analysis of proportional mean residual life model with latent variables end stage renal disease esrd is one of the most serious diabetes complications numerous studies have been devoted to revealing the risk factors of the onset time of esrd in this article we propose a proportional mean residual life mrl model with latent variables to assess the effects of observed and latent risk factors on the mrl function of esrd in a cohort of chinese type 2 diabetic patients the proposed model generalizes the conventional proportional mrl model to accommodate the latent risk factor that cannot be measured by a single observed variable we employ a factor analysis model to characterize the latent risk factors via multiple observed variables we develop a borrow strength estimation procedure which incorporates the expectation maximization algorithm and an extended estimating equation approach the asymptotic properties of the proposed estimators are established simulation shows that the performance of the proposed methodology is satisfactory the application to the study of type 2 diabetes reveals insights into the prevention of esrd copyright 2016 john wiley sons ltd

cauchy like and pellet like results for polynomials abstract we obtain several cauchy like and pellet like results for the zeros of a general complex polynomial by considering similarity transformations of the squared companion matrix and by treating the zeros of a scalar polynomial as the eigenvalues of a matrix polynomial

robust linear static panel data models using e contamination abstract the paper develops a general bayesian framework for robust linear static panel data models using e contamination a two step approach is employed to derive the conditional type ii maximum likelihood ml ii posterior distribution of the coefficients and individual effects the ml ii posterior means are weighted averages of the bayes estimator under a base prior and the data dependent empirical bayes estimator two stage and three stage hierarchy estimators are developed and their finite sample performance is investigated through a series of monte carlo experiments these include standard random effects as well as mundlak type chamberlain type and hausman taylor type models the simulation results underscore the relatively good performance of the three stage hierarchy estimator within a single theoretical framework our bayesian approach encompasses a variety of specifications while conventional methods require separate estimators for each case

ten methods to bound multiple roots of polynomials given a univariate polynomial p with a k fold multiple root or a k fold root cluster near some z we discuss nine different methods to compute a disc near z which either contains exactly or contains at least k roots of p many of the presented methods are known some are new we are especially interested in the behaviour of methods when implemented in a rigorous way that is when taking into account all possible effects of rounding errors in other words every result shall be mathematically correct we display extensive test sets comparing the methods under different circumstances based on the results we present a tenth a hybrid method combining five of the previous methods which for given z i detects the number k of roots near z and ii computes an including disc with in most cases a radius of the order of the numerical sensitivity of the root cluster therefore the resulting discs are numerically nearly optimal

linear latent variable models and covariance structures abstract the observed vector is taken as a linear combination of latent unobservable vector variables the loading matrices are functions of a vector parameter the covariance matrix of one latent vector may depend on another vector parameter and the covariance matrices of the other latent vectors are unrestricted positive definite matrices and the different latent vectors are uncorrelated the covariance matrix of the observed vector is a function of the two parameter vectors and the covariance matrices of the latent vectors the maximum likelihood estimator when the latent variables are normally distributed is characterized the asymptotic distribution of the maximum likelihood estimator derived under normality is shown to be valid generally if the different latent variables are independent not just uncorrelated one latent vector is only required to have a sample covariance matrix that has a probability limit tests of the covariance structure are also asymptotically robust

inclusion of the roots of a polynomial based on gerschgorin s theorem in this note a new companion matrix is presented which can be interpreted as a product of werner s companion matrices 13 gerschgorin s theorem yields an inclusion of the roots of a polynomial which is best in the sense of 4 and generalizes a result of l elsner 5 this inclusion is better than the one due to w borsch supan in 1

bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix we derive some new bounds for the distance between the roots of two polynomials in terms of their coefficients and for the distance between the eigenvalues of two matrices in terms of the norm of their difference

parameters of interest nuisance parameters and orthogonality conditions an application to autoregressive error component models abstract in general when one considers a set of orthogonality conditions the parameters can be divided into parameters of interest that the econometrician wants to estimate the coefficient of the lagged endogenous variable in the case of an autoregressive error component arec model for instance and nuisance parameters most of the second order terms in an arec model we demonstrate that the elimination of such nuisance parameters using their empirical counterpart does not entail an efficiency loss when only the parameters of interest are estimated applications of our results to both autoregressive error component models and time varying individual fixed effects models are discussed at length they show the nature of the efficiency losses when some orthogonality conditions are left aside

