lower bounds of the topological entropy of maps of y abstract we give the best lower bound of the topological entropy of a continuous map of the space y z c z 3 0 1 into itself with 0 0 as a function of its set of periods

the filtering problem for continuous time linear systems with markovian switching coefficients abstract the stochastic model under consideration is a markovian jump process with finite state space feeding the parameters of a linear diffusion process x the processes y and z observe linearly and separately x and in independent white noises some properties of the finite optimal filter for the x and processes given the history of measurements z are investigated apart from their theoretical interest these results have an interesting practical bearing on the general filtering problem by providing a natural finite suboptimal solution preliminary experimental results show the effectiveness of our approach to estimate the state trajectory even with a relatively low signal to noise ratio on the measurement processes

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

maximal versus strong solution to algebraic riccati equations arising in infinite markov jump linear systems abstract we deal with a perturbed algebraic riccati equation in an infinite dimensional banach space which appears for instance in the optimal control problem for infinite markov jump linear systems from now on imjls infinite or finite here has to do with the state space of the markov chain being infinite countable or finite see e g m d fragoso j baczynski optimal control for continuous time lq problems with infinite markov jump parameters siam j control optim 40 1 2001 270 297 by using a certain concept of stochastic stability a sort of l 2 stability we have proved in j baczynski m d fragoso maximal solution to algebraic riccati equations linked to infinite markov jump linear systems internal report lncc no 6 2006 existence and uniqueness of maximal solution for this class of equations as it is noticed in this paper unlike the finite case including the linear case we cannot guarantee anymore that maximal solution is a strong solution in this setting via a discussion on the main mathematical hindrance behind this issue we devise some mild conditions for this implication to hold specifically our main result here is that under stochastic stability along with a condition related with convergence in the infinite dimensional scenario and another one related to spectrum weaker than spectral continuity we ensure the maximal solution to be also a strong solution these conditions hold trivially in the finite case allowing us to recover the result of strong solution of c e de souza m d fragoso on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control systems control lett 14 1990 233 239 set for mjls the issue of whether the convergence condition is restrictive or not is brought to light and together with some counterexamples unveil further differences between the finite and the infinite countable case

a semiparametric single index model with heterogeneous impacts on an unobserved variable this paper proposes a single index semiparametric model in which the unknown function has cross sectional unit specific weights the initial motivation comes from the search for a better measure of liquidity in stock trading which is captured by the unknown function here the model is estimated by semiparametric least squares developed by ichimura 1993 and ichimura and lee 1991 the proposed technique differs from theirs in at least two aspects first i show that the estimator has desirable asymptotic properties under less restrictive assumptions on data second the form of the unknown function is fixed however the coefficients are allowed to differ across the cross sectional units

optimal control for infinite dimensional stochastic differential equations with infinite markov jumps and multiplicative noise abstract in this paper we solve an infinite horizon linear quadratic control problem for a class of differential equations with countably infinite markov jumps and multiplicative noise the global solvability of the associated differential riccati type equations is studied under detectability hypotheses a nonstochastic operatorial approach is used some properties of the linear stochastic systems such as stability stabilizability and detectability are also discussed on the basis of a new solution representation result a generalized ito s formula which applies to infinite dimensional stochastic differential equations with countably infinite markov jumps is also provided

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

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

pseudo maximum likelihood estimation in two classes of semiparametric diffusion models abstract two classes of semiparametric diffusion models are considered where either the drift or the diffusion term is parameterized while the other term is left unspecified we propose a pseudo maximum likelihood estimator pmle of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in it is demonstrated how models and estimators can be used in a two step specification testing strategy of semiparametric and fully parametric models and shown that approximate simulated versions of the pmle inherit the properties of the actual but infeasible estimator a simulation study investigates the finite sample performance of the pmle

some remarks on the riccati equation arising in an optimal control problem with state and control dependent noise this paper solves a quadratic optimal control for a linear stochastic evolution equation with unbounded coefficients it is assumed that the stochastic noise depends both on the state and on the control the dynamic programming approach is used and attention is focused on the riccati equation in 5 and 6 some attractivity and maximality properties of the solutions of the algebraic riccati equation are proved and it is shown that in some special cases there exists a maximal solution

