme for time series models examined in this paper is as follows the state vector yt that determines asset prices is assumed to follow a time homogeneous markov process whose transi tion function depends on an unknown parameter vector 3 0 asset prices and possibly other relevant data are observed as f yt 0 for some given function f of the underlying state and parameter vector in parallel a simulated state process y is generated analytically or numerically from the economic model and corresponding simulated observations f yj3 13 are taken for a given parameter choice f3 the parameter is chosen so as to match moments that is to minimize the distance between sample moments of the data f y 8030 and those of the simulated series f yt f3 in a sense to be made precise the proposed sme extends the generalized method of moments gmm estimator hansen 1982 to a large class of asset pricing models for which the moment restrictions of interest do not have analytic representations in terms of observable variables and the unknown parameter vector we provide conditions on the transition function of yt and the observation function f under which the sme of 030 is consistent and characterize the normalized asymptotic distribu tion of the estimator for two reasons neither the regularity conditions underly ing hansen s 1982 analysis of gmm estimators for time series models without

pictorial representations of fuzzy connectives part ii cases of compensatory operators and self dual operators abstract as the continuation of part i in which pictorial representations of t norms t conorms and averaging operators were made with the aid of a computer this paper discusses compensatory operators and proposes generalized compensatory operators which can be obtained from averaging operators self dual operators are discussed which can be defined by using t norms t conorms and averaging operators finally symmetric sums are reviewed which are also self dual operators the pictorial representations of these operators are also made

the method of simulated scores for the estimation of ldv models the method of simulated scores mss is presented for estimating limited dependent variables models ldv with flexible correlation structure in the unobservables we propose simulators that are continuous in the unknown parameter vectors and hence standard optimization methods can be used to compute the mss estimators that employ these simulators the first continuous method relies on a recursive conditioning of the multivariate normal density through a cholesky triangularization of its variance covariance matrix the second method combines results about the conditionals of the multivariate normal distribution with gibbs resampling techniques we establish consistency and asymptotic normality of the mss estimators and derive suitable rates at which the number of simulations must rise if biased simulators are used

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

on probabilistic timed automata we propose a model of probabilistic timed automaton which substitutes for the nondeterminism of an ordinary timed automaton a new one directly drawn from markov decision processes by means of actions which provide a probabilistic distribution over transitions using buchi acceptance conditions timed automata can refer timing properties as during every open time interval of length 1 at least one message is delivered a policy is a mechanism which solves the non determinism by choosing for each finite run an action and the time moment of the next transition step implied by this action we prove that given a probabilistic timed automaton a there exists a markov memoryless policy which maximizes the probability p of the set of accepting runs realized by this policy this policy as well as the maximal value of p are computable in polytime in the size of the region automaton of a this result provides an algorithm of model checking for properties like there is a policy which realizes a correct behavior of the system with probability at least p

pairwise difference estimators of censored and truncated regression models abstract this paper proposes a class of estimators of the semiparametric censored regression model under the assumption that the error terms are i i d and independent of the covariates the estimators exploit the fact that for a pair of observations a particular transformation of the censored variables depending upon the parameter vector and both covariate vectors will be identically distributed therefore the difference in the transformed dependent variables will be symmetrically distributed around zero when the transformation is evaluated at the true parameter vector an analogous class of estimators for the truncated regression model includes the bhattacharya chernoff and yang 1983 estimator as a special case the estimators are defined as minimizers of u processes so the large sample theory for classical m estimators is extended to this case conditions are given to ensure root n consistency and asymptotic normality of the estimators and a small scale simulation study for the censored regression estimator suggest that it will be well behaved in finite samples

reconstruction possibilities for fuzzy sets towards a new level of understanding abstract using the methodological approach of rational reconstruction some possible explications of the notion of fuzzy set are critically discussed with respect to their intuitive meaning plausibility and consistency together with a historical survey we try to provide a better understanding of the development of various concepts within traditional fuzzy set theory based on the approaches of 39 and 18 we show that zadeh s original intuition of a fuzzy set and its formalization as generalized membership function can be reinterpreted in a plausible and consistent way and thus are supported not only on a formal level by mathematical results but can also be justified in principle on a semantical level hence both the operational as well as the traditional valuational viewpoint have their own rights in their corresponding areas of modeling reality and it is shown how the latter can be given a sound foundation based upon the former

fuzzy sets a topos logical point of view abstract benabou deduction categories are defined with a set of additional assumptions that define categories with formal finite limits resp formal regular categories formal logoi formal topoi they are shown to be generalized structures in which higher order many sorted languages can be realized the corresponding gentzen type higher order calculus of sequents is explicited and the soundness theorem is formulated a construction is given which associates to each deduction category with formal properties a real category with the corresponding real properties in a universal way the corresponding sounddess and completeness properties are formulated for the real categories thus obtained fuzzy sets as generalized by goguen are introduced considered as the objects of a category fuz h which turns out to be the real category associated to a very simple formal topos and thus to be itself a topos furthermore this is proved to be a grothendieck topos which is a strictly full epireflective subcategory of higgs category of h valued sets topoi are proposed as generalized fuzzy sets and deductio0 categories as generalized 2 fuzzy sets some related topics such as arbib manes fuzzy theories probability many valued and fuzzy logics intensional logic are very briefly touched upon

fuzzy sets do not form a topos abstract the relationship between fuzzy sets and h valued sets is briefly examined and a claim of eytan s that the former comprise the objects of a topos is corrected

on algebraic properties of f spaces abstract recently a new perspective of fuzzy set theory has been presented under the name f set theory here we investigate the most fundamental algebraic properties of f subsetness f intersection f union and f complementation the latter one is shown not only to have intuitive and operational roots but also to arise if one starts the generalization process from algebraic instead of arithmetical representation for classical complementation

from fuzzy set theory to fuzzy set theory some critical remarks on existing concepts abstract our aim in this paper is to give some foundational remarks on the nature of fuzziness and their modeling by fuzzy sets we will reveal some fundamental misunderstandings which have pervaded fuzzy set theory just from its very beginnings at the end of the paper we give three examples demonstrating the differences and advantages of our new conception our approach in heavily based on an operational and set theoretical background contrasting hisdal s tee model

large sample theory for semiparametric regression models with two phase outcome dependent sampling outcome dependent two phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by lawless kalbfleisch and wild 1999 under two phase sampling designs we show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient the efficient influence function for the parametric part agrees with the more general information bound calculations of robins hsieh and newey 1995 by verifying the conditions of murphy and van der vaart 2000 for a least favorable parametric submodel we provide asymptotic justification for statistical inference based on profile likelihood

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

an adaptive composite quantile approach to dimension reduction sufficient dimension reduction li 1991 has long been a prominent issue in multivariate nonparametric regression analysis to uncover the central dimension reduction space we propose in this paper an adaptive composite quantile approach compared to existing methods 1 it requires minimal assumptions and is capable of revealing all dimension reduction directions 2 it is robust against outliers and 3 it is structure adaptive thus more efficient asymptotic results are proved and numerical examples are provided including a real data analysis

estimation of type 3 tobit models using symmetric trimming and pairwise comparisons abstract this paper considers estimation of the semiparametric type 3 tobit model we construct two step estimators that use the ideas of symmetric trimming and pairwise comparisons which have been proposed for the censored regression model by powell 1986 and honore and powell 1994 the estimators are consistent and asymptotically normal under two identifying assumptions conditional symmetry and independence between the errors and regressors the ideas and techniques are also implementable in other selection models that are variations of the basic type 3 tobit model we demonstrate this by applying the proposed method in estimating an empirical model considered by udry 1994

