conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

adaptive estimation of the dynamics of a discrete time stochastic volatility model abstract this paper is concerned with the discrete time stochastic volatility model y i exp x i 2 i x i 1 b x i x i i 1 where only y i is observed the model is rewritten as a particular hidden model z i x i e i x i 1 b x i x i i 1 where i and e i are independent sequences of i i d noise moreover the sequences x i and e i are independent and the distribution of e is known then our aim is to estimate the functions b and 2 when only observations z 1 z n are available we propose to estimate b f and b 2 2 f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces by ratio strategy estimators of b and 2 are then deduced the mean square risk of the resulting estimators are studied and their rates are discussed lastly simulation experiments are provided constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples

influences of large height differences and overhangs on the dynamic scaling behavior of discrete models abstract in order to investigate the influences of large height differences and overhangs on the dynamic scaling behavior of discrete models meanwhile reducing the finite size effects the etching model is modified to reduce large height differences and the overhangs in ballistic deposition surfaces are removed under certain principles numerical simulations are carried out for the modified models and the results show that the modified surfaces lead to good dynamic scaling behavior even on small system length scales the values of the dynamic scaling exponents are in excellent agreement with theoretical predictions of the kardar parisi zhang equation in 1 1 dimensions

on reduced convex qp formulations of monotone lcps techniques for transforming convex quadratic programs qps into monotone linear complementarity problems lcps and vice versa are well known we describe a class of lcps for which a reduced qp formulation one that has fewer constraints than the standard qp formulation is available we mention several instances of this class including the known case in which the coefficient matrix in the lcp is symmetric

extremely large scale simulation of a kardar parisi zhang model using graphics cards the octahedron model introduced recently has been implemented onto graphics cards which permits extremely large scale simulations via binary lattice gases and bit coded algorithms we confirm scaling behavior belonging to the two dimensional kardar parisi zhang universality class and find a surface growth exponent 0 2415 15 on 2 17 2 17 systems ruling out 1 4 suggested by field theory the maximum speedup with respect to a single cpu is 240 the steady state has been analyzed by finite size scaling and a growth exponent 0 393 4 is found correction to scaling exponent are computed and the power spectrum density of the steady state is determined we calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered we provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width

composition duality and maximal monotonicity this paper shows how the attouch thera duality principle for operator inclusions can be extended to compositions of multifunctions so that the primal and dual inclusions may involve operators between different pairs of spaces we first present the extension and give an example from computational economics to demonstrate that it has practical utility then we consider a particular case often found in applications involving real hilbert spaces and maximal monotone operators we show that in this case our duality framework includes those previously developed by rockafellar mosco and gabay finally we demonstrate that in this case under very simple hypotheses the duality transformation preserves the maximal monotonicity of the operators involved this proof uses an apparently new criterion for maximal monotonicity of operators of the form l tl where t is maximal monotone and l is linear and continuous with adjoint l

roughness fluctuations roughness exponents and the universality class of ballistic deposition abstract in order to estimate roughness exponents of interface growth models we propose the calculation of effective exponents from the roughness fluctuation in the steady state we compare the finite size behavior of these exponents and the ones calculated from the average roughness w 2 for two models in the 2 1 dimensional kardar parisi zhang kpz class and for a model in the 1 1 dimensional villain lai das sarma vlds class the values obtained from provide consistent asymptotic estimates eventually with smaller finite size corrections for the vlds nonlinear molecular beam epitaxy class we obtain 0 93 0 01 improving previous estimates we also apply this method to two versions of the ballistic deposition model in two dimensional substrates in order to clarify the controversy in terms of its universality class raised by numerical results and a recent derivation of its continuous equation effective exponents calculated from suggest that both versions are in the kpz class additional support for this conclusion is obtained by a comparison of the full roughness distributions of these models and the distribution of other discrete kpz models

classification of 2 1 dimensional growing surfaces using schramm loewner evolution statistical behavior and scaling properties of isoheight lines in three different saturated two dimensional grown surfaces with controversial universality classes are investigated using ideas from schramm loewner evolution text sle ensuremath kappa we present some evidence that the isoheight lines in the ballistic deposition bd eden and restricted solid on solid rsos models have conformally invariant properties all in the same universality class as the self avoiding random walk saw equivalently text sle 8 3 this leads to the conclusion that all these discrete growth models fall into the same universality class as the kardar parisi zhang kpz equation in two dimensions

longest increasing subsequence as expectation of a simple nonlinear stochastic partial differential equation with a low noise intensity we report some observations concerning the statistics of longest increasing subsequences lis we argue that the expectation of lis its variance and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation in the limit of very low noise intensity

smoothed and corrected score approach to censored quantile regression with measurement errors censored quantile regression is an important alternative to the cox proportional hazards model in survival analysis in contrast to the usual central covariate effects quantile regression can effectively characterize the covariate effects at different quantiles of the survival time when covariates are measured with errors it is known that naively treating mismeasured covariates as error free would result in estimation bias under censored quantile regression we propose smoothed and corrected estimating equations to obtain consistent estimators we establish consistency and asymptotic normality for the proposed estimators of quantile regression coefficients compared with the naive estimator the proposed method can eliminate the estimation bias under various measurement error distributions and model error distributions we conduct simulation studies to examine the finite sample properties of the new method and apply it to a lung cancer study supplementary materials for this article are available online

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

generalized linear complementarity problems it has been shown by lemke that if a matrix is copositive plus on n then feasibility of the corresponding linear complementarity problem implies solvability in this article we show under suitable conditions that feasibility of ageneralized linear complementarity problem i e defined over a more general closed convex cone in a real hilbert space implies solvability whenever the operator is copositive plus on that cone we show that among all closed convex cones in a finite dimensional real hilbert space polyhedral cones are theonly ones with the property that every copositive plus feasible glcp is solvable we also prove a perturbation result for generalized linear complementarity problems

errors in variables in linear systems this paper extends the simple errors in variable bound to the setting of systems of equations both diagonal and nondiagonal measurement error covariance matrices are considered in the nondiagonal case the analogue of the simple errors in variable interval of estimates is an ellipsoid with diagonal equal to the line segment connecting the direct least squares with a two stage least squares estimate for the diagonal case the set of estimates under some conditions must lie within the convex hull of 2k points

robust linear and support vector regression the robust huber m estimator a differentiable cost function that is quadratic for small errors and linear otherwise is modeled exactly in the original primal space of the problem by an easily solvable simple convex quadratic program for both linear and nonlinear support vector estimators previous models were significantly more complex or formulated in the dual space and most involved specialized numerical algorithms for solving the robust huber linear estimator numerical test comparisons with these algorithms indicate the computational effectiveness of the new quadratic programming model for both linear and nonlinear support vector problems results are shown on problems with as many as 20000 data points with considerably faster running times on larger problems

numerical study of the kardar parisi zhang equation we integrate numerically the kardar parisi zhang kpz equation in 1 1 and 2 1 dimensions using a euler discretization scheme and the replacement of nablah 2 by exponentially decreasing functions of that quantity to suppress instabilities when applied to the equation in 1 1 dimensions the method of instability control provides values of scaling amplitudes consistent with exactly known results in contrast to the deviations generated by the original scheme in 2 1 dimensions we spanned a range of the model parameters where transients with edwards wilkinson or random growth are not observed in box sizes 8 or l or 128 we obtain a roughness exponent of 0 37 or alpha or 0 40 and steady state height distributions with skewness s 0 25 0 01 and kurtosis q 0 15 0 1 these estimates are obtained after extrapolations to the large l limit which is necessary due to significant finite size effects in the estimates of effective exponents and height distributions on the other hand the steady state roughness distributions show weak scaling corrections and evidence of stretched exponential tails these results confirm previous estimates from lattice models showing their reliability as representatives of the kpz class

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

estimation of linear and nonlinear errors in variables models using validation data abstract consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed the estimation procedures are based on least squares methods with regression functions replaced by wide sense conditional expectation functions the methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model they are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions

what is the connection between ballistic deposition and the kardar parisi zhang equation ballistic deposition bd is believed to belong to the kardar parisi zhang kpz universality class in this paper we study the validity of this belief by rigorously deriving a continuum equation from the bd microscopic rules which deviates from the kpz equation we show that in one dimension and in the presence of noise the deviation is not important this is not the case in the absence of noise in more than one dimension and in the presence of noise we obtain an equation that superficially seems to be a continuum equation but in which the symmetry under rotations around the growth direction is broken

the linear l 1 estimator and the huber m estimator relationships between a linear l1 estimation problem and the huber m estimator problem can be easily established by their dual formulations the least norm solution of a linear programming problem studied by mangasarian and meyer siam j control optim 17 1979 pp 745 752 provides a key link between the dual problems based on the dual formulations we establish a local linearity property of the huber m estimators with respect to the tuning parameter gamma and prove that the solution set of the huber m estimator problem is lipschitz continuous with respect to perturbations of the tuning parameter gamma as a consequence the set of the linear l1 estimators is the limit of the set of the huber m estimators as gamma to 0 thus the huber m estimator problem has many solutions for small tuning parameter gamma if the linear l1 estimation problem has multiple solutions a recursive version of madsen and nielsen s algorithm siam j optim 3 1993 pp 223 235 based on computation of the huber m estimator is proposed for finding a linear l1 estimator

approximations for regression with covariate measurement error abstract the effect of covariate measurement error on maximum likelihood and maximum quasilikelihood estimates mle s or mqle s of regression parameters is considered the naive estimates obtained by ignoring error are modified to account for it the modified estimates can be computed explicitly from the naive ones and have less bias for small error they are particularly useful for berkson error models examples illustrate their application to linear and nonlinear regression errors in continuous covariates and misclassification of discrete covariates the estimates are applied to data relating air pollution to respiratory disease in children analytic methods and simulations are used to compare the estimates to others that have been proposed for dealing with covariate measurement errors the basic idea is that the mle or mqle of the parameter is a function of the size of the error when 0 and there is no error is the usual mle or mqle for small an improvement over is in many cases of

a simple estimator for nonlinear error in variable models we propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data such as validation data or double measurements are available we assume that the marginal distributions of the measurement errors are laplace double exponential with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other under these assumptions we derive simple revised moment conditions in terms of the observed variables they are used to make inference about the model parameters and the variance of the measurement error the results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute our estimation method is particularly useful in situations where no additional data are available which is the case in many economic data sets simulation study demonstrates good finite sample properties of our proposed estimator we also examine the performance of the estimator in the case where the error distribution is misspecified

semiparametric estimation in logistic measurement error models summary we describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors the particular measurement error model consists of a primary data set in which only the response y and a fallible surrogate w of the true predictor x are observed plus a smaller validation data set for which y x w are observed except for the underlying assumption of a logistic model in the true predictor no parametric distributional assumption is made about the true predictor or its surrogate we develop a semiparametric parameter estimate of the logistic regression parameter which is asymptotically normally distributed and computationally feasible the estimate relies on kernel regression techniques for scalar predictors by a detailed analysis of the mean squared error of the parameter estimate we obtain a representation for an optimal bandwidth

scaling cumulant ratios and height distribution of ballistic deposition in 3 1 and 4 1 dimensions we investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by alves et al phys rev e 90 052405 2014 in d 2 1 dimensions where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account in the present work we show that this concept holds for d 3 1 and 4 1 dimensions we have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models presenting small finite time corrections to the scaling that in principle belong to the kardar parisi zhang kpz universality class in both d 3 1 and 4 1 our results constitute further evidence that the upper critical dimension of the kpz class if it exists is larger than 4

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

a reduction method for variational inequalities this paper explains a method by which the number of variables in a variational inequality having a certain form can be substantially reduced by changing the set over which the variational inequality is posed the method applies in particular to certain economic equilibrium problems occurring in applications we explain and justify the method and give examples of its application including a numerical example in which the solution time for the reduced problem was approximately 2 of that for the problem in its original form 1998 the mathematical programming society inc published by elsevier science b v

kinetic roughening of the urban skyline we analyze the morphology of the modern urban skyline in terms of its roughness properties this is facilitated by a database of 10 7 building heights in cities throughout the netherlands which allows us to compute the asymptotic height difference correlation function in each city we find that in cities for which the height correlations display power law scaling as a function of distance between the buildings the corresponding roughness exponents are commensurate to the edwards wilkinson and kardar parisi zhang equations for kinetic roughening based on analogy to discrete deposition models we argue that these two limiting classes emerge because of possible height restriction rules for buildings in some cities

growth exponents of the etching model in high dimensions in this work we generalize the etching model mello et al 2001 phys rev e 63 041113 t o d 1 dimensions the dynamic exponents of this model are compatible with those of the kardar parisi zhang universality class we investigate the roughness dynamics with surfaces up to d 6 we show that the data from all substrate lengths and for all dimensions can be collapsed into one common curve we determine the dynamic exponents as a function of the dimension moreover our results suggest that d 4 is not an upper critical dimension for the etching model and that it fulfills the galilean invariance

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

consistent estimation for some nonlinear errors in variables models abstract the issues of identification and estimation of nonlinear errors in variables models are explored the deficiencies of the conventional definition of identification are discussed and an alternative definition in terms of observed samples is suggested the consistency and asymptotic normality of minimum distance estimators are studied to simplify the computation a two step estimation procedure is also suggested in which a consistent estimate of a subset of parameters is first obtained and treated as if they were known in the second step estimation of the rest of the parameters conditions for the consistency of this two step estimator and its asymptotic variance covariance matrix are also derived

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

multisurface coding simulations of the restricted solid on solid model in four dimensions we study the restricted solid on solid model for surface growth in spatial dimension d 4 by means of a multisurface coding technique that allows us to analyze samples of size up to 256 4 in the steady state regime for such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations a careful finite size scaling analysis of the critical exponents clearly indicate that d 4 is not the upper critical dimension of the model

treatment effect estimation with covariate measurement error this paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates the approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects the approximations can be estimated using data on observed outcomes the treatment indicator and error contaminated covariates without employing additional information from validation data or instrumental variables the results can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects

corrected loss estimation for quantile regression with covariate measurement errors we study estimation in quantile regression when covariates are measured with errors existing methods require stringent assumptions such as spherically symmetric joint distribution of the regression and measurement error variables or linearity of all quantile functions which restrict model flexibility and complicate computation in this paper we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression the proposed method is simple to implement its validity requires only linearity of the particular quantile function of interest and it requires no parametric assumptions on the regression error distributions finite sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional wolf villain model abstract although extensive analytical and numerical work has focus on investigating the 2 1 dimensional wolf villain wv model some problems concerning its asymptotical behaviors such as the universality class to which it belongs remain controversial the schramm loewner evolution sle theory is an attractive approach to describe the fluctuation phenomena and random processes and has also been applied to the analysis of the stochastic growth of surfaces in this work we applied sle theory to the analysis of the saturated surface to conduct in depth research with a new perspective on the asymptotical behaviors of the 2 1 dimensional wv model on the basis of the analysis of the saturated surface contour lines we determine that the diffusion coefficient calculated for 2 1 dimensional wv model is 2 91 0 01 and that for family model is 2 88 0 01 accordingly we can conclude from the view of sle theory that the 2 1 dimensional wv model similar to the family model also belongs to the edwards wilkinson universality class

on the distribution of surface extrema in several one and two dimensional random landscapes we study here a standard next nearest neighbor nnn model of ballistic growth on one and two dimensional substrates focusing our analysis on the probability distribution function p m l of the number m of maximal points i e local peaks of growing surfaces our analysis is based on two central results i the proof presented here of the fact that uniform one dimensional ballistic growth process in the steady state can be mapped onto rise and descent sequences in the ensemble of random permutation matrices and ii the fact established in ref g oshanin and r voituriez j phys a math gen 37 6221 2004 that different characteristics of rise and descent patterns in random permutations can be interpreted in terms of a certain continuous space hammersley type process for one dimensional system we compute p m l exactly and also present explicit results for the correlation function characterizing the enveloping surface for surfaces grown on 2d substrates we pursue similar approach considering the ensemble of permutation matrices with long ranged correlations determining exactly the first three cumulants of the corresponding distribution function we define it in the scaling limit using an expansion in the edgeworth series and show that it converges to a gaussian function as l

coarse grained approach for volume conserving models abstract volume conserving surface vcs models without deposition and evaporation as well as ideal molecular beam epitaxy models are prototypes to study the symmetries of conserved dynamics in this work we study two similar vcs models with conserved noise which differ from each other by the axial symmetry of their dynamic hopping rules we use a coarse grained approach to analyze the models and show how to determine the coefficients of their corresponding continuous stochastic differential equation sde within the same universality class the employed method makes use of small translations in a test space which contains the stationary probability density function spdf in case of the symmetric model we calculate all the coarse grained coefficients of the related conserved kardar parisi zhang kpz equation with respect to the symmetric model the asymmetric model adds new terms which have to be analyzed first of all the diffusion term whose coarse grained coefficient can be determined by the same method in contrast to other methods the used formalism allows to calculate all coefficients of the sde theoretically and within limits numerically above all the used approach connects the coefficients of the sde with the spdf and hence gives them a precise physical meaning