lyapunov coupled equations for continuous time infinite markov jump linear systems this paper deals with lyapunov equations for continuous time markov jump linear systems mjls out of the bent which wends most of the literature on mjls we focus here on the case in which the markov chain has a countably infinite state space it is shown that the infinite mjls is stochastically stabilizable ss if and only if the associated countably infinite coupled lyapunov equations have a unique norm bounded strictly positive solution it is worth mentioning here that this result do not hold for mean square stabilizability mss since ss and mss are no longer equivalent in our set up see e g j baczynski optimal control for continuous time lq problems with infinite markov jump parameters ph d thesis federal university of rio de janeiro ufrj coppe 2000 to some extent a decomplexification technique and tools from operator theory in banach space and in particular from semigroup theory are the very technical underpinning of the paper

infinite markov jump bounded real lemma abstract a bounded real lemma is established providing an equivalent condition to stochastic stability ss of a continuous time infinite markovian jump linear system mjls with a prescribed l 2 stochastic disturbance attenuation level in terms of existence of solutions to an infinite set of coupled linear matrix inequalities lmis besides the interest in its own right the main result provides a fundamental tool for the development of an h like theory devoted to this class of systems

on an infinite dimensional perturbed riccati differential equation arising in stochastic control existence and uniqueness of solutions for a class of infinite dimensional perturbed riccati differential equations in a certain banach space is our main concern in this paper besides the interest in its own right this class arises in control problems involving linear systems with countably infinite markov jump parameters

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

characterization of the asymptotic distribution of semiparametric m estimators this paper develops a concrete formula for the asymptotic distribution of two step possibly non smooth semiparametric m estimators under general misspecification our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature the first stage nonparametric estimation may depend on finite dimensional parameters we characterize 1 conditions under which the first stage estimation of nonparametric components do not affect the asymptotic distribution 2 conditions under which the asymptotic distribution is affected by the derivatives of the first stage nonparametric estimator with respect to the finite dimensional parameters and 3 conditions under which one can allow non smooth objective functions our framework is illustrated by applying it to three examples 1 profiled estimation of a single index quantile regression model 2 semiparametric least squares estimation under model misspecification and 3 a smoothed matching estimator 2010 elsevier b v all rights reserved

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

electric load model synthesis by diffusion approximation of a high order hybrid state stochastic system a statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners the importance of such loads is twofold first they account for a significant portion of power system dynamics following a power outage second because they are associated with energy storage they are often selected for load shedding within a load management program the derivation of the aggregate electrical dynamics is considered first for a homogeneous group of devices subsequently a perturbation analysis yields the dynamics for a nonhomogeneous group the homogeneons group aggregrate load model is a system of coupled ordinary and partial differential equations fokker planck equations it is obtained by writing evolution equations for the probability density of a hybrid state markov system used to model the switching dynamics of individual devices this result is new and could give a clue to the analysis of a broad class of hybrid state stochastic systems in turn this could provide a new impetus not only in the area of electric load modeling but other areas such as power system reliability and the design of relay control systems where stochastic hybrid state models occur frequently simulation results which illustrate the dynamical properties of the model are presented

penalized spline estimation for partially linear single index models single index models are potentially important tools for multivariate nonparametric regression they generalize linear regression by replacing the linear combination 0tx with a nonparametric component 0 0tx where 0 is an unknown univariate link function by reducing the dimensionality from that of a general covariate vector x to a univariate index 0tx single index models avoid the so called curse of dimensionality we propose penalized spline p spline estimation of 0 in partially linear single index models where the mean function has the form 0 0tx 0tz the p spline approach offers a number of advantages over other fitting methods for single index models all parameters in the p spline single index model can be estimated simultaneously by penalized nonlinear least squares as a direct least squares fitting method our approach is rapid and computationally stable standard nonlinear least squares software can be used moreover joint inference for 0 0 and 0 is possible by

estimation of marginal effects in semiparametric selection models with binary outcomes this paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting we focus on developing an estimator for the marginal effects this marginal effect estimator uses only observations where the selection probability is above a certain threshold a key innovation is that this high probability set is adaptive to the data we establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends monte carlo studies show that these estimators perform well in finite samples