finite sample inference for quantile regression models abstract under minimal assumptions finite sample confidence bands for quantile regression models can be constructed these confidence bands are based on the conditional pivotal property of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear and nonlinear quantile models with endogenous or exogenous covariates the confidence regions can be computed using markov chain monte carlo mcmc methods we illustrate the finite sample procedure through two empirical examples estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling we find pronounced differences between asymptotic and finite sample confidence regions in cases where the usual asymptotics are suspect

estimation of semiparametric models when the criterion function is not smooth we provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated our results extend existing theories such as those of pakes and pollard 1989 andrews 1994a and newey 1994 we also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters we apply our results to two examples a hit rate and a partially linear median regression with some endogenous regressors

simulated maximum likelihood estimation of dynamic discrete choice statistical models some monte carlo results this article reports monte carlo results on the simulated maximum likelihood estimation of discrete dynamic panel models introduced by james heckman 1981a the simulated maximum likelihood method is numerically stable even for long panels regression models and polya and renewal models can be better estimated than markov models with a moderate number of simulation draws most of these complex models can be adequately estimated for panels with length up to 30 polya and renewal models can be accurately estimated for panels up to 50 periods estimates of markov models can be sensitive to misspecified initial states but polya renewal and habit persistence models may not

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

semiparametric estimation of a bivariate tobit model abstract the existing semiparametric estimation literature has mainly focused on univariate tobit models and no semiparametric estimation has been considered for bivariate tobit models in this paper we consider semiparametric estimation of the bivariate tobit model proposed by amemiya 1974 under the independence condition without imposing any parametric restriction on the error distribution our estimator is shown to be consistent and asymptotically normal and simulation results show that our estimator performs well in finite samples it is also worth noting that while amemiya s 1974 instrumental variables estimator iv requires the normality assumption our semiparametric estimator actually outperforms his iv estimator even when normality holds our approach can be extended to higher dimensional multivariate tobit models

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

categorical properties of f set theory abstract in the first part of the paper we show that the interpretation of a fuzzy set as a bundle of sets over a base space makes the category of fuzzy sets into a topos f set v i e to paraphrase pitts 5 fuzzy sets do form a topos the second part exhibit close connections to operations proposed for fuzzy set theory from an intuitive and operational viewpoint by toth 7 these two results together seem to indicate that there are two essentially different ways to understand the concept of a fuzzy set either as an evaluation over a universe or as a collection of evaluated objects the latter one being a set theoretical interpretation and henceforth leading to a topos

pictorial representations of fuzzy connectives part i cases of t norms t conorms and averaging operators part i of this paper shows a number of examples of existing t norms and t conorms which are known as good models of fuzzy set theoretic intersection and union and then the pictorial representations of t norms and t conorms are made with the aid of a computer several new examples of t norms and t conorms are also given averaging operators between min and max are summarized and their pictorial representations are also made

sieve estimation of constant and time varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error this article considers estimation of constant and time varying coefficients in nonlinear ordinary differential equation ode models where analytic closed form solutions are not available the numerical solution based nonlinear least squares nls estimator is investigated in this study a numerical algorithm such as the runge kutta method is used to approximate the ode solution the asymptotic properties are established for the proposed estimators considering both numerical error and measurement error the b spline is used to approximate the time varying coefficients and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach our results show that if the maximum step size of the p order numerical algorithm goes to zero at a rate faster than n 1 p 4 the numerical error is negligible compared to the measurement error this result provides a theoretical guidance in selection of the step size for numerical evaluations of odes moreover we have shown that the numerical solution based nls estimator and the sieve nls estimator are strongly consistent the sieve estimator of constant parameters is asymptotically normal with the same asymptotic co variance as that of the case where the true ode solution is exactly known while the estimator of the time varying parameter has the optimal convergence rate under some regularity conditions the theoretical results are also developed for the case when the step size of the ode numerical solver does not go to zero fast enough or the numerical error is comparable to the measurement error we illustrate our approach with both simulation studies and clinical data on hiv viral dynamics

on fuzzy convergence abstract we propose and examine two concepts of convergence for sequences of elements of a set x with respect to a fuzzy topology on x such concepts are obtained by interpreting in a multivalued logic two different first order formulas expressing the classical convergence

the method of simulated quantiles we introduce an inference method based on quantiles matching which is useful for situations where the density function does not have a closed form but it is simple to simulate and or moments do not exist functions of theoretical quantiles which depend on the parameters of the assumed probability law are matched with sample quantiles which depend on observations since the theoretical quantiles may not be available analytically the optimization is based on simulations we illustrate the method with the estimation of stable distributions a thorough monte carlo study and an illustration to 22 nancial indexes show

multiplicative censoring renewal processes deconvolution and decreasing density nonparametric estimation on donne un estimateur du maximum de vraisemblance non parametrique pour une distribution de durees de vie il est base sur un modele d observations censurees de facon multiplicative et il generalise des problemes statistiques courants tels que l estimation d une fonction de repartition sous une contrainte de densite decroissante la deconvolution non parametrique d une variable aleatoire exponentielle ou un probleme d estimation dans les processus de renouvellement

on l fuzzy topological spaces abstract l fuzzy sets and subsequently l fuzzy topological spaces are considered in this paper where l is a complete and completely distributive non atomic boolean algebra a few separation properties as well as subspace l fuzzy topology are defined here in the light of an earlier paper these are more similar to ordinary topological spaces than to fuzzy topological spaces

constraint markov chains notions of specification implementation satisfaction and refinement together with operators supporting stepwise design constitute a specification theory we construct such a theory for markov chains mcs employing a new abstraction of a constraint mc constraint mcs permit rich constraints on probability distributions and thus generalize prior abstractions such as interval mcs linear polynomial constraints suffice for closure under conjunction respectively parallel composition this is the first specification theory for mcs with such closure properties we discuss its relation to simpler operators for known languages such as probabilistic process algebra despite the generality all operators and relations are computable

maximal inequalities for degenerate u processes with applications to optimization estimators maximal inequalities for degenerate u processes of order k k geq 1 are established the results rest on a moment inequality due to bonami for k th order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes rates of uniform convergence are obtained the maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having u process structure as an application a semiparametric regression estimator that maximizes a u process of order 3 is shown to be sqrt n consistent and asymptotically normally distributed

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

conditional moment models under semi strong identification we consider conditional moment models under semi strong identification identification strength is directly defined through the conditional moments that flatten as the sample size increases our new minimum distance estimator is consistent asymptotically normal robust to semi strong identification and does not rely on the choice of a user chosen parameter such as the number of instruments or some smoothing parameter heteroskedasticity robust inference is possible through wald testing without prior knowledge of the identification pattern simulations show that our estimator is competitive with alternative estimators based on many instruments being well centered with better coverage rates for confidence intervals

subvector inference when the true parameter vector may be near or at the boundary abstract extremum estimators are not asymptotically normally distributed when the estimator satisfies the restrictions on the parameter space such as the non negativity of a variance parameter and the true parameter vector is near or at the boundary this possible lack of asymptotic normality makes it difficult to construct tests for testing subvector hypotheses that control asymptotic size in a uniform sense and have good local asymptotic power irrespective of whether the true parameter vector is at near or far from the boundary we propose a novel estimator that is asymptotically normally distributed even when the true parameter vector is near or at the boundary and the objective function is not defined outside the parameter space the proposed estimator allows the implementation of a new test based on the conditional likelihood ratio statistic that is easy to implement controls asymptotic size and has good local asymptotic power properties furthermore we show that the test enjoys certain asymptotic optimality properties when the parameter of interest is scalar in an application of the random coefficients logit model berry levinsohn and pakes 1995 to the european car market we find that for most parameters the new test leads to tighter confidence intervals than the two sided t test commonly used in practice

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

minimum distance from independence estimation of nonseparable instrumental variables models abstract i develop a semiparametric minimum distance from independence estimator for a nonseparable instrumental variables model an independence condition identifies the model for many types of discrete and continuous instruments the estimator is taken as the parameter value that most closely satisfies this independence condition implementing the estimator requires a quantile regression of the endogenous variables on the instrument so the procedure is two step with a finite or infinite dimensional nuisance parameter in the first step i prove consistency and establish asymptotic normality for a parametric but flexibly nonlinear outcome equation the consistency of the nonparametric bootstrap is also shown i illustrate the use of the estimator by estimating the returns to schooling using data from the 1979 national longitudinal survey

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

universal donsker classes and metric entropy when mathfrak f is a universal donsker class then for independent indetically distributed i i d observation mathbf x 1 ldots mathbf x n with an unknown law p for any mathfrak f i in mathfrak f i 1 ldots m quad n 1 2 left mathfrak f 1 left mathbf x 1 right ldots mathfrak f i left mathbf x n right right 1 leq i leq m is asymptotically normal with mean vector n 1 2 left int mathfrak f i left mathbf x n right d mathbf p left x right right 1 leq i leq m and covariance matrix int mathfrak f i mathfrak f j d mathbf p int mathfrak f id mathbf p int mathfrak f jd mathbf p uniformly for mathfrak f i in mathfrak f then for certain statistics formed frome the mathfrak f i left mathbf x k right even where mathfrak f i may be chosen depending on the mathbf x k there will be asymptotic distribution as n rightarrow infty for example for mathbf x 2 statistics where f i are indicators of disjoint intervals depending suitably on mathbf x 1 ldots mathbf x n whose union is the real line mathbf x 2 quadratic forms have limiting distributions roy 1956 and watson 1958 which may however not be mathbf x 2 distributions and may depend on p chernoff and lehmann 1954 universal donsker classes of sets are up to mild measurability conditions just classes satisfying the vapnik cervonenkis comdinatorial conditions defined later in this section donsker the vapnik cervonenkis combinatorial conditions defined later in this section durst and dudley 1981 and dudley 1984 chapter 11 the use of such classes allows a variety of extensions of the roy watson results to general multidimensional sample spaces pollard 1979 and moore and subblebine 1981 vapnik and cervonenkis 1974 indicated application of their families of sets to classification pattern recognition problems more recently the classes have been applied to tree structured classifiacation breiman friedman olshen and stone 1984 chapter 12

structural estimation of pairwise stable networks with nonnegative externality abstract this paper develops a framework to structurally estimate pairwise stable networks with nonnegative externality we characterize pairwise stable equilibria as a fixed point of a certain mapping and show that the set of pairwise stable equilibria with nonnegative externality is a complete lattice we extend the characterization to an econometric framework for structural estimation based on the moment inequality model we apply our methodology to friendship networks of students in the united states using data from add health we find that the preference toward racial homophily is overestimated if we do not control for the preference toward clustering

probabilities and fuzzy events an operational approach abstract this paper tries to give a redesign of a well established research area of traditional fuzzy set theory the notion of a probability of a fuzzy event as well as related results are reexamined and new definitions for them are given which are based on the operational viewpoint of f set theory and on some concepts of operational statistics a critical survey of existing concepts will show some advantages of the operational approach

a method of simulated moments for estimation of discrete response models without numerical integration this paper proposes a simple modification of a conventional method of moments estimator for a discrete response model replacing response probabilities that require numerical integration with estimators obtained by monte carlo simulation this method of simulated moments msm does not require precise estimates of these probabilities for consistency and asymptotic normality relying instead on the law of large numbers operating across observations to control simulation error and hence can use simulations of practical size the method is useful for models such as high dimensional multinomial probit mnp where computation has restricted applications

on ranking and generalization bounds the problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features in this paper we consider ranking estimators that minimize the empirical convex risk we prove generalization bounds for the excess risk of such estimators with rates that are faster than 1 n we apply our results to commonly used ranking algorithms for instance boosting or support vector machines moreover we study the performance of considered estimators on real data sets

