the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

a two stage estimator for probit models with structural group effects this paper outlines a two stage technique for estimation and inference in probit models with structural group effects the structural group specification belongs to a broader class of random components models in particular individuals in a given group share a common component in the specification of the conditional mean of a latent variable for a number of computational reasons existing random effects models are impractical for estimation and inference in this type of problem our two stage estimator provides an easily estimable alternative to the random effects specification in addition we conduct a monte carlo simulation comparing the performance of alternative es timators and find that the two stage estimator is superior both in terms of estimation and inference to traditional estimators

residual maximum likelihood reml estimation of a neighbour model for field experiments a spatial analysis of field experiments is proposed which takes account of association between neighbouring plots the residual maximum likelihood reml method of patterson and thompson 1971 biometrika 58 545 554 is used to estimate parameters of a general neighbour model which can be expressed as an autoregressive moving average arma model three data sets are analysed to i highlight the need for a model selection procedure ii illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design and iii illustrate the environmental variation within an experiment using prediction of trend

conditional lie backlund symmetry second order differential constraint and direct reduction of diffusion systems abstract the equivalence relation between conditional lie backlund symmetry higher order differential constraint and direct reduction is presented in the case of evolution systems the second order nonlinear conditional lie backlund symmetries and corresponding induced differential constraints admitted by nonlinear diffusion systems are identified as an application of the conditional lie backlund symmetry of evolution systems consequently the corresponding symmetry reductions are obtained due to the compatibility of the resulting differential constraints and the governing systems

on families of systems pointwise local global isomorphism problems let and be two families of linear dynamical systems or almost equivalently let and be two systems over a ring this paper addresses itself to the question what if anything can be said about the relations between and if it is known that and are pointwise isomorphic for all or almost all of the parameter values

cross section regression with common shocks this paper considers regression models for cross section data that exhibit cross section dependence due to common shocks such as macroeconomic shocks the paper analyzes the properties of least squares ls estimators in this context the results of the paper allow for any form of cross section dependence and heterogeneity across population units the probability limits of the ls estimators are determined and necessary and sufficient conditions are given for consistency the asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling the t wald and f statistics are found to have asymptotic standard normal x 2 and scaled x 2 distributions respectively under the null hypothesis when the conditions required for consistency of the parameter under test hold however the absolute values of t wald and f statistics are found to diverge to infinity under the null hypothesis when these conditions fail confidence intervals exhibit similarly dichotomous behavior hence common shocks are found to be innocuous in some circumstances but quite problematic in others models with factor structures for errors and regressors are considered using the general results conditions are determined under which consistency of the ls estimators holds and fails in models with factor structures the results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units

efficient estimation and inference in linear pseudo panel data models we consider pseudo panel data models constructed from repeated cross sections in which the number of individuals per group is large relative to the number of groups and time periods first we show that when time invariant group fixed effects are neglected the ols estimator does not converge in probability to a constant but rather to a random variable second we show that while the fixed effects fe estimator is consistent the usual t statistic is not asymptotically normally distributed and we propose a new robust t statistic whose asymptotic distribution is standard normal third we propose efficient gmm estimators using the orthogonality conditions implied by grouping and we provide t tests that are valid even in the presence of time invariant group effects our monte carlo results show that the proposed gmm estimator is more precise than the fe estimator and that our new t test has good size and is powerful

new exact solutions for a free boundary system a method for constructing explicit exact solutions to nonlinear evolution equations is further developed the method is based on consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation the method is then applied to a free boundary problem based on the process of precipitant assisted protein crystal growth

iterations of the non classical symmetries method and conditional lie backlund symmetries iterations of the non classical symmetries method give rise to new nonlinear equations which inherit the lie point symmetry algebra of the original equation invariant solutions of these heir equations supply new solutions of the original equation we show that particular cases of such invariant solutions correspond to zhdanov s conditional lie backlund symmetries