on single index coefficient regression models abstract in this article we investigate a class of single index coefficient regression models under dependence this includes many existing models such as the smooth transition threshold autoregressive star model of chan and tong the functional coefficient autoregressive far model of chen and tsay and the single index model of ichimura compared to the varying coefficient model of hastie and tibshirani our model can avoid the curse of dimensionality in multivariate nonparametric estimations another advantage of this model is that a threshold variable is chosen automatically an estimation method is proposed and the corresponding estimators are shown to be consistent and asymptotically normal some simulations and applications are also reported

a proportional likelihood ratio model we propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate this model extends the generalized linear model by leaving the distribution unspecified and has a strong connection with semiparametric models such as the selection bias model gilbert et al 1999 the density ratio model qin 1998 fokianos kaimi 2006 the single index model ichimura 1993 and the exponential tilt regression model rathouz gao 2009 a maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived an example and simulation study illustrate the use of the model copyright 2012 oxford university press

rates of convergence for estimating regression coefficients in heteroskedastic discrete response models abstract in this paper we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term it is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction the semiparametric information bound is zero even when the homoskedastic error term is parametrically specified hence it is impossible to attain the parametric convergence rate for the parameters of interest however for ordered response models where the response variable can take at least three different values the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption two estimation procedures are proposed the first estimator based on a parametric restriction on the homoskedastic component of the error term is a two step maximum likelihood estimators where the unknown scale function is estimated nonparametrically in the first stage the second procedure which does not require the parametric restriction estimates the parameters by a kernel weighted least squares procedure under regularity conditions which are standard in the literature both estimators are shown to be n consistent and asymptotically normal

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

generalized partially linear single index model for zero inflated count data count data often arise in biomedical studies while there could be a special feature with excessive zeros in the observed counts the zero inflated poisson model provides a natural approach to accounting for the excessive zero counts in the semiparametric framework we propose a generalized partially linear single index model for the mean of the poisson component the probability of zero or both we develop the estimation and inference procedure via a profile maximum likelihood method under some mild conditions we establish the asymptotic properties of the profile likelihood estimators the finite sample performance of the proposed method is demonstrated by simulation studies and the new model is illustrated with a medical care dataset

a model free test for reduced rank in multivariate regression we propose a test of dimension in multivariate regression this test is in the spirit of tests on the rank of the coefficient matrix in a multivariate linear model but it does not require a prespecified model the test may be particularly useful at the outset of an analysis before a multivariate model is posited because it can lead to low dimensional summary plots that are inferred to contain all of the sample information on the multivariate mean function

semiparametric gee analysis in partially linear single index models for longitudinal data in this article we study a partially linear single index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases a semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations gee is introduced to estimate the two parameter vectors as well as the unknown link function under some mild conditions we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios from which we find that the convergence rates and asymptotic variances of the proposed estimators for sparse longitudinal data would be substantially different from those for dense longitudinal data we also discuss the estimation of the covariance or weight matrices involved in the semiparametric gee method furthermore we provide some numerical studies including monte carlo simulation and an empirical application to illustrate our methodology and theory

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

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

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

jump linear quadratic gaussian control in continuous time the optimal quadratic control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes is addressed the systems are also subject to gaussian input and measurement noise the optimal solution for the jump linear quadratic gaussian jlqc problem is given this solution is based on a separation theorem the optimal state estimator is sample path dependent if the plant parameters are constant in each value of the underlying jumping process then the controller portion of the compensator converges to a time invariant control law however the filter portion of the optimal infinite time horizon jlqc compensator is not time invariant thus a suboptimal filter which does converge to a steady state solution under certain conditions is derived and a time invariant compensator is obtained

rate optimal estimation for a general class of nonparametric regression models with unknown link functions this paper discusses a nonparametric regression model that naturally generalizes neural network models the model is based on a finite number of one dimensional transformations and can be estimated with a one dimensional rate of convergence the model contains the generalized additive model with unknown link function as a special case for this case it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion