a semi parametric censored regression estimator abstract this paper introduces a semi parametric method for estimating regression co underlying parent population of errors in censored the method is an example of the method of sieves and it provides simultaneous estimates of the regression coefficients and the density of the underlying parent population in the very simplest terms the underlying unknown density is approximated by a spline with mesh size approaching zero with the sample size the values of the density at the knots are then added to the list of the usual unknown parameters in a censored regression model e g the regression coefficients and scale parameter a quasi likelihood function using the approximate spline density is then maximized over all the parameters mentioned above the method is shown to result in strongly consistent parameter estimates

on the finite sample behavior of adaptive estimators abstract we explore the finite sample performance of adaptive estimators in linear time series regression models our results show that for samples of only 50 observations the 90 percent confidence interval of the adaptive estimator is 20 to 50 percent smaller than the corresponding interval for its gls counterpart across a range of symmetrical distributions when the assumption of symmetry is relaxed smaller gains are observed these results are sensitive to the degree of departure from normality and the precision of the measurement exercise we further observe that the estimated standard errors are biased downward

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

asymptotic efficiency in semi parametric models with censoring abstract we consider a regression model subject to bivariate censoring in which the errors are independent of the explanatory variables our objective is to drop the assumption of bivaraite normality and obtain an information bound on asymptotic efficiency when the error distribution is unrestricted except for smoothness and regularity conditions this bound has simple form if there are no exclusion restrictions on the selection equation then positive information requires a restriction on the regression slope parameters and a continuous distribution for a component of the explanatory variables we also consider a binary choice model under the weak assumption that the error distribution has zero median conditional on the explanatory variables here the semi parametric information bound is zero hence although a consistent estimator exists it is not possible to attain covergence at rate 1 n

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

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

binary regression models for contaminated data on etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires on propose un modele simple qui permet qu un petit nombre de reponses binaires soit mal enregistre

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

consistency of deviance based m estimators summary in a general estimation problem the deviance function generates statistics that are similar to squared standardized residuals a deviance based m estimator dbme is defined as an adaptively weighted maximum likelihood estimator where the weights depend upon the deviances in both a single parameter and a regression setting we give some general conditions under which a dmbe is consistent for a suitable weighting scheme these conditions are satisfied in many continuous cramer rao regular families and in related linear or nonlinear regression cases the conditions fail and the estimator is inconsistent in most discrete families

notes on a slice distance for singular lp bundles abstract a slice distance for the class of weak abelian l p bundles in 3 dimensions was introduced in 20 where it was used to prove the closure of such class of bundles for the weak l p convergence we further investigate this distance here and we prove more properties of it for example we show that it is holder continuous on the slices of an l p bundle using the same distance we give a notion of a boundary trace which allows to use the direct method for minimization problems on weak bundles with fixed trace we then state some conjectures and some open questions

weighted likelihood equations with bootstrap root search abstract we discuss a method of weighting likelihood equations with the aim of obtaining fully efficient and robust estimators we discuss the case of continuous probability models using unimodal weighting functions these weighting functions downweight observations that are inconsistent with the assumed model at the true model therefore the proposed estimating equations behave like the ordinary likelihood equations we investigate the number of solutions of the estimating equations via a bootstrap root search the estimators obtained are consistent and asymptotically normal and have desirable robustness properties an extensive simulation study and real data examples illustrate the operating characteristics of the proposed methodology

connecting rational homotopy type singularities let n be a compact simply connected smooth riemannian manifold and for p 2 3 w 1 p r p 1 n be the sobolev space of measurable maps from r p 1 into n whose gradients are in l p the restriction of u to almost every p dimensional sphere s in r p 1 is in w 1 p s n and defines an homotopy class in p n white 1988 evaluating a fixed element z of hom p n r on this homotopy class thus gives a real number z u s the main result of the paper is that any w 1 p weakly convergent limit u of a sequence of smooth maps in c r p 1 n z u has a rectifiable poincare dual left gamma overrightarrow gamma theta right here is a a countable union of c 1 curves in r p 1 with hausdorff user1 mathcal h 1 measurable orientation overrightarrow gamma gamma to s p and density function r the intersection number between left gamma overrightarrow gamma theta right and s evaluates z u s for almost every p sphere s moreover we exhibit a non negative integer n z depending only on homotopy operation z such that int gamma left theta right p mathord left vphantom p left p n z right right kern nulldelimiterspace left p n z right d user1 mathcal h 1 infty even though the mass int gamma left theta right d user1 mathcal h 1 may be infinite we also provide cases of n p and z for which this rational power p p n z is optimal the construction of this poincare dual is based on 1 dimensional bubbling described by the notion of scans which was introduced in hardt and riviere 2003 we also describe how to generalize these results to r m for any m p 1 in which case the bubbling is described by an m p rectifiable set with orientation and density function determined by restrictions of the mappings to almost every oriented euclidean p sphere

on estimation and adaptive estimation for locally asymptotically normal families locally asymptotically minimax lam estimates are constructed for locally asymptotically normal lan families under very mild additional assumptions adaptive estimation is also considered and a sufficient condition is given for an estimate to be locally asymptotically minimax adaptive incidently it is shown that a well known lower bound due to hajek 1972 for the local asymptotic minimax risk is not sharp

adaptive estimation in time series regression models this work develops adaptive estimators for a linear regression model with serially correlated errors we show that these results continue to hold when the order of the arma process characterizing the errors is unknown the finite sample results are promising indicating that substantial efficiency gains may be possible for samples as small as 50 observations we use these estimators to investigate the behavior of the forward foreign exchange market

monte carlo evidence on adaptive maximum likelihood estimation of a regression on examine la performance des estimateurs du maximum de vraisemblance adaptatifs lorsque ces parametres sont preselectionnes ou alternativement determines par une methode du bootstrap basee sur les donnees

removable singularities in yang mills fields we show that a field satisfying the yang mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite we obtain the result that every yang mills field overr4 with bounded functional l2 norm may be obtained from a field ons4 r4 hodge or coulomb gauges are constructed for general small fields in arbitrary dimensions including 4

the properties of the parameterization of armax systems and their relevance for structural estimation and dynamic specification armax systems in structural specification are considered topological and geometric properties of the parameter space and of the parameterization which are important for the properties of the estimators regardless of their special form are investigated and the specification of the maximum lag lengths is discussed

linear instrumental variable estimation of limited dependent variable models with endogenous explanatory variables abstract the purpose of this paper is to present and analyze an instrumental variables estimator for limited dependent variable models that does not require functional form assumptions for the distribution of disturbances this estimator is a weighted instrumental variables estimator where the weight is the ratio of a multivariate normal density to the actual density of the instrumental variables a semi non parametric estimator of the weights is presented and some conjectures concerning the asymptotic distribution of the estimator are discussed

the resolution of the yang mills plateau problem in super critical dimensions abstract we study the minimization problem for the yang mills energy under fixed boundary connection in supercritical dimension n 5 we define the natural function space a g in which to formulate this problem in analogy to the space of integral currents used for the classical plateau problem the space a g can be also interpreted as a space of weak connections on a real measure theoretic version of reflexive sheaves from complex geometry we prove the existence of weak solutions to the yang mills plateau problem in the space a g we then prove the optimal regularity result for solutions of this plateau problem on the way to prove this result we establish a coulomb gauge extraction theorem for weak curvatures with small yang mills density this generalizes to the general framework of weak l 2 curvatures previous works of meyer riviere and tao tian in which respectively a strong approximability property and an admissibility property were assumed in addition

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

resistant fits for some commonly used logistic models with medical application logistic regression type models are used in many applications some examples include the classical dose response experiment prospective and retrospective studies of disease incidence with and without matching and the analysis of ordinal data in most instances the model is fitted by the method of maximum likelihood which like least squares is sensitive to atypical observations an alternative to maximum likelihood is proposed and illustrated by examples

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

robust measures of location for directional data established techniques for robust m estimation of a location parameter are adapted for use in directional data in particular a periodic version of any of the commonly used functions can be used to define a comparable estimator of angular location this technique is illustrated with a numerical example and a small simulation study the proposed estimators appear to perform at efficiency levels similar to those of ordinary m estimators in the linear case

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models