a comparison estimate of toponogov type for ricci curvature it seems a natural question to ask to what extent the results and tools for sectional curvature remain valid for ricci curvature there is rapid progress in both positive and negative directions toponogov comparison theorem has been the most powerful tool in the study of sectional curvature underlying the proof of the soul theorem the diameter sphere theorem the uniform estimate of betti numbers and the finiteness theorems toponogov comparison theorem is also the characterizing property of lower or upper sectional curvature bounds which led to generalizations of the concept of sectional curvature bounds to non smooth space thus it could not possibly hold for ricci curvature which makes problems a lot harder for ricci curvature from a geometric point of view it also makes the ricci curvature very different from the sectional curvature as one gradually comes to realize it is interesting then that we find a comparison estimate of toponogov type for ricci curvature a hinge in a complete riemannian manifold consists of two geodesic segments vi y2 such that yi ii 2 0 9 we denote it by 1 2 where z l o we will be using the following modified version of the conjugate radius function pc p

improving the performance of random coefficients demand models the role of optimal instruments abstract we shed new light on the performance of berry levinsohn and pakes 1995 gmm estimator of the aggregate random coefficient logit model based on an extensive monte carlo study we show that the use of chamberlain s 1987 optimal instruments overcomes many problems that have recently been documented with standard non optimal instruments optimal instruments reduce small sample bias but they prove even more powerful in increasing the estimator s efficiency and stability we consider a wide variety of data generating processes and an empirical application to the automobile market we also consider the gains of other recent methodological advances when combined with optimal instruments

minimum distance estimation in random coefficient regression models random coefficient regression models are important in modeling heteroscedastic multivariate linear regression in econometrics the analysis of panel data is one example in statistics the random and mixed effects models of anova deconvolution models and affine mixture models are all special cases of random coefficient regression some inferential problems such as constructing prediction regions for the modeled response require a good nonparametric estimator of the unknown coefficient distribution this paper introduces and studies a consistent nonparametric minimum distance method for estimating the coefficient distribution our estimator translates the difficult problem of estimating an inverse radon transform into a minimization problem

unobserved heterogeneity in auctions under restricted stochastic dominance abstract we study the identification of first price auctions with nonseparable unobserved heterogeneity in particular we extend hu et al 2013 by relaxing the first order stochastic dominance condition instead we assume restricted stochastic dominance relations among value quantile functions and show that the same relations pass to bid quantile functions an ordered tree summarizes these relations and provides a total ordering relying on the proposed restricted stochastic dominance ordering we extend a list of identification results in the empirical auction literature

zeta elements in the k theory of drinfeld modular varieties beilinson contemp math 55 1 34 1986 constructs special elements in the second k group of an elliptic modular curve and shows that the image under the regulator map is related to the special values of the l functions of elliptic modular forms in this paper we give an analogue of this result in the context of drinfeld modular varieties

nonparametric estimation in random coefficients binary choice models this paper considers random coefficients binary choice models the main goal is to estimate the density of the random coefficients nonparametrically this is an ill posed inverse problem characterized by an integral transform a new density estimator for the random coefficients is developed utilizing fourier laplace series on spheres this approach offers a clear insight on the identification problem more importantly it leads to a closed form estimator formula that yields a simple plug in procedure requiring no numerical optimization the new estimator therefore is easy to implement in empirical applications while being flexible about the treatment of unobserved heterogeneity extensions including treatments of nonrandom coefficients and models with endogeneity are discussed

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

kronecker limit formula over global function fields the aim of this paper is to present a function field analogue of the classical kronecker limit formula we first introduce a non holomorphic eisenstein series on the drinfeld half plane and connect its second term with gekeler s discriminant function one application is to express the taguchi height of rank 2 drinfeld modules with complex multiplication in terms of the logarithmic derivative of the corresponding zeta functions moreover from the integral form of the rankin type l function associated to two drinfeld type newforms we then derive a formula for a non central special derivative of the l function in question adapting the classical approach we also obtain a kronecker type solution for pell s equation over function fields

alternative em methods for nonparametric finite mixture models summary this research focuses on a general class of maximum likelihood problems in which it is desired to maximise a nonparametric mixture likelihood with finitely many known component densities over the set of unknown weight parameters convergence of the conventional em algorithm for this problem is extremely slow when the component densities are poorly separated and when the maximum likelihood estimator requires some of the weights to be zero as the algorithm can never reach such a boundary point alternative methods based on the principles of em are developed using a two stage approach first a new data augmentation scheme provides improved convergence rates in certain parameter directions secondly two cyclic versions of this data augmentation are created by changing the missing data formulation between the em steps these extend the acceleration directions to the whole parameter space giving another order of magnitude increase in convergence rate examples indicate that the new cyclic versions of the data augmentation schemes can converge up to 500 times faster than the conventional em algorithm for fitting nonparametric finite mixture models