variances of locally minimum variance quadratic unbiased estimators mivque s of variance components minimum variance quadratic unbiased estimators mivque s of variance components from unbalanced data are functions of the components they are to estimate to use the mivque expressions for estimation under the one way classification random model for example the unknown between and within treatments components 2 a and 2 e must be replaced by a priori estimates 2 ao and 2 eo the resulting estimators are called mivque s for the one way classification expressions for the variances and covariance of the mivque s are obtained under normality numerical comparisons indicate that when 2 a 2 e 1 approximately and unless 2 ao 2 eo q 2 a 2 e a the mivque s have variances near their lower bounds and b the mivque of 2 a is more efftcient than the anova estimator when 2 a 2 e 1 the mivque s are more dependent on accurate specification of 2 ao 2 eo the mivque and anova estimator of 2 e have nearly equal variances unless 2 eo 2 eo 2 a 2 e when the anova e

random group effects and the precision of regression estimates abstract when explanatory variable data in a regression model are drawn from a population with grouped structure the regression errors are often correlated within groups error component and random coefficient regression models are considered as models of the intraclass correlation this paper analyzes several empirical examples to investigate the applicability of random effects models and the consequences of inappropriately using ordinary least squares ols estimation in the presence of random group effects the principal findings are that the assumption of independent errors is usually incorrect and the unadjusted ols standard errors often have a substantial downward bias suggesting a considerable danger of spurious regression

pooling an experimental study of alternative testing and estimation procedures in a two way error component model abstract this paper considers a two way error component model with no lagged dependent variable and investigates the performance of various testing and estimation procedures applied to this model by means of monte carlo experiments the following results were found 1 the chow test performed poorly in testing the stability of cross section regressions over time and in testing the stability of time series regression across regions 2 the roy zellner test performed well and is recommended for testing the poolability of the data 3 the hausman specification test employed to test the orthogonality assumption gave a low frequency of type i errors 4 the lagrange multiplier test employed to test for zero variance components did well except in cases where it was badly needed 5 the problem of negative estimates of the variance components was found to be more serious in the two way model than in the one way model however replacing the negative variance estimates by zero did not have a serious effect on the performance of the second round gls estimates of the regression coefficients 6 as in the one way model all the two stage estimation methods performed reasonably well 7 better estimates of the variance components did not necessarily lead to better second round gls estimates of the regression coefficients

lie symmetries of nonlinear multidimensional reaction diffusion systems ii we present a complete description of the classical lie symmetries of a coupled system of partial differential equations comprising a pair of semilinear reaction diffusion equations with constant diffusivities and arbitrary nonlinearities in the reaction terms in any number of spatial dimensions part i cherniha r m and king j r 2000 j phys a math gen 33 267 82 j phys a math gen 33 7839 41 addressed the case of unequal diffusivities here we complete the analysis by treating the case of equal diffusivities in which the symmetry structure is richer still such models arise in the description of numerous physical chemical and biological systems and we also indicate the possible application in such contexts of some of the specific cases arising from the group classification specifically a variety of lie s ansatze and exact solutions of the so called reaction diffusion systems of a type that arises in mathematical biology are constructed

exact polynomial solutions to some nonlinear diffusion equations abstract a class of non group invariant exact solutions to a number of nonlinear diffusion equations is constructed expressed in the appropriate variables these solutions are polynomials in the spatial variable the method is mainly applicable to equations which may be written in an appropriate quadratically nonlinear form a number of equivalence transformations between various nonlinear diffusion equations are also derived

a nonparametric test for poolability using panel data this paper derives a nonparametric procedure for testing poolability in a panel data framework this is contrasted with alternative parametric tests which are not robust to functional misspecification this test is illustrated with an earning equation using data from the panel study of income dynamics psid

new non lie ansatze and exact solutions of nonlinear reaction diffusion convection equations a constructive method for obtaining new exact solutions of nonlinear evolution equations is further developed the method is based on the consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation using this method new non lie ansatze and exact solutions are obtained for two classes of diffusion equations with power and exponential nonlinearities which describe real processes in physics chemistry and biology the analysis of the found solutions and the relation of the proposed method to some approaches which have been suggested in several recently published papers are presented

pseudo gaussian and rank based optimal tests for random individual effects in large n small t panels we consider the problem of detecting unobserved heterogeneity that is the problem of testing the absence of random individual effects in an n t panel we establish a local asymptotic normality property with respect to intercept regression coefficient the scale parameter of the error and the scale parameter u of individual effects which is the parameter of interest for given scaled density f 1 of the error terms when n tends to infinity and t is fixed this result allows via the hk representation theorem for developing asymptotically optimal rank based tests for the null hypothesis u 0 absence of individual effects these tests are locally asymptotically optimal at correctly specified innovation densities f 1 but remain valid irrespective of the actual underlying density the limiting distribution of our test statistics is obtained both under the null and under sequences of contiguous alternatives a local asymptotic linearity property is established in order to control for the effect of substituting estimators for nuisance parameters the asymptotic relative efficiencies of the proposed procedures with respect to the corresponding pseudo gaussian parametric tests are derived in particular the van der waerden version of our rank based tests uniformly dominates from the point of view of pitman efficiency the classical honda test small sample performances are investigated via a monte carlo study and confirm theoretical findings

exact solutions to nonlinear equations with quadratic nonlinearity based on the concepts of the generalized conditional symmetry and of the invariant subspace a constructive way to derive nonlinear equations with quadratic nonlinearity that admit exact solutions as well as many new examples is presented this type of solution found by galaktionov describes the blowup phenomena examples of exact solutions that do not correspond to the invariant subspace are also presented and explained by the nonlinear generalized conditional symmetries

direct reduction and differential constraints direct reductions of partial differential equations to systems of ordinary differential equations are in one to one correspondence with compatible differential constraints the differential constraint method is applied to prove that a parabolic evolution equation admits infinitely many characteristic second order reductions but admits a non characteristic second order reduction if and only if it is linearizable

lie symmetries and form preserving transformations of reaction diffusion convection equations abstract new lie symmetry classification of the known class of reaction diffusion convection equations is presented the classification method is based on combining the standard group classification method and the form preserving transformation approach

nonlinear reaction diffusion systems with a non constant diffusivity q conditional symmetries nonclassical symmetries for a general class of two component reaction diffusion systems with non constant diffusivities are studied the work is a natural continuation of our paper conditional symmetries and exact solutions of nonlinear reaction diffusion systems with non constant diffusivities cherniha and davydovych 2012 1 in order to extend the results on so called no go case using the notion of q conditional symmetries of the first type an exhaustive list of reaction diffusion systems admitting such symmetry is derived the results obtained are compared with those derived earlier the symmetries for reducing reaction diffusion systems to two dimensional dynamical systems ode systems and finding exact solutions are applied as result multiparameter families of exact solutions in the explicit form for nonlinear reaction diffusion systems with an arbitrary power law diffusivity are constructed and their properties for possible applicability are established

on the simplification of the form of lie transformation groups admitted by systems of evolution differential equations abstract for a system of two partial differential equations in two independent variables the lie point symmetry generator has the form t x u v t t x u v x t x u v u t x u v v we consider a system of evolution equations of general class and we provide restrictions on the functional forms of the coefficient functions of the lie generator these restrictions reduce the amount of calculations in determining the lie symmetries of the system under study we show that t except in one special case and we present further restrictions on the remaining coefficient functions

lie and conditional symmetries of the three component diffusive lotka volterra system lie and q conditional symmetries of the classical three component diffusive lotka volterra system in the case of one space variable are studied the group classification problems for finding lie symmetries and q conditional symmetries of the first type are completely solved notably non lie symmetries q conditional symmetry operators for a multi component nonlinear reaction diffusion system are constructed for the first time the results are compared with those derived for the two component diffusive lotka volterra system the conditional symmetry obtained for the non lie reduction of the three component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found particularly the exact solution describing different scenarios of competition between three species is constructed

properties of ordinary least squares estimators in regression models with nonspherical disturbances abstract a general discussion is presented of the properties of the ols estimator in regression models where the disturbances do not have a scalar identity covariance matrix several new and interesting characterizations are provided together with a synthesis of existing results a distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference the theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians

monte carlo comparison of anova mivque reml and ml estimators of variance components for the one way classification random model with unbalanced data we compare five estimators of 2 a and 2 e the among and within treatments variance components analysis of variance anova maximum likelihood ml restricted maximum likelihood reml and two minimum variance quadratic unbiased mivque estimators mivque 0 is mivque with a priori values 0 and 1 mivque a is mivque with the anova estimates used as a priori s we enforce nonnegativity for all estimators setting any negative estimate to zero in accord with usual practice the estimators are compared through their biases and mse s estimated by monte carlo simulation our results indicate that the anova estimators perform well except with seriously unbalanced data when 2 a 2 e 1 ml is excellent when 2 a 2 e 0 5 and mivque a is adequate further iteration to the reml estimates is unnecessary when 2 a 2 e 1 mivque 0 the default for sass procedure varcomp is poor for estimating 2 a and very poor for 2 e

alternative tests of the error components model the error components regression model is now widely applied in econometics and statistics given the potentially high costs of incorrectly excluding the component from the model an error components test should have high power in addition if a test is to gain acceptance from practitioners the test should be computed easily to obtain improved critical value approximations we introduce a standardized lagrange multiplier slm test statistic which is centered and scaled to have a zero mean and unit variance under the null hypothesis we also examine the f test which is easily computed and has a well known exact distribution under the null hypothesis if the regression errors are normally distributed

simultaneous equations with error components abstract in this paper we derive a limited as well as a full information estimator for the structural parameters of a simultaneous equations model with error components under this model the gain in efficiency by performing these estimators rather than the classical two stage and three stage least squares procedures is demonstrated it is shown that the full information estimator will reduce to the limited information estimator when the disturbances of different structural equations are uncorrelated with each other but not necessarily when all structural equations are just identified this is different from the analogous situation in the classical case

a comparison of variance component estimates for arbitrary underlying distributions abstract large sample covariance matrices for the analysis of variance anova minimum norm quadratic unbiased estimator minque restricted maximum likelihood reml and maximum likelihood ml estimates of variance components are presented for the unbalanced one way model when the underlying distributions are not necessarily normal the limiting variances depend on the design sequence on the actual values of the variance components and on the kurtosis parameters of the underlying distributions the skewness parameters and other moments do not affect the limiting distributions because all estimates are consistent and asymptotically normal it is reasonable to compare the estimates using their asymptotic variances thus the efficiency of one estimate relative to another is defined as the ratio of their asymptotic variances and these efficiencies are evaluated numerically and analytically for a variety of nonnormal situations various authors including hocking and kutner 1975 corbeil and searl

clustering spatial correlations and randomization inference it is a standard practice in regression analyses to allow for clustering in the error covariance matrix if the explanatory variable of interest varies at a more aggregate level e g the state level than the units of observation e g individuals often however the structure of the error covariance matrix is more complex with correlations not vanishing for units in different clusters here we explore the implications of such correlations for the actual and estimated precision of least squares estimators our main theoretical result is that with equal sized clusters if the covariate of interest is randomly assigned at the cluster level only accounting for nonzero covariances at the cluster level and ignoring correlations between clusters as well as differences in within cluster correlations leads to valid confidence intervals however in the absence of random assignment of the covariates ignoring general correlation structures may lead to biases in standard errors we illustrate our findings

global reduction to the kronecker canonical form of a cr family of time invariant linear systems abstract we present an approach to the kronecker equivalence of quadruples of matrices a b c d based on a natural equivalence relation between pairs of linear mappings we apply this approach to smooth families of quadruples of constant kronecker type obtaining smooth families of transformation matrices that pointwise reduce each quadruple to its kronecker canonical form

estimating multi way error components models with unbalanced data structures abstract i develop simple matrix algebra techniques that simplify and unify much of the previous literature on estimating error components models ecms in fact the simple analytic results provided here are useful for analyzing a very broad set of models with complex error structures to illustrate the techniques i develop the algebra for three and four way ecms explicitly in addition i provide monte carlo simulation evidence on the performance of several estimators for the three way ecm and estimate the model using data from a retail market where the three dimensions of data variation are products selling in many locations over time

generalized least squares inference in panel and multilevel models with serial correlation and fixed effects in this paper i consider generalized least squares gls estimation in fixed effects panel and multilevel models with autocorrelation the presence of fixed effects complicates implementation of gls as estimating the fixed effects will typically render standard estimators of the covariance parameters necessary for obtaining feasible gls estimates inconsistent i focus on the case where the disturbances follow an ar p process and offer a simple to implement bias correction for the ar coefficients the usefulness of gls and the derived bias correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the current population survey

the efficiency of rotating panel designs in an analysis of variance model in this paper we consider the relative efficiency of rotating panel designs in analysis of variance models throughout we assume that the parameter of interest is a linear combination of period means in the analysis of variance model results from spectral theory are used to obtain manageable expressions for the variance of the blue of this parameter relative efficiencies of the blue for rotating panels with different rotation periods are presented e g for the period means themselves of differences or of averages of means moreover we present bounds on the relative efficiency which are valid irrespective of the parameter of interest the analysis shows that the gains from choosing an optimal rotation design can be quite substantial even if the cost of a reinterview equals the cost of a first observation in many cases either the smallest or the highest possible rotation period is optimal the analysis is illustrated with an empirical example concerning monthly consumer expenditures on food and clothing

difference in difference meets generalized least squares higher order properties of hypotheses tests we investigate the estimation and inference in difference in difference econometric models used in the analysis of treatment effects when the innovations in such models display serial correlation commonly used ordinary least squares ols procedures are inefficient and may lead to tests with incorrect size implementation of feasible generalized least squares fgls procedures is often hindered by too few observations in the cross section to allow for unrestricted estimation of the weight matrix without leading to tests with similar size distortions as conventional ols based procedures we analyze the small sample properties of fgls based tests with a formal higher order edgeworth expansion that allows us to construct a size corrected version of the test we also address the question of optimal temporal aggregation as a method to reduce the dimension of the weight matrix we apply our procedure to data on regulation of mobile telephone service prices we find that a size corrected fgls based test outperforms tests based on ols

asymptotic inference from multi stage samples i develop a gmm based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering i set up the estimation problem derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample design effects the analysis is then extended to nonparametric regression and to semiparametric estimation based on u processes empirical illustrations are provided using consumption expenditure data from the complexly designed indian national household survey

new exact solutions of a nonlinear cross diffusion system a system of two reaction diffusion equations with cross diffusion and quadratic nonlinearities is considered the system is a particular case the well known model proposed by shigesada et al 1979 j theor biol 79 83 new non lie ansatze special type substitutions reducing the system to systems of first order ordinary differential equations are obtained and applied to find its exact solutions several families of exact solutions are constructed their asymptotic behavior is investigated and some biological interpretation of the solutions is provided lie symmetry of this system is also discussed

equivalence transformations and differential invariants of a generalized nonlinear schrodinger equation by using lie s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear schrodinger equations with variable coefficients we construct the differential invariants of order 1 starting from a special equivalence subalgebra we apply these latter ones to find the most general subclass of variable coefficient nonlinear schrodinger equations which can be mapped by means of an equivalence transformation of to the well known cubic schrodinger equation we also provide the explicit form of the transformation

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

iterating the nonclassical symmetries method we show that iterations of the nonclassical symmetries method for any evolution equation give raise to new nonlinear equations which inherit the symmetry algebra of the given equation invariant solutions of these heir equations supply new solutions of the original equation the same method generates heir equations for hyperbolic and elliptic equations some examples are given

non linear reaction diffusion systems with variable diffusivities lie symmetries ansatze and exact solutions abstract this work first considers the classical lie symmetry analysis of a class of systems of two quasilinear reaction diffusion equations having variable diffusivities subsequently non lie reductions to systems of first order ordinary differential equations are obtained for a subclass of these systems in particular families of exact solutions of a diffusive lotka volterra type system are constructed

systems of reaction convection diffusion equations invariant under galilean algebras abstract systems which are invariant under galilean algebras with and without mass operator and their main extensions by operators of scale and projective transformations are selected from a class of systems of reaction convection diffusion equations for two dimensional vector field with one space variable

the pointwise local global principle for solutions of generic linear equations abstract the problem studied in this paper is to determine some conditions on a matrix a over a ring r which will insure that the matrix equation au f is solvable over r if it is solvable over the residue field for every spec r if r is a regular local ring containing a field a polynomial ring over an algebraically close field or the ring of holomorphic functions on a stein manifold then a sufficient condition on a for pointwise solvability to imply global solvability is that a be generic a concept which is defined in the paper for the rings of functions pointwise solvability will mean solvability over r m for a certain set of maximal ideals the relationship between this notion of pointwise solvability and solvability over for all prime ideals is studied by introducing various types of closure operations on submodules mather has previously proved a theorem similar to the main result of this paper for the case of rings of smooth real valued functions on open subsets of euclidean space

asymptotic theory and wild bootstrap inference with clustered errors abstract we study inference based on cluster robust variance estimators for regression models with clustered errors focusing on the wild cluster bootstrap we state conditions under which asymptotic and bootstrap tests and confidence intervals are asymptotically valid these conditions put limits on the rates at which the cluster sizes can increase as the number of clusters tends to infinity we also derive edgeworth expansions for the asymptotic and bootstrap test statistics simulation experiments illustrate the theoretical results and suggest that alternative variants of the wild cluster bootstrap may perform quite differently the edgeworth expansions explain the overrejection of asymptotic tests and shed light on the choice of auxiliary distribution and whether to use restricted or unrestricted estimates in the bootstrap data generating process