econometric analysis of multivariate realised qml estimation of the covariation of equity prices under asynchronous trading estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading in this paper we develop a multivariate realised quasi likelihood qml approach carrying out inference as if the observations arise from an asynchronously observed vector scaled brownian model observed with error under stochastic volatility the resulting realised qml estimator is positive semi definite uses all available data is consistent and asymptotically mixed normal the quasi likelihood is computed using a kalman filter and optimised using a relatively simple em algorithm which scales well with the number of assets we derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence we show how to make itobtain the non parametric efficiency bound for this problem the estimator is also analysed usingmonte carlo methods and applied to equity data with varying levels of liquidity

a verified method for bounding clusters of zeros of analytic functions in this paper we propose a verified method for bounding clusters of zeros of analytic functions our method gives a disk that contains a cluster of m zeros of an analytic function f z complex circular arithmetic is used to perform a validated computation of n degree taylor polynomial p z of f z some well known formulae for bounding zeros of a polynomial are used to compute a disk containing a cluster of zeros of p z a validated computation of an upper bound for taylor remainder series of f z and a lower bound of p z on a circle are performed based on these results rouche s theorem is used to verify that the disk contains the cluster of zeros of f z this method is efficient in computation of the initial disk of a method for finding validated polynomial factor of an analytic function numerical examples are presented to illustrate the efficiency of the proposed method

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

fixed effects dynamic panel models a factor analytical method we consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions individual fixed effects and time fixed effects as well as incidental parameters in the variances we adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves in the presence of cross sectional heteroskedasticity the factor method estimates the average of the cross sectional variances instead of the individual variances the method thereby eliminates the incidental parameter problem in the means and in the variances over the cross sectional dimension we further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental parameter bias even when t and n are comparable moreover efficient and robust estimation is obtained by jointly estimating heteroskedasticities

regression analysis of additive hazards model with latent variables we propose an additive hazards model with latent variables to investigate the observed and latent risk factors of the failure time of interest each latent risk factor is characterized by correlated observed variables through a confirmatory factor analysis model we develop a hybrid procedure that combines the expectation maximization em algorithm and the borrow strength estimation approach to estimate the model parameters we establish the consistency and asymptotic normality of the parameter estimators various nice features including finite sample performance of the proposed methodology are demonstrated by simulation studies our model is applied to a study concerning the risk factors of chronic kidney disease for type 2 diabetic patients supplementary materials for this article are available online

heteroscedastic factor analysis summary two moment based model fitting procedures for the heteroscedastic factor analysis model are introduced and compared the procedures produce consistent parameter estimators and asymptotically valid inferences for heteroscedasticity without specifying the distributional forms for the factor and heteroscedastic errors also an individual specific inference procedure for the factor score is developed simulation studies show the practical usefulness of the procedures an example from a morphological measurement study is described

asymptotic conditional singular value decomposition for high dimensional genomic data high dimensional data such as those obtained from a gene expression microarray or second generation sequencing experiment consist of a large number of dependent features measured on a small number of samples one of the key problems in genomics is the identification and estimation of factors that associate with many features simultaneously identifying the number of factors is also important for unsupervised statistical analyses such as hierarchical clustering a conditional factor model is the most common model for many types of genomic data ranging from gene expression to single nucleotide polymorphisms to methylation here we show that under a conditional factor model for genomic data with a fixed sample size the right singular vectors are asymptotically consistent for the unobserved latent factors as the number of features diverges we also propose a consistent estimator of the dimension of the underlying conditional factor model for a finite fixed sample size and an infinite number of features based on a scaled eigen decomposition we propose a practical approach for selection of the number of factors in real data sets and we illustrate the utility of these results for capturing batch and other unmodeled effects in a microarray experiment using the dependence kernel approach of leek and storey 2008 proceedings of the national academy of sciences of the united states of america 105 18718 18723

scaling law and asymptotic distribution of lyapunov exponents in conservative dynamical systems with many degrees of freedom the authors study by numerical means the infinite product of 2n 2n conservative random matrices which mimics the chaotic behaviour of hamiltonian systems with n 1 degrees of freedom made of weakly nearest neighbour coupled oscillators the maximum lyapunov exponent lambda 1 exhibits a power law behaviour as a function of the coupling constant epsilon lambda 1 approximately epsilon beta with either beta 1 2 or beta 2 3 depending on the probability distribution of the matrix elements these power laws do not depend on n and moreover increasing n lambda 1 rapidly tends to an asymptotic value lambda 1 which only depends on epsilon and on the kind of probability distribution chosen for building up the matrices they also compute the spectrum of the lyapunov exponents and show that is has a thermodynamic limit of large n this suggests the existence of a kolmogorov entropy per degree of freedom proportional to lambda 1

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

adjustments for kurtosis in factor analysis with elliptically distributed errors on donne des corrections simples aux tests d ajustement de la theorie normale pour le modele d analyse factorielle dans le cas ou les facteurs communs ont des distributions arbitraires et ou les erreurs ont une distribution de la classe elliptique

analysis of covariance structures under elliptical distributions abstract this article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions it is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asymptotic properties of normal theory methods if a scale adjustment is applied the likelihood ratio tests of fit have the usual asymptotic chi squared distributions difference tests retain their property of asymptotic independence and maximum likelihood estimators retain their relative asymptotic efficiency within the class of estimators based on the sample covariance matrix an adjustment to the asymptotic covariance matrix of normal theory maximum likelihood estimators for elliptical distributions is provided this adjustment is particularly simple in models for patterned covariance or co

covariance structure analysis with heterogeneous kurtosis parameters summary this paper discusses the analysis of covariance structures in a wide class of multivariate distributions whose marginal distributions may have heterogeneous kurtosis parameters elliptical distributions often used as a generalization of the normal theory are members of this class it is shown that a simple adjustment of the weight matrix of normal theory using kurtosis estimates results in an asymptotically efficient estimator of structural parameters within the class of estimators that minimize a general discrepancy function results are obtained for arbitrary covariance structures as well as those that meet a scale invariance assumption two real data sets are analyzed for illustrative purposes

greatest lower bound to the elliptical theory kurtosis parameter on montre que le parametre d aplatissement pour une distribution elliptique continue a p variables et matrice de covariance definie positive reelle doit etre strictement plus grand que 2 p 2

model implied instrumental variable generalized method of moments miiv gmm estimators for latent variable models the common maximum likelihood ml estimator for structural equation models sems has optimal asymptotic properties under ideal conditions e g correct structure no excess kurtosis etc that are rarely met in practice this paper proposes model implied instrumental variable generalized method of moments miiv gmm estimators for latent variable sems that are more robust than ml to violations of both the model structure and distributional assumptions under less demanding assumptions the miiv gmm estimators are consistent asymptotically unbiased asymptotically normal and have an asymptotic covariance matrix they are distribution free robust to heteroscedasticity and have overidentification goodness of fit j tests with asymptotic chi square distributions in addition miiv gmm estimators are scalable in that they can estimate and test the full model or any subset of equations and hence allow better pinpointing of those parts of the model that fit and do not fit the data an empirical example illustrates miiv gmm estimators two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes

a bibliography on roots of polynomials abstract a categorized bibliography on roots of polynomials is presented covering the period from the earliest times until late 1990 the actual bibliography is on a computer diskette accompanying this issue together with programs designed to print parts of the main work such as entries belonging to a certain category

simulated maximum likelihood estimation of dynamic discrete choice statistical models some monte carlo results this article reports monte carlo results on the simulated maximum likelihood estimation of discrete dynamic panel models introduced by james heckman 1981a the simulated maximum likelihood method is numerically stable even for long panels regression models and polya and renewal models can be better estimated than markov models with a moderate number of simulation draws most of these complex models can be adequately estimated for panels with length up to 30 polya and renewal models can be accurately estimated for panels up to 50 periods estimates of markov models can be sensitive to misspecified initial states but polya renewal and habit persistence models may not

multilevel analysis of structural equation models summary this paper considers the multilevel analysis of structural equation models with unbalanced sampling designs the analysis is based on the maximum likelihood and the generalized least squares approaches basic statistical results for inference such as the asymptotic distribution of the estimators goodness of fit test statistics for the validity of the model and functional constraints are developed computationally the applications of the scoring algorithm and the gauss newton algorithm are discussed

a semiparametric quantile panel data model with an application to estimating the growth effect of fdi abstract this paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant a three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated a simple and easily implemented procedure for making inferences is proposed monte carlo simulation is conducted to examine the finite sample performance of the proposed estimators finally using the cross country panel data we find a strong empirical evidence of the existence of the absorptive capacity hypothesis together with another new finding that fdi has much stronger growth effects for countries with fast economic growth than for those with slow economic growth