maximum likelihood estimation with partially censored data suppose one observes independent samples of size n from both the mixture density int p x mid z d eta z and from the distribution eta the kernel p x mid z is known we show asymptotic normality and efficiency of the maximum likelihood estimator for eta

semiparametric estimation of a censored regression model with endogeneity abstract censoring and endogeneity are common in empirical applications however the existing semiparametric estimation methods for the censored regression model with endogeneity under an independence restriction are associated with some drawbacks in this paper we propose a new semiparametric estimator that overcomes these drawbacks we derive conditional quantile moment conditions for all the conditional quantiles and propose a moment based estimator in particular we construct two types of moment conditions and develop a computationally attractive estimator we show that our estimator is consistent and asymptotic normal a monte carlo study indicates that our estimator performs well in finite samples and compares favorably with existing methods

large sample study of empirical distributions in a random multiplicative censoring model consider an incomplete data problem with the following specifications there are three independent samples x 1 ldots x m z 1 ldots z n and u 1 ldots u n the first two samples are drawn from a common lifetime distribution function g while the third sample is drawn from the uniform distribution over the interval 0 1 in this paper we derive the large sample properties of hat g m n the nonparametric maximum likelihood estimate of g based on the observed data x 1 ldots x m and y 1 ldots y n where y i equiv z iu i i 1 ldots n the z s and u s are unobservable in particular we show that if m and n approach infinity at a suitable rate then sup t hat g m n t g t rightarrow 0 a s sqrt m n hat g m n g converges weakly to a gaussian process and the estimate hat g m n is asymptotically efficient in a nonparametric sense

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

on rank estimators in increasing dimensions abstract the family of rank estimators including han s maximum rank correlation han 1987 as a notable example has been widely exploited in studying regression problems for these estimators although the linear index is introduced for alleviating the impact of dimensionality the effect of large dimension on inference is rarely studied this paper fills this gap via studying the statistical properties of a larger family of m estimators whose objective functions are formulated as u processes and may be discontinuous in increasing dimension set up where the number of parameters p n in the model is allowed to increase with the sample size n first we find that often in estimation as p n n 0 p n n 1 2 rate of convergence is obtainable second we establish bahadur type bounds and study the validity of normal approximation which we find often requires a much stronger scaling requirement than p n 2 n 0 third we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent and show that the step size in implementing the covariance estimator has to be adjusted with respect to p n all theoretical results are further backed up by simulation studies

statistical inference in the multinomial multiperiod probit model abstract statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions posterior distributions or moment conditions in these models we describe three alternative estimators implemented using simulation based approaches to inference that circumvent the integration problem posterior means computed using gibbs sampling and data augmentation gibbs simulated maximum likelihood sml estimation using the ghk probability simulator and method of simulated moment msm estimation using ghk we perform a set of monte carlo experiments to compare the sampling distributions of these estimators although all three estimators perform reasonably well some important differences emerge our most important finding is that holding simulation size fixed the relative and absolute performance of the classical methods especially sml gets worse when serial correlation in disturbances is strong in data sets with an ar 1 parameter of 0 50 the rmses for sml and msm based on ghk with 20 draws exceed those of gibbs by 9 and 0 respectively but when the ar 1 parameter is 0 80 the rmses for sml and msm based on 20 draws exceed those of gibbs by 79 and 37 respectively and the number of draws needed to reduce the rmses to within 10 of gibbs are 160 and 80 respectively also the sml estimates of serial correlation parameters exhibit significant downward bias thus while conventional wisdom suggests that 20 draws of ghk is enough to render the bias and noise induced by simulation negligible our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strong

efficient two step estimation via targeting abstract the standard description of two step extremum estimation amounts to plugging in a first step estimator of nuisance parameters to simplify the optimization problem and then deducing a user friendly but potentially inefficient estimator for the parameters of interest in this paper we consider a more general setting of two step estimation where we do not necessarily have nuisance parameters but rather awkward occurrences of the parameters of interest the efficiency problem associated with two step estimators in this context is more difficult than with standard nuisance parameters as even if the true unknown value of the parameters were plugged in to alleviate the awkward occurrences of the parameters the resulting second step estimator may not be efficient in addition standard approaches to restore efficiency for two step procedures may not work due to a consistency issue to alleviate this potential issue we propose a new computationally simple two step estimation procedure that relies on targeting and penalization to enforce consistency with the second step estimators maintaining asymptotic efficiency we compare this new method with existing iterative methods in the framework of copula models and asset pricing models simulation results illustrate that this new method performs better than existing iterative procedures and is nearly computationally equivalent

a limit theorem for a smooth class of semiparametric estimators abstract we consider an econometric model based on a set of moment conditions which are indexed by both a finite dimensional vector of interest and an infinite dimensional parameter h which in turn depends upon both and another infinite dimensional parameter the population moment conditions equal zero at 0 estimators of 0 are obtained by forming nonparametric estimates of h and substituting them into the sample analog of the moment conditions and choosing that value of that makes the sample moments as close as possible to zero using independence and smoothness assumptions the paper provides consistency n consistency and asymptotic normality proofs for the resultant estimator as an example we consider olley and pakes 1991 use of semiparametric techniques to control for both simultaneity and selection biases in estimating production functions the example illustrates how semiparametric techniques an be used to overcome both computational problems and the need for strong functional form restrictions in obtaining estimates from structural models it also illustrates the impacts of 1 i alternative estimators for the nonparametric components of the problem and 2 ii alternative estimators for the standard errors of the estimated

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

a stopping rule for the computation of generalized method of moments estimators to obtain consistency and asymptotic normality a generalized method of moments gmm estimator typically is defined to be an approximate global minimizer of a gmm criterion function to compute such an estimator however can be problematic because of the difficulty of global optimization in consequence practitioners usually ignore the problem and take the gmm estimator to be the result of a local optimization algorithm this yields an estimator that is not necessarily consistent and asymptotically normal the use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function which makes it difficult to know when to stop the algorithm to alleviate these problems of global and local optimization we propose a stopping rule sr procedure for computing gmm estimators the sr procedure eliminates the need for global search with high probability and it provides an explicit sr for problems of stability that may arise with local optimization problems

minimal counterexamples for linear time probabilistic verification abstract counterexamples for property violations have a number of important applications like supporting the debugging of erroneous systems and verifying large systems via counterexample guided abstraction refinement in this paper we propose the usage of minimal critical subsystems of discrete time markov chains and markov decision processes as counterexamples for violated regular properties minimality can thereby be defined in terms of the number of states or transitions this problem is known to be np complete for markov decision processes we show how to compute such subsystems using mixed integer linear programming and evaluate the practical applicability in a number of experiments they show that our method yields substantially smaller counterexample than using existing techniques

symbolic optimal expected time reachability computation and controller synthesis for probabilistic timed automata in this paper we consider the problem of computing the optimal minimum or maximum expected time to reach a target and the synthesis of an optimal controller for a probabilistic timed automaton pta although this problem admits solutions that employ the digital clocks abstraction or statistical model checking symbolic methods based on zones and priced zones fail due to the difficulty of incorporating probabilistic branching in the context of dense time we work in a generalisation of the setting introduced by asarin and maler for the corresponding problem for timed automata where simple and nice functions are introduced to ensure finiteness of the dense time representation we find restrictions sufficient for value iteration to converge to the optimal expected time on the uncountable markov decision process representing the semantics of a pta we formulate bellman operators on the backwards zone graph of a pta and prove that value iteration using these operators equals that computed over the pta s semantics this enables us to extract an optimal controller from value iteration in the standard way