hypothesis testing in linear models when the error covariance matrix is nonscalar a well developed exact statistical theory exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic in the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n in this paper higher order asymptotic expansions are developed for comparing the size and power of some common procedures for testing linear hypotheses on the regression coefficients in a class of generalized normal linear models the class investigated is essentially the same as in breusch 4 and magnus 6 and includes many of the examples of heteroscedasticity and autocorrelation discussed in the literature we assume simply that the regressors are nonrandom and that the error covariance matrix is a smooth function of a few parameters that can be efficiently estimated by maximum likelihood tests based on the wald likelihood ratio and lagrange multiplier principles are considered these principles lead to three tests which though distinct in finite samples are locally asymptotically equivalent and share certain asymptotic optimality properties of course there are infinitely many other tests that are asymptotically equivalent to the ones examined here although the techniques of this paper can be applied to any of them our results concern only the tests arising from the three traditional principles we show that to a second order of approximation under local alternatives the likelihood ratio test statistic is a simple average of the wald statistic and the lagrange multiplier statistic when the null hypothesis is one dimensional the three tests are to second order equally powerful that is after the critical regions are adjusted so that the tests have to order n i the same size the local power functions differ by terms of smaller order than n when the null hypothesis contains more than one

regression systems for unbalanced panel data a stepwise maximum likelihood procedure abstract the estimation of systems of regression equations with random individual effects from unbalanced panel data where the unbalance is due to random attrition or accretion by generalized least squares gls and maximum likelihood ml is considered in order to utilize the previous results for the balanced case it is convenient to arrange the individuals in groups according to the number of times they are observed it is shown that the gls estimator can be interpreted as a matrix weighted average of the group specific gls estimators with weights equal to the inverse of their respective covariance matrices a stepwise algorithm for solving the ml problem which can be interpreted as a compromise between the solution to the group specific ml problems is presented

separation of variables solutions of nonlinear reaction diffusion systems sign invariance plays an important role in the study of an explicit solution to single partial differential equations in this paper we extend the sign invariant theory to study the nonlinear reaction diffusion system as a consequence we obtain some new explicit solutions to the resulting systems and we illustrate the exact solutions for a nonlinear parabolic system

the unbalanced nested error component regression model abstract this paper considers a nested error component model with unbalanced data and proposes simple analysis of variance anova maximum likelihood mle and minimum norm quadratic unbiased estimators minque type estimators of the variance components these are natural extensions from the biometrics statistics and econometrics literature the performance of these estimators is investigated by means of monte carlo experiments while the mle and minque methods perform the best in estimating the variance components and the standard errors of the regression coefficients the simple anova methods perform just as well in estimating the regression coefficients these estimation methods are also used to investigate the productivity of public capital in private production

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

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

incomplete panels a comparative study of alternative estimators for the unbalanced one way error component regression model abstract this paper considers a one way error component regression model with unbalanced data and investigates by means of monte carlo experiments the performance of anova mle and mivque type estimators of the variance components some of the basic findings are the following 1 for the regression coefficients the computationally simple anova methods perform reasonably well when compared with the computationally involved mle and mivque methods 2 mle and mivque perform better than the anova methods in the estimation of the individual variance component especially for severely unbalanced patterns and large variance component ratio however for the remainder variance component there is nothing much to choose among these methods 3 better estimates of the variance components do not necessarily imply better estimates of the regression coefficients 4 making the data balanced by dropping observations worsens the performance of these estimators when compared to those from the entire unbalanced data

asymptotic theory for clustered samples abstract we provide a complete asymptotic distribution theory for clustered data with a large number of independent groups generalizing the classic laws of large numbers uniform laws central limit theory and clustered covariance matrix estimation our theory allows for clustered observations with heterogeneous and unbounded cluster sizes our conditions cleanly nest the classical results for i n i d observations in the sense that our conditions specialize to the classical conditions under independent sampling we use this theory to develop a full asymptotic distribution theory for estimation based on linear least squares 2sls nonlinear mle and nonlinear gmm