finite mixtures in confirmatory factor analysis models in this paper various types of finite mixtures of confirmatory factor analysis models are proposed for handling data heterogeneity under the proposed mixture approach observations are assumed to be drawn from mixtures of distinct confirmatory factor analysis models but each observation does not need to be identified to a particular model prior to model fitting several classes of mixture models are proposed these models differ by their unique representations of data heterogeneity three different sampling schemes for these mixture models are distinguished a mixed type of the these three sampling schemes is considered throughout this article the proposed mixture approach reduces to regular multiple group confirmatory factor analysis under a restrictive sampling scheme in which the structural equation model for each observation is assumed to be known by assuming a mixture of multivariate normals for the data maximum likelihood estimation using the em expectation maximization algorithm and the as approximate scoring method are developed respectively some mixture models were fitted to a real data set for illustrating the application of the theory although the em algorithm and the as method gave similar sets of parameter estimates the as method was found computationally more efficient than the em algorithm some comments on applying the mixture approach to structural equation modeling are made

the asymptotic covariance matrix of maximum likelihood estimates in factor analysis the case of nearly singular matrix of estimates of unique variances this paper is concerned with the asymptotic covariance matrix acm of maximum likelihood estimates mles of factor loadings and unique variances when one element of mles of unique variances is nearly zero i e the matrix of mles of unique variances is nearly singular in this situation standard formulas break down we give explicit formulas for the acm of mles of factor loadings and unique variances that could be used even when an element of mles of unique variances is very close to zero we also discuss an alternative approach using the augmented information matrix under a nearly singular matrix of mles of unique variances and derive the partial derivatives of the alternative constraint functions with respect to the elements of factor loadings and unique variances 2000 elsevier science inc all rights reserved ams classification 62h25 62f12

on newton type methods for multiple roots with cubic convergence we introduce two families of newton type methods for multiple roots with cubic convergence a further newton type method for multiple roots with cubic convergence is presented that is related to quadrature we also provide numerical tests that show that these new methods are competitive to other known methods for multiple roots

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

estimation for polynomial structural equation models abstract structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing subject matter needs for considering nonlinear structural models have been well documented but current fitting procedures are available only for a limited class of models in this article a systematic statistical approach is developed for the general polynomial structural equation model the new procedure applies a method of moments procedure similar to the one used in errors in variables regression to the factor score estimates from the measurement model fit the asymptotic properties of the estimator are derived and a modified estimator with better small sample properties is introduced simulation studies are reported to show the usefulness of the procedure and to compare its performance to other methods an example from a substance abuse prevention study is also discussed

asymptotic biases in exploratory factor analysis and structural equation modeling formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the wishart maximum likelihood estimation for normally and nonnormally distributed variables when multivariate normality is satisfied considerable simplification is obtained for the models of unstandardized variables formulas for the models of standardized variables are also provided numerical examples with monte carlo simulations in factor analysis show the accuracy of the formulas and suggest the asymptotic robustness of the asymptotic biases with normality assumption against nonnormal data some relationships between the asymptotic biases and other asymptotic values are discussed

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

a quantile correlated random coefficients panel data model abstract we propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data specifically we extend the correlated random coefficients representation of linear quantile regression e g koenker 2005 section 2 6 we show that panel data allows the econometrician to i introduce dependence between the regressors and the random coefficients and ii weaken the assumption of comonotonicity across them i e to enrich the structure of allowable dependence between different coefficients we adopt a fixed effects approach leaving any dependence between the regressors and the random coefficients unmodeled we motivate different notions of quantile partial effects in our model and study their identification for the case of discretely valued covariates we present analog estimators and characterize their large sample properties when the number of time periods t exceeds the number of random coefficients p identification is regular and our estimates are n consistent when t p our identification results make special use of the subpopulation of stayers units whose regressor values change little over time in a way which builds on the approach of graham and powell 2012 in this just identified case we study asymptotic sequences which allow the frequency of stayers in the population to shrink with the sample size one purpose of these discrete bandwidth asymptotics is to approximate settings where covariates are continuously valued and as such there is only an infinitesimal fraction of exact stayers while keeping the convenience of an analysis based on discrete covariates when the mass of stayers shrinks with n identification is irregular and our estimates converge at a slower than n rate but continue to have limiting normal distributions we apply our methods to study the effects of collective bargaining coverage on earnings using the national longitudinal survey of youth 1979 nlsy79 consistent with prior work e g chamberlain 1982 vella and verbeek 1998 we find that using panel data to control for unobserved worker heterogeneity results in sharply lower estimates of union wage premia we estimate a median union wage premium of about 9 percent but with in a more novel finding substantial heterogeneity across workers the 0 1 quantile of union effects is insignificantly different from zero whereas the 0 9 quantile effect is of over 30 percent our empirical analysis further suggests that on net unions have an equalizing effect on the distribution of wages

on the unbiased asymptotic normality of quantile regression with fixed effects abstract nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data in a large class of such models including probit proportional hazard and quantile regression to name just a few it is impossible to difference out the individual effects and inference is usually justified in a large n large t asymptotic framework however there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions such as probit and proportional hazard and quantile regression in the present paper we show that this gap can be bridged and establish unbiased asymptotic normality for fixed effects quantile regression panels under conditions on n t that are very close to what is typically assumed in standard nonlinear panels our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data in terms of n t as other commonly used nonlinear panel data models thorough numerical experiments confirm our theoretical findings

forecasting and turning point predictions in a bayesian panel var model we provide methods for forecasting variables and predicting turning points in panel bayesian vars we specify a flexible model which accounts for both interdependencies in the cross section and time variations in the parameters posterior distributions for the parameters are obtained for hierarchical and for minnesota type priors formulas for multistep multiunit point and average forecasts are provided an application to the problem of forecasting the growth rate of output and of predicting turning points in the g 7 illustrates the approach a comparison with alternative forecasting methods is also provided

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

circumplex models for correlation matrices structural models that yield circumplex inequality patterns for the elements of correlation matrices are reviewed particular attention is given to a stochastic process defined on the circle proposed by t w anderson it is shown that the anderson circumplex contains the markov process model for a simplex as a limiting case when a parameter tends to infinity anderson s model is intended for correlation matrices with positive elements a replacement for anderson s correlation function that permits negative correlations is suggested it is shown that the resulting model may be reparametrzed as a factor analysis model with nonlinear constraints on the factor loadings an unrestricted factor analysis followed by an appropriate rotation is employed to obtain parameter estimates these estimates may be used as initial approximations in an iterative procedure to obtain minimum discrepancy estimates practical applications are reported

perturbation bounds for polynomials using two different elementary approaches we derive a global and a local perturbation theorem on polynomial zeros that significantly improve the results of ostrowski acta math 72 99 257 1940 elsner et al linear algebra appl 142 195 209 1990 a comparison of different perturbation bounds shows that our results are better in many cases than the similar local result of beauzamy can math bull 42 1 3 12 1999 using the matrix theoretical approach we also improve the backward stability result of edelman and murakami proceedings of the fifth siam conference on applied linear algebra siam philapdelphia 1994 math comput 64 210 763 1995

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

the fixed scale transformation approach to spatiotemporal intermittency in coupled map lattices abstract a one dimensional array of nonlinear maps with laplacian couplings is studied at the phase transition between the asymptotically turbulent and laminar phases along the critical boundary where spatiotemporal intermittency is observed turbulent sites form a fractal set the fixed scale transformation approach allows us to simultaneously determine the fractal dimension of the turbulent sites and the invariant asymptotic measure defining scale invariant conditional probabilities and taking into account the nearest neighbour correlations exactly we determine an asymptotic distribution function for the variables pertaining to sites on or neighbouring the turbulent clusters at any given level of coarse graining and obtain the fractal dimension analytically

improving spectral variation bounds with chebyshev polynomials a new spectral variation bound is established for linear operators a and b on finite dimensional vector spaces this bound is v a b c a b 1n a b n 1 n with c 8 this result affirmatively answers a conjecture of friedland

on estimation of the noise variance in high dimensional probabilistic principal component analysis in this paper we develop new statistical theory for probabilistic principal component analysis models in high dimensions the focus is the estimation of the noise variance which is an important and unresolved issue when the number of variables is large in comparison with the sample size we first unveil the reasons of a widely observed downward bias of the maximum likelihood estimator of the variance when the data dimension is high we then propose a bias corrected estimator using random matrix theory and establish its asymptotic normality the superiority of the new bias corrected estimator over existing alternatives is first checked by monte carlo experiments with various combinations of p n dimension and sample size in order to demonstrate further potential benefits from the results of the paper to general probability pca analysis we provide evidence of net improvements in two popular procedures ulfarsson and solo 2008 bai and ng 2002 for determining the number of principal components when the respective variance estimator proposed by these authors is replaced by the bias corrected estimator the new estimator is also used to derive new asymptotics for the related goodness of fit statistic under the high dimensional scheme

robustness of statistical inference in factor analysis and related models summary a class of latent variable models which includes the unrestricted factor analysis model is considered it is shown that minimum discrepancy test statistics and estimators derived under normality assumptions retain their asymptotic properties when the common factors are not normally distributed but the unique factors do have a multivariate normal distribution the minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic and maximum likelihood estimators

self validating methods abstract we present some ideas on self validating sv methods this note is especially intended to give some background for the articles in this special volume of laa it is not intended to be a survey of the big variety of all possible aspects of sv methods but rather a summary of some basic concepts especially some common misconceptions are mentioned and explored

sigmoid like functions and root finding methods abstract an efficient method for finding an initial approximation to a real root of nonlinear equation f x 0 is proposed the presented approach is based on numerical integration of the transform functions tanh m f x arctan m f x m 0 and sgn f x of sigmoidal type combining numerical integration method and rapidly convergent iterative methods we construct a hybrid method of great efficiency the introduced sigmoid like functions are also convenient for the detection of a cluster of zeros or a multiple zero lying in a given interval the presented numerical examples demonstrate the feasibility and efficiency of the proposed procedures

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

a property of the nearly optimal root bound the importance of root bounds for practical and theoretical algorithms for polynomial root approximation is well known the root bound by fujiwara was shown to be near optimal by van der sluis and is the most often used in practice we show here that this bound always compares favorably with kojima s bound a question left open in the work of van der sluis

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

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

a family of root finding methods with accelerated convergence a parametric family of iterative methods for the simultaneous determination of simple complex zeros of a polynomial is considered the convergence of the basic method of the fourth order is accelerated using newton s and halley s corrections thus generating total step methods of orders five and six further improvements are obtained by applying the gauss seidel approach accelerated convergence of all proposed methods is attained at the cost of a negligible number of additional operations detailed convergence analysis and two numerical examples are given

determinants of standard errors of mles in confirmatory factor analysis this paper studies changes of standard errors se of the normal distribution based maximum likelihood estimates mle for confirmatory factor models as model parameters vary using logical analysis simplified formulas and numerical verification monotonic relationships between ses and factor loadings as well as unique variances are found conditions under which monotonic relationships do not exist are also identified such functional relationships allow researchers to better understand the problem when significant factor loading estimates are expected but not obtained and vice versa what will affect the likelihood for heywood cases negative unique variance estimates is also explicit through these relationships empirical findings in the literature are discussed using the obtained results

the triangular model with random coefficients abstract the triangular model is a very popular way to allow for causal inference in the presence of endogeneity in this model an outcome is determined by an endogenous regressor which in turn is first caused by an instrument we study the triangular model with random coefficients and additional exogenous regressors in both equations and establish non identification of the joint distribution of random coefficients this implies that counterfactual outcomes are not identified either non identification continues to hold if we confine ourselves to the joint distribution of coefficients in the outcome equation or indeed any marginal except the one on the endogenous regressor nonidentification prevails as well if we focus on means of random coefficients implying that iv is asymptotically biased based on these insights we derive bounds on the joint distribution of economically relevant functionals e g counterfactual outcomes and suggest an additional restriction that allows to point identify the distribution of random coefficients in the outcome equation we extend the model to cover the case where the regressors and instruments have limited support and analyze semi and nonparametric sample counterpart estimators in finite and large samples and we provide an application to consumer demand

estimation for the multivariate errors in variables model with estimated error covariance matrix the errors in variables model in which the unobserved true values satisfy multiple linear restrictions is considered under the assumptions that the unobservable true values are normally distributed and that an estimator of the covariance matrix of the measurement error is available the maximum likelihood estimators are derived the limiting properties of the estimators are obtained for a wide range of assumptions including the assumption of fixed true values

enclosing clusters of zeros of polynomials lagrange interpolation and partial fraction expansion can be used to derive a gerschgorin type theorem that gives simple and powerful a posteriori error bounds for the zeros of a polynomial if approximations to all zeros are available compared to bounds from a corresponding eigenvalue problem a factor of at least two is gained the accuracy of the bounds is analyzed and special attention is given to ensure that the bounds work well not only for single zeros but also for multiple zeros and clusters of close zeros a rouche type theorem is also given that in many cases reduces the bound even further

using principal component analysis and correspondence analysis for estimation in latent variable models abstract correspondence analysis ca and principal component analysis pca are often used to describe multivariate data in certain applications they have been used for estimation in latent variable models the theoretical basis for such inference is assessed in generalized linear models where the linear predictor equals j xi j or aj bj xi xi j 2 i 1 n j 1 m and xi is treated as a latent fixed effect the pca and ca eigenvectors column scores are evaluated as estimators of j and uj and as estimators of uj with m fixed and n consistent estimators cannot be obtained due to the incidental parameters problem unless sufficient moment conditions are imposed on xi pca is equivalent to maximum likelihood estimation for the linear gaussian model and gives a consistent estimator of j up to a scale change when the second sample moment of xi is positive and finite in the limit it is inconsistent for poisson and bernoulli distributions but when bj is constant its first and or sec

selection corrections for panel data models under conditional mean independence assumptions some new methods for testing and correcting for sample selection bias in panel data models are proposed the assumptions allow the unobserved effects in both the regression and selection equations to be correlated with the observed variables the error distribution in the regression equation is unspecified arbitrary serial dependence in the idiosyncratic errors of both equations is allowed and all idiosyncratic errors can be heterogeneously distributed compared with maximum likelihood and other estimators derived under fully parametric assumptions the new estimators are much more robust and have significant computational advantages

multiscaling of the graph length in coupled map lattices we consider generalized scaling exponents for the graph of a scalar function to allow for multiscaling of the graph length these generalized exponents are related to the moments of the distribution of roughness over the support of the graph we report numerical computations of these exponents for the graphs of coupled map lattices exhibiting phase transitions between laminar and turbulent behaviour we observe multiscaling of the graph in the transition region furthermore the generalized dimensions d q are computed for a conserved measure of graph roughness

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

theory and methods of panel data models with interactive effects this paper considers the maximum likelihood estimation of the panel data models with interactive effects motivated in economics and other social sciences a notable feature of the model is that the explanatory variables are correlated with the unobserved effects the usual within group estimator is inconsistent existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient the maximum likelihood estimator has desirable properties and is easy to implement as illustrated by the monte carlo simulations this paper develops the inferential theory for the maximum likelihood estimator including consistency rate of convergence and the limiting distributions we further extend the model to include time invariant regressors and common regressors cross section invariant the regression coefficients for the time invariant regressors are time varying and the coefficients for the common regressors are cross sectionally varying

an efficient higher order family of root finders a one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial based on a cubically convergent hansen patrick s family is studied we show that the convergence of the basic family of the fourth order can be increased to five and six using newton s and halley s corrections respectively since these corrections use the already calculated values the computational efficiency of the accelerated methods is significantly increased further acceleration is achieved by applying the gauss seidel approach single step mode one of the most important problems in solving nonlinear equations the construction of initial conditions which provide both the guaranteed and fast convergence is considered for the proposed accelerated family these conditions are computationally verifiable they depend only on the polynomial coefficients its degree and initial approximations which is of practical importance some modifications of the considered family providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions are also studied numerical examples demonstrate the convergence properties of the presented family of root finding methods

on the asymptotic distributions of two statistics for two level covariance structure models within the class of elliptical distributions since data in social and behavioral sciences are often hierarchically organized special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures most of these developments are based on a multivariate normality distribution assumption which may not be realistic for practical data it is of interest to know whether normal theory based inference can still be valid with violations of the distribution condition various interesting results have been obtained for conventional covariance structure analysis based on the class of elliptical distributions this paper shows that similar results still hold for 2 level covariance structure models specifically when both the level 1 within cluster and level 2 between cluster random components follow the same elliptical distribution the rescaled statistic recently developed by yuan and bentler asymptotically follows a chi square distribution when level 1 and level 2 have different elliptical distributions an additional rescaled statistic can be constructed that also asymptotically follows a chi square distribution our results provide a rationale for applying these rescaled statistics to general non normal distributions and also provide insight into issues related to level 1 and level 2 sample sizes

fixed scale transformation for ising and potts clusters the fractal dimension of ising and potts clusters are determined via the fixed scale transformation approach which exploits both the self similarity and the dynamical invariance of these systems at criticality the results are easily extended to droplets a discussion of the interrelationships between the present approach and renormalization group methods as well as glauber type dynamics is provided

asymptotic theory of overparameterized structural models abstract a theory of overparameterized structural models is presented in such a model some redundant parameters are involved the parameter vector is not identified and the information matrix is not nonsingular the minimum discrepancy function mdf test statistic is shown to have an asymptotic chi squared distribution almost everywhere for a wide class of discrepancy functions asymptotic distribution properties of the mdf estimators are investigated the factor analysis model is discussed as an example

characterisation of intermittency in chaotic systems the authors discuss the characterisation of intermittency in chaotic dynamical systems by means of the time fluctuations of the response to a slight perturbation on the trajectory a set of exponents is introduced which generalise the maximum lyapunov characteristic exponent the link with the statistical mechanics formalism is emphasised and they show that the exponents are connected to a free energy formally defined for chaotic systems they perform some analytical computations in simple cases and give a few numerical examples

computational error bounds for multiple or nearly multiple eigenvalues abstract in this paper bounds for clusters of eigenvalues of non selfadjoint matrices are investigated we describe a method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues and for a basis of the corresponding invariant subspaces the input matrix may be real or complex dense or sparse the method is based on a quadratically convergent newton like method it includes the case of defective eigenvalues uncertain input matrices and the generalized eigenvalue problem computational results show that verified bounds are still computed even if other eigenvalues or clusters are nearby the eigenvalues under consideration

spatiotemporal chaos and noise low dimensional chaotic dynamical systems can exhibit many characteristic properties of stochastic systems such as broad fourier spectra they are distinguishable from stochastic processes through finite values for their dimension lyapunov exponents and kolmogorov sinai entropy we discuss how these characteristic observables are modified in spatiotemporal chaotic systems like coupled map lattices we analyze with the help of lyapunov concepts how the stochastic limit is approached and how these properties can be observed directly through local dimension measurements from reconstructed time series finally we discuss the interaction of spatiotemporal attractors with external noise and possible connections to problems of pattern selection and stability

on normal theory based inference for multilevel models with distributional violations data in social and behavioral sciences are often hierarchically organized though seldom normal yet normal theory based inference procedures are routinely used for analyzing multilevel models based on this observation simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions for characterizing the distribution of parameter estimates sandwich type covariance matrices are derived standard errors based on these covariance matrices remain consistent under distributional violations implications of various covariance estimators are also discussed for evaluating the quality of a multilevel model a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model the rescaled statistic improving the likelihood ratio statistic by estimating one extra parameter approaches the same mean as its reference distribution a simulation study with a 2 level factor model implies that the rescaled statistic is preferable

theory of laplacian fractals diffusion limited aggregation and dielectric breakdown model abstract we describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the laplace equation and a stochastic field this new theory provides a systematic method for the calculation of the fractal dimension d and of the multifractal spectrum of the growth probability a detailed application to the dielectric breakdown model and diffusion limited aggregation in two dimensions is presented our approach exploits the scale invariance of the laplace equation that implies that the structure is self similar both under growth and scale transformation this allows one to introduce a fixed scale transformation instead of coarse graining as in the renormalization group theory that defines a functional equation for the fixed point of the distribution of basic diagrams used in the coarse graining process for the calculation of the matrix elements of this transformation one has to consider an infinite but rapidly convergent number of processes that occurs outside a considered diagram

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

on new higher order families of simultaneous methods for finding polynomial zeros abstract two one parameter families of iterative methods for the simultaneous determination of simple zeros of algebraic polynomials are presented the construction of these families are based on a one parameter family of the third order for finding a single root of nonlinear equation f x 0 some previously derived simultaneous methods can be obtained from the presented families as special cases we prove that the local convergence of the proposed families is of the order four numerical results are included to demonstrate the convergence properties of considered methods

gmm inference when the number of moment conditions is large abstract asymptotic theory typically presumes that the dimensionality of econometric models is independent of the sample size even though this presumption is often quite unrealistic in gmm estimation whenever optimal instruments are not available it can frequently be shown that adding over identifying restrictions moment conditions will increase asymptotic precision however the conventional asymptotics which underlies this view insists that the number of moment conditions remain finite even though the number of available moment conditions may grow without bound we consider the explicit dependence of the number of moment conditions or instruments q n on the sample size n and establish that under conventional regularity conditions for the estimation of a linear model with general heteroskedasticity q n 3 n 0 is a sufficient condition for the validity of conventional asymptotic inference about the gmm estimator

intrinsic stochasticity with many degrees of freedom we study a simple model equation describing a system with an infinity of degrees of freedom which displays an intrinsically chaotic behavior some concepts of fully developed turbulence are discussed in relation to this model we also develop an approach based on lyapunov exponent measurements numerical results on the distribution of lyapunov numbers and the power spectrum of the associated lyapunov vectors are presented and briefly discussed