persistence filter based control for systems with time varying control gains the paper addresses the generic problem of devising stabilizing control laws for systems with time varying control gains and unstable drift terms specifically a large class of single input linear control affine systems are considered wherein the control gains coefficients can become singular at certain instants in time or stay singular for large time intervals thus amounting to pointwise in time loss of controllability the time varying components of the control gains are assumed to be sufficiently smooth and possess certain structure expressed in terms of persistent excitation conditions a novel persistence filter construction is developed which helps achieve stabilization objectives some preliminary results on bounded trajectory tracking are also provided

parameter expansion to accelerate em the px em algorithm summary the em algorithm and its extensions are popular tools for modal estimation but ar e often criticised for their slow convergence we propose a new method that can often make em much faster the intuitive idea is to use a covariance adjustment to correct the analysis of the m step capitalising on extra information captured in the imputed complete data the way we accomplish this is by parameter expansion we expand the complete data model while preserving the observed data model and use the expanded complete data model to generate em this parameter expanded ei m px em algorithm shares the simplicity and stability of ordinary em but has a faster rate of convergence since its m step performs a more efficient analysis the px em algorithm is illustrated for the multivariate t distribution a random effects model factor analysis probit regression and a poisson imaging model

a jammer s perspective of reachability and lq optimal control this article treats two problems dealing with control of linear systems in the presence of a jammer that can sporadically turn off the control signal the first problem treats the standard reachability problem and the second treats the standard linear quadratic regulator problem under the above class of jamming signals we provide necessary and sufficient conditions for optimality based on a nonsmooth pontryagin maximum principle

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

correlated probit analysis of repeatedly measured ordinal and continuous outcomes with application to the health and retirement study the health and retirement study was designed to evaluate changes in health and labor force participation during and after the transition from working to retirement every 2 years participants provided information about their self rated health srh body mass index bmi smoking status and other characteristics our goal was to assess the effects of smoking and gender on trajectories of change in bmi and srh over time joint longitudinal analysis of outcome measures is preferable to separate analyses because it allows to account for the correlation between the measures to test the effects of predictors while controlling type i error and potentially to improve efficiency however because srh is an ordinal measure while bmi is continuous formulating a joint model and parameter estimation is challenging a joint correlated probit model allowed us to seamlessly account for the correlations between the measures over time established estimating procedures for such models are based on quasi likelihood or numerical approximations that may be biased or fail to converge therefore we proposed a novel expectation maximization algorithm for parameter estimation and a monte carlo bootstrap approach for standard errors approximation expectation maximization algorithms have been previously considered for combinations of binary and or continuous repeated measures however modifications were needed to handle combinations of ordinal and continuous responses a simulation study demonstrated that the algorithm converged and provided approximately unbiased estimates with sufficiently large sample sizes in the health and retirement study male gender and smoking were independently associated with steeper deterioration in self rated health and with lower average bmi copyright 2016 john wiley sons ltd

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

limited information estimators and exogeneity tests for simultaneous probit models a two step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators conditions under which each estimator attains the cramer rao lower bound are obtained simple tests for exogeneity based on the new two step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator finite sample comparisons between the new and alternative estimators are presented based on some monte carlo evidence the performance of the proposed tests for exogeneity is also assessed

augmented lagrangian approach to design of structured optimal state feedback gains we consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers these constraints are in the form of sparsity requirements for the feedback matrix implying that each controller has access to information from only a limited number of subsystems the minimizer of this constrained optimal control problem is sought using the augmented lagrangian method notably this approach does not require a stabilizing structured gain to initialize the optimization algorithm motivated by the structure of the necessary conditions for optimality of the augmented lagrangian we develop an alternating descent method to determine the structured optimal gain we also utilize the sensitivity interpretation of the lagrange multiplier to identify favorable communication architectures for structured optimal design examples are provided to illustrate the effectiveness of the developed method

bartlett adjustment of empirical discrepancy statistics summary we introduce two classes of empirical discrepancy statistics that extend empirical likelihood and establish simple conditions under which they admit bartlett adjustment

stabilization of two dimensional persistently excited linear control systems with arbitrary rate of convergence we consider the control system dot x a x alpha t b u where the pair a b is controllable x in mathbb r 2 u is a scalar control and the unknown signal alpha satisfies a persistent excitation condition we study the stabilization of this system and we prove that it is globally asymptotically stable with arbitrarily large exponential rate uniformly with respect to all signals satisfying a common persistent excitation condition and a common lipschitz continuity bound

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

value function in maximum hands off control for linear systems in this brief paper we study the value function in maximum hands off control maximum hands off control also known as sparse control is the l 0 optimal control among the feasible controls although the l 0 measure is discontinuous and non convex we prove that the value function or the minimum l 0 norm of the control is a continuous and strictly convex function of the initial state in the reachable set under an assumption on the controlled plant model we then extend the finite horizon maximum hands off control to model predictive control mpc and prove the recursive feasibility and the stability by using the continuity and convexity properties of the value function

partially generalized least squares and two stage least squares estimators abstract a class of partially generalized least squares estimators and a class of partially generalized two stage least squares estimators in regression models with heteroscedastic errors are proposed by using these estimators a researcher can attain higher efficiency than that attained by the least squares or the two stage least squares estimators without explicitly estimating each component of the heteroscedastic variances however the efficiency is not as high as that of the generalized least squares or the generalized two stage least squares estimator calculated using the knowledge of the true variances hence the use of the term partial

a correlated probit model for joint modeling of clustered binary and continuous responses a difficulty in joint modeling of continuous and discrete response variables is the lack of a natural multivariate distribution for joint modeling of clustered observations on binary and continuous responses we study a correlated probit model that has an underlying normal latent variable for the binary responses catalano and ryan have factored the model into a marginal and a conditional component and used generalized estimating equations methodology to estimate the effects we propose a monte carlo expectation conditional maximization algorithm for finding maximum likelihood estimates of the mixed model itself extending and accelerating an algorithm for models with binary responses we demonstrate the methodology with a developmental toxicity study measuring fetal weight and a binary malformation status for several litters of mice a simulation study suggests that efficiency gains of joint fittings over separate fittings of the response variables occur mainly for small datasets with strong correlation

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

the stochastic difference between econometric statistics dans un contexte general et dans divers cas particuliers on calcule l ordre en probabilite de la difference entre des racines consistantes d equations d estimation rivales

maximum likelihood estimation for probit linear mixed models with correlated random effects the probit normal model for binary data mcculloch 1994 journal of the american statistical association 89 330 335 is extended to allow correlated random effects to obtain maximum likelihood estimates we use the em algorithm with its m step greatly simplified under the assumption of a probit link and its e step made feasible by gibbs sampling standard errors are calculated by inverting a monte carlo approximation of the information matrix rather than via the sem algorithm a method is also suggested that accounts for the monte carlo variation explicitly as an illustration we present a new analysis of the famous salamander mating data unlike previous analyses we find it necessary to introduce different variance components for different species of animals finally we consider models with correlated errors as well as correlated random effects

extensions of estimation methods using the em algorithm abstract the em algorithm described by dempster laid and rubin 1977 is reviewed with the purpose of clarifying several misconceptions in the statistical and econometric literature the clarifications lead to several applications of the algorithm to models that have appeared to be less tractable the relationship between the em algorithm and the method of scoring is also explained providing estimators of the score and the information from the em algorithm the em algorithm is extended to missing data problems and an estimation method based on simulations

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

on the covariance structure of earnings and hours changes this paper presents an empirical analysis of individual earnings and hours data from three different longitudinal surveys in the first part of the paper we catalog the main features of the covariance structure of earnings and hours changes we find that this structure is very similar across data sets and may be adequately summarized by a simple components of variance model in the second part of the paper we offer an interpretation of this model in terms of a simple life cycle labor supply model

bivariate modelling of clustered continuous and ordered categorical outcomes simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution the approach is then extended to allow for clustering of the bivariate outcomes the model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome this factorization suggests convenient parameter estimation using estimating equations foetal weight and malformation data from a developmental toxicity experiment illustrate the results

likelihood inference in a correlated probit regression model correlated binary observations arise in a variety of applications for example in animal studies the term litter effect is used to describe the greater alikeness of responses within a litter as compared to that between litters at a given set of experimental conditions in a setting that motivated this work cells on individual atomic bomb survivors were scored as to the presence or absence of chromosomal aberrations the number of aberrant cells varied among subjects at a specified radiation exposure estimate age at exposure city of exposure and sex in a manner that substantially exceeds that consistent with a binomial error structure otake prentice 1984 this extra binomial variation or overdispersion reflects the fact that the binary response of cells from a given survivor tend to be more alike than are the responses of cells from distinct survivors having the same estimated radiation exposure level and other covariate values such overdispersion may result from individual differences in susceptibility to radiation damage from omitted covariates or most plausibly in this setting from substantial random errors in the estimated radiation exposure levels failure to acknowledge overdispersion may lead to serious underestimation of the standard errors associated with regression parameter estimates and to unduly precise inferences

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented