exact thresholds for dpll on random xor sat and np complete extensions of xor sat this paper discusses a model of constraint satisfaction problems known as uniquely extendible constraint satisfaction problems this model includes and generalizes xor sat and the model includes an np complete problem that appears to share many of the threshold characteristics of random sat in this paper we find an exact threshold in the behavior of two versions of dpll on random instances of this problem one version uses the unit clause heuristic and the other uses the generalized unit clause heuristic specifically for dpll with the unit clause heuristic we prove that there is a clause density c smaller than the satisfiability threshold such that for random instances with density smaller than this threshold dpll with unit clause will find a satisfying assignment in linear time with uniformly positive probability however for random instances with density larger than this threshold dpll with unit clause will require exponential time with uniformly positive probability to find a satisfying assignment we then find the equivalent threshold density for dpll with the generalized unit clause heuristic we also prove the analog of the 2 p sat conjecture for this class of problems

random constraint satisfaction easy generation of hard satisfiable instances in this paper we show that the models of random csp instances proposed by xu and li k xu w li exact phase transitions in random constraint satisfaction problems journal of artificial intelligence research 12 2000 93 103 k xu w li many hard examples in exact phase transitions with application to generating hard satisfiable instances technical report corr report cs cc 0302001 revised version in theoretical computer science 355 2006 291 302 are of theoretical and practical interest indeed these models called rb and rd present several nice features first it is quite easy to generate random instances of any arity since no particular structure has to be integrated or property enforced in such instances then the existence of an asymptotic phase transition can be guaranteed while applying a limited restriction on domain size and on constraint tightness in that case a threshold point can be precisely located and all instances have the guarantee to be hard at the threshold i e to have an exponential tree resolution complexity next a formal analysis shows that it is possible to generate forced satisfiable instances whose hardness is similar to unforced satisfiable ones this analysis is supported by some representative results taken from an intensive experimentation that we have carried out using complete and incomplete search methods

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

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

influence of errors on the two microphone method for measuring acoustic properties in ducts using the two microphone method acoustic properties in ducts as for example reflection coefficient and acoustic impedance can be calculated from a transfer function measurement between two microphones in this paper a systematic investigation of the various measurement errors that can occur and their effect on the calculated quantities is made the input data for the calculations are the measured transfer function the microphone separation and the distance between one microphone and the sample first errors in the estimate of the transfer function are treated conclusions concerning the most favorable measurement configuration to avoid these errors are drawn next the length measurement errors are treated measurements were made to study the question of microphone interference the influence of errors on the calculated quantities has been investigated by numerical simulation from this conclusions are drawn on the useful frequency range for a given microphone separation and on the magnitude of errors to expect for different cases

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

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

combinatorial sharpness criterion and phase transition classification for random csps we investigate the nature of the phase transition sharp or coarse for random constraint satisfaction problems we first give a sharp threshold criterion specified for csps which is derived from friedgut bourgain s one thus we get a complete and precise classification of the nature of the threshold for symmetric boolean csps in particular we show that it is governed by two local properties strongly related to the problems 1 sat and 2 xor sat

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

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

an algorithm for random signed 3 sat with intervals interval k sat k isat is a generalization of classical k sat where the variables can take values in 0 1 instead of 0 1 and the literals are of the form x i for intervals i 0 1 it falls within the class of signed satisfiability problems we propose an algorithm for 3 isat and analyze it on uniformly random formulas the algorithm follows the unit clause paradigm enhanced by a very limited backtracking option using wormald s ode method we prove that if m n 2 3 with high probability our algorithm succeeds in finding an assignment of values to the variables satisfying the formula

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

rigorous results for random 2 p sat in recent years there has been significant interest in the study of random k sat formulae for a given set of n boolean variables let bk denote the set of all possible disjunctions of k distinct non complementary literals from its variables k clauses a random k sat formula fk n m is formed by selectinguniformly and independently m clauses from bk and takingtheir conjunction motivated by insights from statistical mechanics that suggest a possible relationship between the order of phase transitions and computational complexity monasson and zecchina phys rev e 56 2 1997 1357 proposed the random 2 p sat model for a given p 0 1 a random 2 p sat formula f2 p n m has m randomly chosen clauses over n variables where pm clauses are chosen from b3 and 1 p m from b2 usingthe heuristic replica method of statistical mechanics monasson and zecchina gave a number of non rigorous predictions on the behavior of random 2 p sat formulae in this paper we give the 1rst rigorous results for random 2 p sat including the following surprising fact for p 2 5 with probability 1 o 1 a random 2 p sat formula is satisfiable if its 2 sat subformula is satisfiable that is for p 6 2 5 random 2 p sat behaves like random 2 sat

statistical inference method for liner impedance eduction with a shear grazing flow this paper presents a statistical inference method for impedance eduction in a flow duct facility the acoustic impedance is recast into a random variable and bayes s theorem is used to obtain the

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

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

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

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

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

models for random constraint satisfaction problems we introduce a class of models for random constraint satisfaction problems this class includes and generalizes many previously studied models we characterize those models from our class which are asymptotically interesting in the sense that the limiting probability of satisfiability changes significantly as the number of constraints increases we also discuss models which exhibit a sharp threshold for satisfiability in the sense that the limiting probability jumps from 0 to 1 suddenly as the number of constraints increases

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

dimension reduction for conditional mean in regression in many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors and less concerned with the other aspects of the conditional distribution in this paper we develop dimension reduction methods that incorporate this consideration we introduce the notion of the central mean subspace cms a natural inferential object for dimension reduction when the mean function is of interest we study properties of the cms and develop methods to estimate it these methods include a new class of estimators which requires fewer conditions than phd and which displays a clear advantage when one of the conditions for phd is violated cms also reveals a transparent distinction among the existing methods for dimension reduction ols phd sir and save we apply the new methods to a data set involving recumbent cows

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

double slicing assisted sufficient dimension reduction for high dimensional censored data this paper provides a unified framework and an efficient algorithm for analyzing high dimensional survival data under weak modeling assumptions in particular it imposes neither parametric distributional assumption nor linear regression assumption it only assumes that the survival time t depends on a high dimensional covariate vector mathbf x through low dimensional linear combinations of covariates gamma t mathbf x the censoring time is allowed to be conditionally independent of the survival time given the covariates this general framework includes many popular parametric and semiparametric survival regression models as special cases the proposed algorithm produces a number of practically useful outputs with theoretical guarantees including a consistent estimate of the sufficient dimension reduction subspace of t mid mathbf x a uniformly consistent kaplan meier type estimator of the conditional distribution function of t and a consistent estimator of the conditional quantile survival time our asymptotic results significantly extend the classical theory of sufficient dimension reduction for censored data particularly that of li wang and chen in ann statist 27 1999 1 23 and the celebrated nonparametric kaplan meier estimator to the setting where the number of covariates p diverges exponentially fast with the sample size n we demonstrate the promising performance of the proposed new estimators through simulations and a real data example

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

discontinuous galerkin method for the computation of acoustic modes in lined flow ducts with rigid splices a discontinuous galerkin method for the discretisation of the linearised euler equations is derived for the computation of acoustic modes in an infinite duct of arbitrary geometric shape in presence of axial sheared flow validations are performed with analytical solutions in the case of a uniformly lined duct and comparisons are done with the literature in the case of a lined cylindrical duct with rigid splices we take advantage of the discontinuous formulation to study the behaviour of the acoustic eigenfunctions in the vicinity of the liner splice transition where singular behaviours of the acoustic perturbation are found

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

a dynamic structure for high dimensional covariance matrices and its application in portfolio allocation abstractestimation of high dimensional covariance matrices is an interesting and important research topic in this article we propose a dynamic structure and develop an estimation procedure for high dimensional covariance matrices asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite by exploring a financial application an empirical study shows that portfolio allocation based on dynamic high dimensional covariance matrices can significantly outperform the market from 1995 to 2014 our proposed method also outperforms portfolio allocation based on the sample covariance matrix the covariance matrix based on factor models and the shrinkage estimator of covariance matrix supplementary materials for this article are available online

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

sharp thresholds of graph properties and the sat problem consider g n p to be the probability space of random graphs on n vertices with edge probability p we will be considering subsets of this space defined by monotone graph properties a monotone graph property p is a property of graphs such that a p is invariant under graph automorphisims b if graph h has property p then so does any graph g having h as a subgraph a monotone symmetric family of graphs is a family defined by such a property one of the first observations made about random graphs by erdos and renyi in their seminal work on random graph theory 12 was the existence of threshold phenomena the fact that for many interesting properties p the probability of p appearing in g n p exhibits a sharp increase at a certain critical value of the parameter p bollobas and thomason proved the existence of threshold functions for all monotone set properties 6 and in 14 it is shown that this behavior is quite general and that all monotone graph properties exhibit threshold behavior i e the probability of their appearance increases from values very close to 0 to values close to 1 in a very small interval more precise analysis of the size of the threshold interval is done in 7 this threshold behavior which occurs in various settings which arise in combinatorics and computer science is an instance of the phenomenon of phase transitions which is the subject of much interest in statistical physics one of the main questions that arises in studying phase transitions is how sharp is the transition for example one of the motivations for this paper arose from the question of the sharpness of the phase transition for the property of satisfiability of a random kcnf boolean formula nati linial who introduced me to this problem suggested that although much concrete analysis was being performed on this problem the best approach would be to find general conditions for sharpness of the phase transition answering the question posed in 14 as to the relation between the length of the threshold interval and the value of the critical probability in this paper we indeed introduce a simple condition and prove it is sufficient stated roughly in the setting of random graphs the main theorem states that if a property has a coarse threshold then it can be approximated by the property of having certain given graphs as a subgraph this condition can be applied in a more

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

quantile adaptive model free variable screening for high dimensional heterogeneous data we introduce a quantile adaptive framework for nonlinear variable screening with high dimensional heterogeneous data this framework has two distinctive features 1 it allows the set of active variables to vary across quantiles thus making it more flexible to accommodate heterogeneity 2 it is model free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest under appropriate conditions on the quantile functions without requiring the existence of any moments the new procedure is shown to enjoy the sure screening property in ultra high dimensions furthermore the quantile adaptive framework can naturally handle censored data arising in survival analysis we prove that the sure screening property remains valid when the response variable is subject to random right censoring numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantile specific information from heteroscedastic data

investigation of straightforward impedance eduction in the presence of shear flow abstract a straightforward impedance eduction method is proposed which combines prony s method with the pridmore brown equation to obtain the impedance of acoustic liners in the presence of shear flow particular attention is paid to the reported inconsistency problems associated with the boundary layer effect in the development of impedance eduction techniques a kind of flow insensitive acoustic liner is considered which is placed in a rectangular flow duct containing predominant grazing incidence mode three slip or no slip flow profiles are examined which are the parabola the one seventh power law and the uniform core flow with linear boundary layer a shear flow fem model is also set up to simulate the duct acoustic field the present impedance eduction method has been tested and validated using both the simulated and the published measured data it is shown that despite of their distinct boundary layers the selected flow profiles lead to essentially the same impedance results and also for the impedance eduction the strict consideration of no slip shear flow is very consistent with the use of the ingard myers boundary condition with the uniform flow assumption over the test conditions although not susceptible to the exact shape of flow profile the impedance eduction critically depends on the determination of the cross sectional average mach number the usual practice of approximately representing the duct flow with the midspan profile results in a slight overestimation of the average mach number in the two dimensional acoustic models and thus can considerably affect the accuracy of the impedance eduction to solve this problem the average flow profile is introduced to account for the actual three dimensional flow non uniformity in the rectangular duct it is further found that the effective mach number corresponding to a slightly modified average flow profile can be used to achieve a considerable collapse of the impedance spectra educed at different mach numbers based on the new evaluation of the influence of boundary layer profile the fem simulation using the straightforwardly educed impedance as the boundary condition can achieve an excellent agreement with the benchmark data for the complex sound pressure in the flow duct

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

an adjoint based method for liner impedance eduction validation and numerical investigation abstract an inverse method for liner acoustic impedance eduction in a duct is presented the determination of adjoint equations allows to make explicit the directional derivatives of the objective function needed by the search algorithm direct and adjoint system of equations are spatially discretized by a discontinuous galerkin scheme the propagation model and the eduction process are successfully validated on nasa benchmark data extracted from literature in a no flow configuration objective functions written in terms of acoustic pressure and acoustic velocity are considered successively special attention is given to the possibilities offered by the method such as multiparameter identification with the study of a non homogeneous liner convergence history of the process is also examined revealing interesting properties for the velocity based objective function compared to the pressure based objective function in further developments the method is planned to be used with acoustic velocity fields obtained by laser doppler velocimetry

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

the scaling window of the model d k csp abstract consider the model d k csp which consists of a set of n variables with the domain size d and a set of t r n ln d ln p constraints where each constraint binds k distinct variables and permits p d k tuples of values we prove that the exact phase transition of the model d k csp occurs at r c 1 as long as k ln d ln n where satisfies that 1 2 1 2 2 k 1 e 1 e 0 is a sufficiently small constant more importantly we establish the finite size scaling about this transition specifically let 0 be a given constant the probability of satisfiability of the model d k csp is greater than 1 if r 1 1 n 1 ln d is dependent on the control parameters and is less than if r 1 1 n ln d

kernel and nearest neighbor estimation of a conditional quantile let x 1 z 1 x 2 z 2 x n z n be iid as x z and for 0 p 1 let p x denote the conditional p quantile of z given x x i e p z p x x x p kernel and near est neighbor estimators of p x are proposed in order to study the asymptotics of these estimates bahadur type representations of the sample conditional quantiles are obtained these representations are used to examine the important issue of choosing the smoothing parameter by a local approach for a fixed x based on weak convergence of these estimators the results lead to asymptotic linear models which motivate certain estimators

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