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

induction and restriction of kazhdan lusztig cells abstract barbasch and vogan gave a beautiful rule for restricting and inducing kazhdan lusztig representations of weyl groups in this paper we show that this rule implies and generalizes the littlewood richardson rule for decomposing outer products of representations of the symmetric groups a new recursive rule for computing characters of arbitrary coxeter groups follows another application is a generalization of garsia remmel s algorithm for decomposing certain tensor products of symmetric groups representations

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

the random coefficients logit model is identified the random coecients multinomial choice logit model also known as the mixed logit has been widely used in empirical choice analysis for the last thirty years we prove that the distribution of random coecients in the multinomial logit model is nonparametrically identified

on complete manifolds of nonnegative kth ricci curvature in this paper we establish some vanishing and finiteness theorems for the topological type of complete open riemannian manifolds under certain positivity conditions for curvature key tools are comparison techniques and morse theory of busemann and distance functions

fourier series and the special values of l functions let k be a number field with ring of integers a let x be an idele class character for k which is trivial at each infinite place the l series l s x c x b nb is defined by the sum over all non trivial ideals b of a which are prime to the conductor f of x this sum is absolutely convergent for re s 1 when x is non trivial l s x extends analytically to a neighborhood of s 1 and jc 1 x is o although this value is of great arithmetic interest truly satisfactory formulas for l 1 x have only been obtained in the cases when k q and when k is imaginary quadratic where they are due to dirichlet and kronecker respectively these number fields are precisely the one with a unique archimedean completion k in this case a is a discrete co compact subring of a locally compact field k an analogous situation exists for global function fields k over finite fields let oc be a place of k and let a denote the ring of functions which are regular outside co then a is a discrete co compact subring of the completion k which is a locally compact field if x is an idele class character for k which is trivial at cc and we define l s x as above then for x 1 the series is regular and non zero at s 1 formulas for l 1 x were obtained by galovich and rosen in the case when a is isomorphic to the ring of polynomials over a finite field and by hayes in general in this paper we will reprove all the limit formulas for l 1 x in a uniform manner using fourier analysis on the locally compact field k we shall also obtain the functional equation of l s x following the

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

likelihood approximation by numerical integration on sparse grids the calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions approaches for extending gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions we propose an extension that is very general and easily implemented and does not suffer from the curse of dimensionality monte carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

binary response correlated random coefficient panel data models abstract in this paper we consider binary response correlated random coefficient crc panel data models which are frequently used in the analysis of treatment effects and demand of products we focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors our identification conditions and estimation are based on the framework of the model with a special regressor which is a novel approach proposed by lewbel 1998 lewbel 2000 to solve the heterogeneity and endogeneity problem in the binary response models with the help of the additional information on the special regressor we can transform a binary response crc model to a linear moment relation we also construct a semiparametric estimator for the average slopes and derive the n normality result further we propose a nonparametric method to test the correlations between random coefficients and regressors simulations are given to show the finite sample performance of our estimators and test statistics

nonparametric analysis of a duration model with stochastic unobserved heterogeneity abstract this paper develops nonparametric identification and estimation results for a single spell hazard model where the unobserved heterogeneity is specified as a levy subordinator the identification approach solves a nonlinear volterra integral equation of the first kind with an unknown kernel function both the kernel of the integral operator which models the distribution of the unobserved heterogeneity and the functions that enter it are identified given regularity conditions and minimal variation in the observed covariates the paper proposes a shape constrained nonparametric two step sieve minimum distance estimator rates of convergence are derived and monte carlo experiments show the finite sample performance of the estimator

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

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

estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals this paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables this is a nonparametric nonlinear instrumental variables iv problem we propose a class of penalized sieve minimum distance psmd estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space some of the psmd procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty others use large dimensional sieves with lower semicompact and or convex penalties we establish their consistency and the convergence rates in banach space norms such as a sup norm or a root mean squared norm allowing for possibly noncompact infinite dimensional parameter spaces for both mildly and severely ill posed nonlinear inverse problems our convergence rates in hilbert space norms such as a root mean squared norm achieve the known minimax optimal rate for the nonparametric mean iv regression we illustrate the theory with a nonparametric additive quantile iv regression we present a simulation study and an empirical application of estimating nonparametric quantile iv engel curves

convex optimization shape constraints compound decisions and empirical bayes rules estimation of mixture densities for the classical gaussian compound decision problem and their associated empirical bayes rules is considered from two new perspectives the first motivated by brown and greenshtein introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting bayes rule the second motivated by jiang and zhang proposes a new approach to computing the kiefer wolfowitz nonparametric maximum likelihood estimator for mixtures in contrast to prior methods for these problems our new approaches are cast as convex optimization problems that can be efficiently solved by modern interior point methods in particular we show that the reformulation of the kiefer wolfowitz estimator as a convex optimization problem reduces the computational effort by several orders of magnitude for typical problems by comparison to prior em algorithm based methods and thus greatly expands the practical applicability of the resulting method

maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution abstract we consider a binary response model yi 1 xi i ei 0 with xi independent of the unobservables i e i no finite dimensional parametric restrictions are imposed on f0 the joint distribution of i e i a nonparametric maximum likelihood estimator for f0 is shown to be consistent we analyze some conditions under which f0 is or is not identified in particular we show that if the support of f0 is a subset of any half of the unit hypersphere then f0 is identified relative to all distributions on the unit hypersphere we also provide some monte carlo evidence on the small sample performance of our estimator

examples of manifolds of positive ricci curvature on presente de nouveaux exemples de varietes de riemann simplement connexes de dimension 7 a courbure de ricci positive qui n admettent pas de metrique de courbure sectionnelle non negative dans les cas compacts et non compacts

a bayesian mixed logit probit model for multinomial choice in this paper we introduce a new flexible mixed model for multinomial discrete choice where the key individual and alternative specific parameters of interest are allowed to follow an assumption free nonparametric density specification while other alternative specific coefficients are assumed to be drawn from a multivariate normal distribution which eliminates the independence of irrelevant alternatives assumption at the individual level a hierarchical specification of our model allows us to break down a complex data structure into a set of submodels with the desired features that are naturally assembled in the original system we estimate the model using a bayesian markov chain monte carlo technique with a multivariate dirichlet process dp prior on the coefficients with nonparametrically estimated density we employ a latent class sampling algorithm which is applicable to a general class of models including non conjugate dp base priors the model is applied to supermarket choices of a panel of houston households whose shopping behavior was observed over a 24 month period in years 2004 2005 we estimate the nonparametric density of two key variables of interest the price of a basket of goods based on scanner data and driving distance to the supermarket based on their respective locations our semi parametric approach allows us to identify a complex multi modal preference distribution which distinguishes between inframarginal consumers and consumers who strongly value either lower prices or shopping convenience

nonparametric identification of the distribution of random coefficients in binary response static games of complete information this paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification the main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects under additional independence assumptions we identify the joint density of the interaction coefficients moreover we prove that in the presence of covariates that are common to both players the player specific coefficient densities are identified while the joint density of all random coefficients is not point identified however we do provide bounds on counterfactual probabilities that involve this joint density

a recursive rule for kazhdan lusztig characters abstract a formula for computing kazhdan lusztig characters in hecke algebras of coxeter groups is given this formula holds for products of coxeter elements of parabolic subgroups in an arbitrary coxeter group where the parabolic subgroups are of type a and the kazhdan lusztig representations are of finite dimension the formula yields new combinatorial interpretations of murnaghan nakayama type to these characters and to other related characters

on complete manifolds with nonnegative ricci curvature complete open riemannian manifolds mn g with nonnegative sectional curvature are well understood the basic results are toponogov s splitting theorem and the soul theorem cg1 the splitting theorem has been extended to manifolds of nonnegative ricci curvature cg2 on the other hand the soul theorem does not extend even topologically according to recent examples in gm2 a different method to construct manifolds which carry a metric with ric 0 but no metric with nonnegative sectional curvature has been given by l berard bergery bb this leads to the question cf also y1 is there any finiteness result for complete riemannian manifolds with ric 0 the answer is certainly affirmative in the low dimensional special cases n 2 where all notions of curvature coincide and n 3 where nonnegative ricci curvature has been studied by means of stable minimal surfaces msy sy on the other hand j p sha and d g yang shy have constructed complete manifolds with strictly positive ricci curvature in higher dimensions for example they can choose the underlying space to be r4 x s3 with infinitely many copies of s3 x cp 2 attached to it by surgery cf also shy 1 it is therefore clear that any finiteness result for arbitrary dimensions requires additional assumptions the purpose of this paper is to establish the following main result

nonparametric errors in variables models with measurement errors on both sides of the equation abstract measurement errors are often correlated as in surveys where respondent s biases or tendencies to err affect multiple reported variables we extend schennach 2007 to identify moments of the conditional distribution of a true y given a true x when both are measured with error the measurement errors in y and x are correlated and the true unknown model of y given x has nonseparable model errors after showing nonparametric identification we provide a sieve generalized method of moments based estimator of the model and apply it to nonparametric engel curve estimation in our application measurement errors on the expenditures of a good y are by construction correlated with measurement errors in total expenditures x this problem which is present in many consumption data sets has been ignored in most demand applications we find that accounting for this problem casts doubt on hildenbrand s 1994 increasing dispersion assumption

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables

efficient greedy learning of gaussian mixture models this article concerns the greedy learning of gaussian mixtures in the greedy approach mixture components are inserted into the mixture one after the other we propose a heuristic for searching for the optimal component to insert in a randomized manner a set of candidate new components is generated for each of these candidates we find the locally optimal new component and insert it into the existing mixture the resulting algorithm resolves the sensitivity to initialization of state of the art methods like expectation maximization and has running time linear in the number of data points and quadratic in the final number of mixture components due to its greedy nature the algorithm can be particularly useful when the optimal number of mixture components is unknown experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided