max norm optimization for robust matrix recovery this paper studies the matrix completion problem under arbitrary sampling schemes we propose a new estimator incorporating both max norm and nuclear norm regularization based on which we can conduct efficient low rank matrix recovery using a random subset of entries observed with additive noise under general non uniform and unknown sampling distributions this method significantly relaxes the uniform sampling assumption imposed for the widely used nuclear norm penalized approach and makes low rank matrix recovery feasible in more practical settings theoretically we prove that the proposed estimator achieves fast rates of convergence under different settings computationally we propose an alternating direction method of multipliers algorithm to efficiently compute the estimator which bridges a gap between theory and practice of machine learning methods with max norm regularization further we provide thorough numerical studies to evaluate the proposed method using both simulated and real datasets

a semiparametric regression cure model with current status data summary this paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event the semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable a sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed under some mild conditions the estimators are shown to be strongly consistent the convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed simulation studies were carried out to investigate the performance of the proposed method and the model is fitted to a dataset from a study of calcification of the hydrogel intraocular lenses a complication of cataract treatment

brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

approximate explicit constrained linear model predictive control via orthogonal search tree solutions to constrained linear model predictive control problems can be precomputed off line in an explicit form as a piecewise linear state feedback on a polyhedral partition of the state space avoiding real time optimization we suggest an algorithm that can determine an approximate explicit piecewise linear state feedback by imposing an orthogonal search tree structure on the partition this leads to a real time computational complexity that is logarithmic in the number of regions in the partition and the algorithm yields guarantees on the suboptimality asymptotic stability and constraint fulfillment

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

root n consistent semiparametric estimators of a dynamic panel sample selection model abstract this paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possibly predetermined variables lags of the dependent variables and unobserved individual effects the selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations we derive a set of conditional moment restrictions that are then exploited to construct a three step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term in the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of berkson s minimum chi square sieve method and a first step kernel estimator for the selection probability this second step estimator is of interest in its own right it can be used to semiparametrically estimate a panel data binary response model with a nonparametric individual specific effect without making any other distributional assumptions we show that both estimators second and third stage are n consistent and asymptotically normal

efron stein inequalities for random matrices this paper establishes new concentration inequalities for random matrices constructed from independent random variables these results are analogous with the generalized efron stein inequalities developed by boucheron et al the proofs rely on the method of exchangeable pairs

an alternative root n consistent estimator for panel data binary choice models in this paper we present an alternative root n consistent estimator for panel data fixed effects binary choice models the proposed estimator relaxes one of the key conditions that are required for the consistency of the estimator proposed in honore and lewbel 2002 and is shown to be consistent and asymptotically normally distributed under some sufficient conditions an easy to compute consistent estimator for the asymptotic covariance is provided

sampling from large matrices an approach through geometric functional analysis we study random submatrices of a large matrix a we show how to approximately compute a from its random submatrix of the smallest possible size o rlog r with a small error in the spectral norm where r e vav2f vav22 is the numerical rank of a the numerical rank is always bounded by and is a stable relaxation of the rank of a this yields an asymptotically optimal guarantee in an algorithm for computing low rank approximations of a we also prove asymptotically optimal estimates on the spectral norm and the cut norm of random submatrices of a the result for the cut norm yields a slight improvement on the best known sample complexity for an approximation algorithm for max 2csp problems we use methods of probability in banach spaces in particular the law of large numbers for operator valued random variables

sieve m inference on irregular parameters abstract this paper presents sieve inferences on possibly irregular i e slower than root n estimable functionals of semi nonparametric models with i i d data we provide a simple consistent variance estimator of the plug in sieve m estimator of a possibly irregular functional and the asymptotic standard normality of the sieve t statistic we show that for hypothesis testing of irregular functionals the sieve likelihood ratio statistic is asymptotically chi square distributed these results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds a simulation study and an empirical application of heckman and singer 1984 duration model are presented

a simpler approach to matrix completion this paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix these results improve on prior work by candes and recht 2009 candes and tao 2009 and keshavan et al 2009 the reconstruction is accomplished by minimizing the nuclear norm or sum of the singular values of the hidden matrix subject to agreement with the provided entries if the underlying matrix satisfies a certain incoherence condition then the number of entries required is equal to a quadratic logarithmic factor times the number of parameters in the singular value decomposition the proof of this assertion is short self contained and uses very elementary analysis the novel techniques herein are based on recent work in quantum information theory

regressions with berkson errors in covariates a nonparametric approach this paper establishes that so called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with berkson type measurement error in the regressors an estimator is proposed and proven to be consistent its practical performance and feasibility are investigated via monte carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health these examples illustrate that berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

an algorithm for robust explicit multi parametric model predictive control a new algorithm for robust explicit multi parametric model predictive control mpc for uncertain linear discrete time systems is proposed based on previous work on dynamic programming dp multi parametric programming and robust optimization the proposed algorithm features i a dp reformulations of the mpc optimization problem ii a robust reformulation of the constraints and iii a multi parametric programming step where the control variables are obtained as explicit functions of the state variable such that the state and input constraints are satisfied for all admissible values of the uncertainty a key feature of the proposed procedure is that as opposed to previous methods it only solves a convex multi parametric programming problem for each stage of the dp procedure

a central limit theorem under metric entropy with l_2 bracketing let mathbf s rho be a metric space mathbf v mathscr v mu be a probability space and f mathbf s times mathbf v rightarrow mathbb r be a real valued function on mathbf s times mathbf v which has mean zero and is lipschitz in l 2 mu with respect to rho let v be a random variable defined on mathbf v mathscr v mu and let v i i geq 1 be a sequence of independent copies of v the limiting behavior of the process s n s n 1 2 sum n i 1 f s v i is studied under an integrability condition on the metric entropy with bracketing in l 2 mu this metric entropy condition is analogous to one which implies the continuity of the limiting gaussian process a tightness result is derived which in conjunction with the results of andersen and dobric 1987 shows that a central limit theorem holds for the s n process this result generalizes those of dudley 1978 dudley 1981 and jain and marcus 1975

time dependent cross ratio estimation for bivariate failure times in the analysis of bivariate correlated failure time data it is important to measure the strength of association among the correlated failure times one commonly used measure is the cross ratio motivated by cox s partial likelihood idea we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is examined using simulation studies and it is applied to the australian twin data

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

concentration inequalities for matrix martingales in continuous time this paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time these results extend previously established freedman and bernstein inequalities for series of random matrices to the class of continuous time processes our analysis relies on a new supermartingale property of the trace exponential proved within the framework of stochastic calculus we provide also several examples that illustrate the fact that our results allow us to recover easily several formerly obtained sharp bounds for discrete time matrix martingales

convergence rate of sieve estimates in this paper we develop a general theory for the convergence rate of sieve estimates maximum likelihood estimates mle s and related estimates obtained by optimizing certain empirical criteria in general parameter spaces in many cases especially when the parameter space is infinite dimensional maximization over the whole parameter space is undesirable in such cases one has to perform maximization over an approximating space sieve of the original parameter space and allow the size of the approximating space to grow as the sample size increases this method is called the method of sieves in the case of the maximum likelihood estimation an mle based on a sieve is called a sieve mle we found that the convergence rate of a sieve estimate is governed by a the local expected values variances and l 2 entropy of the criterion differences and b the approximation error of the sieve a robust nonparametric regression problem a mixture problem and a nonparametric regression problem are discussed as illustrations of the theory we also found that when the underlying space is too large the estimate based on optimizing over the whole parameter space may not achieve the best possible rates of convergence whereas the sieve estimate typically does not suffer from this difficulty

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

feedback control of linear discrete time systems under state and control constraints in this paper the problem of stabilizing linear discrete time systems under state and control linear constraints is studied based on the concept of positive invariance existence conditions of linear state feedback control laws respecting both the constraints are established these conditions are then translated into an algorithm of linear programming

inference for a class of transformed hazards models a new class of transformed hazard rate models is considered that contains both the multiplicative hazards model and the additive hazards model as special cases the sieve maximum likelihood estimators are derived for the model parameters and the estimators for the regression coefficients are shown to be consistent and asymptotically normal with variance achieving the semiparametric efficiency bound simulation studies are conducted to examine the small sample properties of the proposed estimates and a real dataset is used to illustrate our approach

nonparametric identification and semiparametric estimation of classical measurement error models without side information virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information e g validation data known error distributions repeated measurements or instruments in contrast we establish that the fully nonparametric classical errors in variables model is identifiable from data on the regressor and the dependent variable alone unless the model takes a very specific parametric form this parametric family includes but is not limited to the linear specification with normally distributed variables as a well known special case this result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions our approach can handle both monotone and nonmonotone specifications provided the latter oscillate a finite number of times given that the very specific unidentified parametric functional form is arguably the exception rather than the rule this identification r

estimation of the binary response model using a mixture of distributions estimator mod abstract in this paper we develop a semiparametric sieve estimator which is termed a mixture of distributions estimator mod to estimate a binary response model when the distribution of the errors is unknown the estimator of the distribution function is composed of a mixture of smooth distributions where the number of mixtures increases with the sample size the model is semiparametric because it is assumed that a parametric index type restriction holds optimal rates of convergence are established for the distribution function under the l 2 norm and conditions are derived under which estimates of the parametric component are asymptotically normal an appealing feature about mod is that it is possible to restrict the estimator of the distribution function a priori to be smooth nonnegative nondecreasing and to integrate to one this has important practical and theoretical implications

efficient estimation of copula based semiparametric markov models this paper considers the efficient estimation of copula based semiparametric strictly stationary markov models these models are characterized by nonparametric invariant one dimensional marginal distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes the markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications we first show that markov processes generated via clayton gumbel and student s t copulas and their survival copulas are all geometrically ergodic we then propose a sieve maximum likelihood estimation mle for the copula parameter the invariant distribution and the conditional quantiles we show that the sieve mles of any smooth functional is root n consistent asymptotically normal and efficient and that their sieve likelihood ratio statistics are asymptotically chi square distributed monte carlo studies indicate that even for markov models generated via tail dependent copulas and fat tailed marginals our sieve mles perform very well

moment inequalities for sums of random matrices and their applications in optimization in this paper we consider various moment inequalities for sums of random matrices which are well studied in the functional analysis and probability theory literature and demonstrate how they can be used to obtain the best known performance guarantees for several problems in optimization first we show that the validity of a recent conjecture of nemirovski is actually a direct consequence of the so called non commutative khintchine s inequality in functional analysis using this result we show that an sdp based algorithm of nemirovski which is developed for solving a class of quadratic optimization problems with orthogonality constraints has a logarithmic approximation guarantee this improves upon the polynomial approximation guarantee established earlier by nemirovski furthermore we obtain improved safe tractable approximations of a certain class of chance constrained linear matrix inequalities secondly we consider a recent result of delage and ye on the so called data driven distributionally robust stochastic programming problem one of the assumptions in the delage ye result is that the underlying probability distribution has bounded support however using a suitable moment inequality we show that the result in fact holds for a much larger class of probability distributions given the close connection between the behavior of sums of random matrices and the theoretical properties of various optimization problems we expect that the moment inequalities discussed in this paper will find further applications in optimization

positively invariant polyhedral sets of discrete time linear systems the problem of the existence of positively invariant polyhedral sets for linear discrete time dynamical systems is studied in the first part of the paper necessary and sufficient conditions for a

implicit improved vertex control for uncertain time varying linear discrete time systems with state and control constraints the problem of regulating an uncertain and or time varying linear discrete time system with state and control constraints to the origin is addressed it is shown that feasibility and a robustly asymptotically stable closed loop can be achieved using an interpolation technique the design method can be seen as an alternative to optimization based control schemes such as robust model predictive control especially for problems requiring complex calculations to find the optimal solution the present method can provide a straightforward suboptimal solution a simulation demonstrates the performance of this class of constrained controllers

explicit robustness and fragility margins for linear discrete systems with piecewise affine control law in this paper we focus on the robustness and fragility problem for piecewise affine pwa control laws for discrete time linear system dynamics in the presence of parametric uncertainty of the state space model a generic geometrical approach will be used to obtain robustness fragility margins with respect to the positive invariance properties for pwa control laws defined over a bounded region in the state space it is shown that these margins can be described in terms of polyhedral sets in parameter space the methodology is further extended to the fragility problem with respect to the partition defining the controller finally several computational aspects are presented regarding the transformation from the theoretical formulations to explicit representations vertex halfspace representation of polytopes of these sets

construction of invariant polytopic sets with specified complexity the problem of construction of controlled invariant polytopic sets with specified complexity for linear systems subject to linear state and control constraints is investigated first geometric conditions for the enlargement of a polytopic set by adding a new vertex in order to produce a polytopic set of specified complexity are established next conditions for such an enlargement of controlled invariant sets to preserve the controlled invariance property are presented the established theoretical results are used to develop methods for the construction of admissible controlled invariant sets with specified complexity two numerical examples show how these results can be used for the computation of monotonic sequences of admissible controlled invariant sets of specified complexity

on maximum likelihood estimation in infinite dimensional parameter spaces an approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions in this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter we provide conditions under which the rate of convergence can be established this rate is essentially governed by the size of the space of score functions as measured by an entropy index we also show that for a large class of smooth functionals the plug in maximum likelihood estimate is asymptotically efficient that is it achieves the minimal fisher information bound the theory is illustrated by several nonparametric or semiparametric examples

restricted strong convexity and weighted matrix completion optimal bounds with noise we consider the matrix completion problem under a form of row column weighted entrywise sampling including the case of uniformentrywise sampling as a special case we analyze the associated random observation operator and prove that with high probability it satisfies a form of restricted strong convexity with respect to weighted frobenius norm using this property we obtain as corollaries a number of error bounds on matrix completion in the weighted frobenius norm under noisy sampling and for both exact and near low rank matrices our results are based on measures of the spikiness and low rankness of matrices that are less restrictive than the incoherence conditions imposed in previous work our technique involves an m estimator that includes controls on both the rank and spikiness of the solution and we establish non asymptotic error bounds in weighted frobenius norm for recovering matrices lying with lq balls of bounded spikiness using information theoretic methods we show that no algorithm can achieve better estimates up to a logarithmic factor over these same sets showing that our conditions on matrices and associated rates are essentially optimal

operator khintchine inequality in non commutative probability abstract for the operator t sum n k 1 a k otimes r k where a k belongs to the schatten class s 2n and where r k are non commutative random variables with mixed moments satisfying a specific condition we prove the following khintchine inequality vert t vert 2n leq d 2n left left vert left sum n k001 a ka k right frac 1 2 right vert s 2n quad quad left vert left sum n k 1 a k a k right frac 1 2 right vert s 2n right we find the optimal constants d 2n in the case when r k are the q gaussian and circular random variables moreover we show that the moments of any probability symmetric measure appear as the optimal constants for some random variables

a sieve m theorem for bundled parameters in semiparametric models with application to the efficient estimation in a linear model for censored data in many semiparametric models that are parameterized by two types of parameters a euclidean parameter of interest and an infinite dimensional nuisance parameter the two parameters are bundled together i e the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument for example in a linear regression model for censored survival data the unspecified error distribution function involves the regression coefficients motivated by developing an efficient estimating method for the regression parameters we propose a general sieve m theorem for bundled parameters and apply the theorem to deriving the asymptotic theory for the sieve maximum likelihood estimation in the linear regression model for censored survival data the numerical implementation of the proposed estimating method can be achieved through the conventional gradient based search algorithms such as the newton raphson algorithm we show that the proposed estimator is consistent and asymptotically normal and achieves the semiparametric efficiency bound simulation studies demonstrate that the proposed method performs well in practical settings and yields more efficient estimates than existing estimating equation based methods illustration with a real data example is also provided

proportional odds regression and sieve maximum likelihood estimation summary this paper introduces under a censoring mechanism an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method the procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative kullback leibler risk to select the best approximation the procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree the proposed procedure is implemented for right censored and so called case 2 interval censored data the estimated regression parameters are shown to be asymptotically normal and efficient the small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients

sieve maximum likelihood estimation of the spatial autoregressive tobit model abstract this paper extends the ml estimation of a spatial autoregressive tobit model under normal disturbances in xu and lee 2015b journal of econometrics to distribution free estimation we examine the sieve mle of the model where the disturbances are i i d with an unknown distribution we show that the spatial autoregressive process with tobit censoring and related variables are spatial near epoch dependent ned a related contribution is that we develop some exponential inequalities for spatial ned random fields with these inequalities we establish the consistency of the estimator asymptotic distributions of structural parameters of the model are derived from a functional central limit theorem and projection simulations show that the sieve mle can improve the finite sample performance upon misspecified normal mles as an empirical application we examine the school district income surtax rates in iowa our results show that the spatial spillover effects are significant but they may be overestimated if disturbances are restricted to be normally distributed

distribution of singular values of random band matrices marchenko pastur law and more we consider the limiting spectral distribution of matrices of the form frac 1 2b n 1 r x r x where x is an n times n band matrix of bandwidth b n and r is a non random band matrix of bandwidth b n we show that the stieltjes transform of esd of such matrices converges to the stieltjes transform of a non random measure and the limiting stieltjes transform satisfies an integral equation for r 0 the integral equation yields the stieltjes transform of the marchenko pastur law

case cohort studies with interval censored failure time data the case cohort design has been widely used as a means of cost reduction in assembling or measuring expensive covariates in large cohort studies the existing literature on the case cohort design is mainly focused on right censored data in practice however the failure time is often subject to interval censoring it is known only to fall within some random time interval in this paper we consider the case cohort study design for interval censored failure time and develop a sieve semiparametric likelihood approach for analyzing data from this design under the proportional hazards model we construct the likelihood function using inverse probability weighting and build the sieves with bernstein polynomials the consistency and asymptotic normality of the resulting regression parameter estimator are established and a weighted bootstrap procedure is considered for variance estimation simulations show that the proposed method works well for practical situations and an application to real data is provided

matrix concentration inequalities via the method of exchangeable pairs this paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix the analysis requires a matrix extension of the scalar concentration theory developed by sourav chatterjee using stein s method of exchangeable pairs when applied to a sum of independent random matrices this approach yields matrix generalizations of the classical inequalities due to hoeffding bernstein khintchine and rosenthal the same technique delivers bounds for sums of dependent random matrices and more general matrix valued functions of dependent random variables

well posedness of measurement error models for self reported data a b s t r a c t this paper considers the widely admitted ill posed inverse problem for measurement error models estimating the distribution of a latent variable x from an observed sample of x a contaminated measurement of x we show that the inverse problem is well posed for self reporting data under the assumption that the probability of truthful reporting is nonzero which is supported by empirical evidences comparing with ill posedness well posedness generally can be translated into faster rates of convergence for the nonparametric estimators of the latent distribution therefore our optimistic result on well posedness is of importance in economic applications and it suggests that researchers should not ignore the point mass at zero in the measurement error distribution when they model measurement errors with self reported data we also analyze the implications of our results on the estimation of classical measurement error models then by both a monte carlo study and an empirical application we show that failing to account for the nonzero probability of truthful reporting can lead to significant bias on estimation of the latent distribution

distribution free estimation of heteroskedastic binary response models using probit logit criterion functions abstract in this paper estimators for distribution free heteroskedastic binary response models are proposed the estimation procedures are based on relationships between distribution free models with a conditional median restriction and parametric models such as probit logit exhibiting multiplicative heteroskedasticity the first proposed estimator is based on the observational equivalence between the two models and is a semiparametric sieve estimator see e g gallant and nychka 1987 ai and chen 2003 and chen et al 2005 for the regression coefficients based on maximizing standard logit probit criterion functions such as nlls and mle this procedure has the advantage that choice probabilities and regression coefficients are estimated simultaneously the second proposed procedure is based on the equivalence between existing semiparametric estimators for the conditional median model manski 1975 manski 1985 horowitz 1992 and the standard parametric probit logit nlls estimator this estimator has the advantage of being implementable with standard software packages such as stata distribution theory is developed for both estimators and a monte carlo study indicates they both perform well in finite samples

noncommutative burkholder rosenthal inequalities we investigate martingale inequalities in noncommutative lp spaces associated with a von neumann algebra equipped with a faithful normal state we prove the noncommutative analogue of the classical burkholder inequality on the conditioned or little square function and extend the noncommutative burkholder gundy inequalities from comm math phys 189 1997 667 698 to this nontracial setting we include several related results

matrix poincare inequalities and concentration abstract we show that any probability measure satisfying a matrix poincare inequality with respect to some reversible markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carre du champ operator this extends to the matrix setting a classical phenomenon in the scalar case moreover the proof gives rise to new matrix trace inequalities which could be of independent interest we then apply this general fact by establishing matrix poincare inequalities to derive matrix concentration inequalities for gaussian measures product measures and for strong rayleigh measures the latter represents the first instance of matrix concentration for general matrix functions of negatively dependent random variables

semi nonparametric estimation of independently and identically repeated first price auctions via an integrated simulated moments method abstract in this paper we propose to estimate the value distribution of independently and identically repeated first price auctions directly via a semi nonparametric integrated simulated moments sieve approach given a candidate value distribution function in a sieve space we simulate bids according to the equilibrium bid function involved we take the difference of the empirical characteristic functions of the actual and simulated bids as the moment function the objective function is then the integral of the squared moment function over an interval minimizing this integral to the distribution functions in the sieve space involved and letting the sieve order increase to infinity with the sample size then yields a uniformly consistent semi nonparametric estimator of the actual value distribution also we propose an integrated moment test for the validity of the first price auction model and an data driven method for the choice of the sieve order finally we conduct a few numerical experiments to check the performance of our approach

brief an algorithm for multi parametric quadratic programming and explicit mpc solutions explicit solutions to constrained linear model predictive control problems can be obtained by solving multi parametric quadratic programs mp qp where the parameters are the components of the state vector we study the properties of the polyhedral partition of the state space induced by the multi parametric piecewise affine solution and propose a new mp qp solver compared to existing algorithms our approach adopts a different exploration strategy for subdividing the parameter space avoiding unnecessary partitioning and qp problem solving with a significant improvement of efficiency

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

profile likelihood and conditionally parametric models in this paper we outline a general approach to estimating the parametric component of a semiparametric model for the case of a scalar parametric component the method is based on the idea of first estimating a one dimensional subproblem of the original problem that is least favorable in the sense of stein the likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem the scalar parameter is then estimated by maximizing this generalized profile likelihood this method of estimation is applied to a particular class of semiparametric models where it is shown that the resulting estimator is asymptotically efficient

on efficient estimation of the ordered response model in this paper we derive efficiency bounds for the ordered response model when the distribution of the errors is unknown furthermore we develop an estimator that is efficient under suitable conditions interestingly neither the bounds nor the estimator are trivial extensions of what has been proposed in the literature for the binary response model the estimator is composed of quadratic b splines and estimation is performed by the method of sieves in addition the estimator of the distribution function is restricted to be a proper distribution function an empirical example on the effect of fees on attendance rates at universities and community colleges is also included we get substantively different results by relaxing the assumption that the distribution of the errors is normal

random vectors in the isotropic position abstract letybe a random vector in r n satisfying e y y id letmbe a natural number and lety1 ymbe independent copies ofy we study the question of approximation of the identity operator by finite sums of the tensorsyi yi we prove that for some absolute constantc e 1 m i 1 m y i y i id c log n m e y log m 1 log m provided that the last expression is smaller than 1 we apply this estimate to improve a result of bourgain concerning the number of random points needed to bring a convex body into a nearly isotropic position

efficient estimation and computation of parameters and nonparametric functions in generalized semi non parametric regression models abstract the efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature bickel et al 1993 in this paper we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi non parametric regression models which cover commonly used semiparametric models such as partially linear models partially linear single index models and two sample semiparametric models we propose a maximum likelihood principle combined with the local linear technique for estimating the parameters and nonparametric functions the proposed estimators of the parameters and a linear functional of the nonparametric functions are consistent and asymptotically normal and are further shown to be semiparametrically efficient an efficient computational algorithm to achieve the maximization is proposed extensive simulation experiments show the superiority of the proposed methods three real data examples are analyzed and presented as an illustration

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

strong converse for identification via quantum channels we present a simple proof of the strong converse for identification via discrete memoryless quantum channels based on a novel covering lemma the new method is a generalization to quantum communication channels of ahlswede s 1979 1992 approach to classical channels it involves a development of explicit large deviation estimates to the case of random variables taking values in self adjoint operators on a hilbert space this theory is presented separately in an appendix and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems

sieve maximum likelihood estimator for semiparametric regression models with current status data in a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event it is often too expensive or even impossible to observe the exact time however the current status of the subject at a random time of inspection is much more natural feasible and practical in terms of cost effectiveness this article considers a semiparametric regression model that consists of parametric and nonparametric regression components a sieve maximum likelihood estimator mle is proposed to estimate the regression parameter allowing exploration of the nonlinear relationship between a certain covariate and the response function asymptotic properties of the proposed sieve mles are discussed under some mild conditions the estimators are shown to be strongly consistent moreover the estimators of the unknown parameters are asymptotically efficient and normally distributed and the estimator of the nonparametric function has an optimal convergence rate simula

efficient shrinkage in parametric models this paper introduces shrinkage for general parametric models we show how to shrink maximum likelihood estimators towards parameter subspaces de ned by general nonlinear restrictions we derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework we show that if the shrinkage dimension exceeds two the asymptotic risk of the shrinkage estimator is strictly less than that of the mle this reduction holds globally in the parameter space we show that the reduction in asymptotic risk is substantial even for moderately large values of the parameters the formula simplify in a very convenient way in the context of high dimensional models we derive a simple bound for the asymptotic risk we also provide a new large sample minimax e ciency bound we use the concept of local asymptotic minimax bounds a generalization of the conventional asymptotic minimax bounds the

on methods of sieves and penalization we develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates mle s in parametric semiparametric and nonparametric models we find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices the degree of smoothness of the functional and the local size of the underlying parameter space we show that when the local size of the parameter space is not very large the substitution standard nonsieve substitution sieve and substitution penalized mle s are asymptotically efficient in the fisher sense under certain stochastic equicontinuity conditions of the loglikelihood moreover when the convergence rate of the estimate is slow the degree of smoothness of the functional needs to compensate for the slowness of the rate in order to achieve efficiency when the size of the parameter space is very large the standard and penalized maximum likelihood procedures may be inefficient whereas the method of sieves may be able to overcome this difficulty this phenomenon is particularly manifested when the functional of interest is very smooth especially in the semiparametric case

lsv based tail inequalities for sums of random matrices the techniques of random matrices have played an important role in many machine learning models in this letter we present a new method to study the tail inequalities for sums of random matrices different from other work ahlswede winter 2002 tropp 2012 hsu kakade zhang 2012 our tail results are based on the largest singular value lsv and independent of the matrix dimension since the lsv operation and the expectation are noncommutative we introduce a diagonalization method to convert the lsv operation into the trace operation of an infinitely dimensional diagonal matrix in this way we obtain another version of laplace transform bounds and then achieve the lsv based tail inequalities for sums of random matrices

optimum bounds for the distributions of martingales in banach spaces a general device is proposed which provides for extension of exponential inequalities for sums of independent real valued random variables to those for martingales in the 2 smooth banach spaces this is used to obtain optimum bounds of the rosenthal burkholder and chung types on moments of the martingales in 2 smooth banach spaces in turn it leads to best order bounds on moments of sums of independent random vectors in any separable banach spaces although the emphasis is put on infinite dimensional martingales most of the results seem to be new even for one dimensional martingales moreover the bounds on moments of the rosenthal burkholder type seem to be to a certain extent new even for sums of independent real valued random variables analogous inequalities for one dimensional supermartingales are given

matrix infinitely divisible series tail inequalities and their applications in this paper we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible i d series which is a finite sum of fixed matrices weighted by i d random variables we obtain several types of tail inequalities including bennett type and bernstein type inequalities this allows us to further bound the expectation of the spectral norm of a matrix i d series moreover by developing a new lower bound function for q s s 1 log s 1 s that appears in the bennett type inequality we derive a tighter tail inequality of the largest eigenvalue of the matrix i d series than the bernstein type inequality when the matrix dimension is high the resulting lower bound function is of independent interest and can improve any bennett type concentration inequality that involves the function q s the class of i d probability distributions is large and includes gaussian and poisson distributions among many others therefore our results encompass the existing work on matrix gaussian series as a special case lastly we show that the tail inequalities of a matrix i d series have applications in several optimization problems including the chance constrained optimization problem and the quadratic optimization problem with orthogonality constraints in addition we also use the resulting tail bounds to show that random matrices constructed from i d random variables satisfy the restricted isometry property rip when it acts as a measurement matrix in compressed sensing

non commutative martingale inequalities we prove the analogue of the classical burkholder gundy inequalites for non commutative martingales as applications we give a characterization for an ito clifford integral to be an lp martingale via its integrand and then extend the ito clifford integral theory in l2 developed by barnett streater and wilde to lp for all 1 p we include an appendix on the non commutative analogue of the classical fefferman duality between h1 and bmo

random sieve likelihood and general regression models abstract consider a semiparametric regression model y f x where f is a known function is an unknown vector consists of a random error and possibly of some unobserved variables and the distribution f of x is unspecified this article introduces in a general setting new methodology for estimating and f the proposed method constructs a profile likelihood defined on random level sets a random sieve the proposed method is related to empirical likelihood but is more generally applicable four examples are discussed including a quadratic model high dimensional semiparametric regression a nonparametric random effects model and linear regression with right censored data simulation results and asymptotic analysis support the utility and effectiveness of the proposed method

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

a sieve semiparametric maximum likelihood approach for regression analysis of bivariate interval censored failure time data abstractinterval censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis however most of the existing methods are for univariate data and there exists only limited research on bivariate data especially on regression analysis of bivariate interval censored data we present a class of semiparametric transformation models for the problem and for inference a sieve maximum likelihood approach is developed the model provides a great flexibility in particular including the commonly used proportional hazards model as a special case and in the approach bernstein polynomials are employed the strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore the estimators are shown to be asymptotically efficient extensive simulation studies are conducted and indicate that the proposed method works well for practical situations supplementary materials for this article are

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

stein s method for concentration inequalities we introduce a version of stein s method for proving concentration and moment inequalities in problems with dependence simple illustrative examples from combinatorics physics and mathematical statistics are provided