set identification via quantile restrictions in short panels this paper studies the identifying power of conditional quantile restrictions in short panels with flxed efiects in contrast to classical flxed efiects models with conditional mean restrictions conditional quantile restrictions are not preserved by taking difierences in the regression equation over time this paper shows however that a conditional quantile restriction in conjunction with a weak conditional independence restriction provides bounds on quantiles of difierences in time varying unobservables across periods these bounds carry observable implications for model parameters which generally result in set identiflcation the analysis of these bounds includes conditions for point identiflcation of the parameter vector as well as weaker conditions that result in identiflcation of individual parameter components

limiting distributions for l sb 1 regression estimators under general conditions it is well known that l 1 estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0 in this paper we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0

global existence and blow up of solutions to a nonlocal quasilinear degenerate parabolic system abstract this paper investigates the properties of nonnegative solutions of a quasilinear degenerate parabolic system u t div u p 2 u a v x t d x v t div v q 2 v b u x t d x with zero dirichlet boundary conditions in a smooth bounded domain r n n 1 where p q 2 1 and a b 0 are positive constants under appropriate hypotheses we first establish the local existence and uniqueness of solutions then we show that whether or not the solution blows up in finite time depends on the initial data and the relations between and p 1 q 1 in the special case of q 1 and p 1 we conclude that the solution exists globally if p 1 d x q 1 d x 1 a b while if p 1 d x q 1 d x 1 a b then the solution blows up in finite time here x and x denote the unique solution of the following elliptic problem div p 2 1 in x 0 and div q 2 1 in x 0 respectively

quantal problems with partial algebraization of the spectrum we discuss a new class of spectral problems discovered recently which occupies an intermediate position between the exactly solvable problems e g harmonic oscillator and all others the problems belonging to this class are distinguished by the fact that a part of the eigenvalues and eigenfunctions can be found algebraically but not the whole spectrum the reason explaining the existence of the quasi exactly solvable problems is a hidden dynamical symmetry present in the hamiltonian for one dimensional motion this hidden symmetry issl 2 r it is shown that other groups lead to a partial algebraization in multidimensional quantal problems in particular sl 2 r sl 2 r so 3 andsl 3 r are relevant to two dimensional motion inducing a class of quasi exactly solvable two dimensional hamiltonians typically they correspond to systems in a curved space but sometimes the curvature turns out to be zero graded algebras open the possibility of constructing quasi exactlysolvable hamiltonians acting on multicomponent wave functions for example with a non minimal superextension ofsl 2 r we get a hamiltonian describing the motion of a spinor particle

extinction properties of solutions for a class of fast diffusive p laplacian equations abstract we consider the extinction properties of solutions for the homogeneous dirichlet boundary value problem for the p laplacian equation u t div u p 2 u u q u r with 1 p 2 q 1 and r 0 for 0 it is known that r p 1 is the critical extinction exponent for the weak solution for 0 we show that r p 1 is still the critical extinction exponent when q 1 moreover the precise decay estimates of solutions before the occurrence of the extinction are derived however extinction can always occur when 0 q r 1

inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

a note on blow up of solutions of a quasilinear heat equation with vanishing initial energy abstract in this work we consider an initial boundary value problem related to the equation u t div u m 2 u f u and prove under suitable conditions on f a blow up result for solutions with vanishing or negative initial energy

a complete characterization of the discrete p laplacian parabolic equations with q nonlocal reaction with respect to the blow up property abstract in this paper we consider the following discrete p laplacian nonlinear parabolic equations with q nonlocal reaction u t x t p u x t y s u y t q 1 u y t x t s 0 u x t 0 x t s 0 u x 0 u 0 0 x s here s is a network with boundary s the goal of this paper is to characterize completely the parameters p 1 and q 0 to see when the solution blows up vanishes or exists globally indeed the blow up rates for the blow up solutions are derived

estimating and testing a quantile regression model with interactive effects this paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables we provide conditions under which the slope parameter estimator is asymptotically gaussian monte carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate meth ods we discuss an approach to testing the model specification against a competing fixed effects specification the paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment the findings show that i a change in the gender composition of a class impacts differently low and high performing students ii while smaller classes are beneficial for low performers larger classes are beneficial for high performers iii reductions in class size do not seem to impact mean and median student performance iv the fixed effects specification is rejected in favor of the interactive effects specification

singular and degenerate anisotropic parabolic equations with a nonlinear source abstract the dirichlet problem in arbitrary domain for degenerate and singular anisotropic parabolic equations with a nonlinear source term is considered we state conditions that guarantee the existence and uniqueness of a global weak solution to the problem a similar result is proved for the parabolic p laplace equation

conservation laws and symmetries of radial generalized nonlinear p laplacian evolution equations abstract a class of generalized nonlinear p laplacian evolution equations is studied these equations model radial diffusion reaction processes in n 1 dimensions where the diffusivity depends on the gradient of the flow for this class all local conservation laws of low order and all lie symmetries are derived the physical meaning of the conservation laws is discussed and one of the conservation laws is used to show that the nonlinear equation can be mapped invertibly into a linear equation by a hodograph transformation in certain cases the symmetries are used to derive exact group invariant solutions from solvable three dimensional subgroups of the full symmetry group which yields a direct reduction of the nonlinear equation to a quadrature the physical and analytical properties of these exact solutions are explored some of which describe moving interfaces and green s functions

tests of linear hypotheses and l 1 estimation statistics of a linear hypothesis in the standard linear model these test statistics which correspond to wald likelihood ratio and lagrange multiplier tests are shown to have the same limiting chi square behavior under mild regularity conditions on design and the distribution of errors the asymptotic theory of the tests is derived for a large class of error distributions thus in huber s 10 terminology we investigate the behavior of the likelihood ratio test under non standard conditions the asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly gaussian errors but may yield large efficiency gains in non gaussian situations the lagrange multiplier test seems particularly attractive from a computational standpoint we derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis extension of these results to hypotheses of the form r 8 r is a straightforward exercise when the density of the error distribution is strictly positive at the median all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null when the variance of the error distribution is bounded analogous results are well known for classical forms of the wald likelihood ratio and lagrange multipler tests based on least squares methods see for example silvey 18 and the discussion in section 4 below

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

global existence and blow up solutions for doubly degenerate parabolic system with nonlocal source abstract this paper deals with the following nonlocal doubly degenerate parabolic system u t div u m p 2 u m a u 1 x t v 1 x t d x v t div v n q 2 v n b u 2 x t v 2 x t d x with null dirichlet boundary conditions in a smooth bounded domain r n where m n 1 p q 2 i i 0 i 1 2 and a b 0 are positive constants we first get the non existence result for a related elliptic systems of non increasing positive solutions secondly by using this non existence result blow up estimates for above non newton polytropic filtration systems with the homogeneous dirichlet boundary value conditions are obtained then under appropriate hypotheses we establish local theory of the solutions and prove that the solution either exists globally or blows up in finite time in the special case 1 n q 1 2 2 m p 1 1 we also give a criterion for the solution to exist globally or blow up in finite time which depends on a b and x x as defined in the main results

a generalized jaynes cummings hamiltonian and supersymmetric shape invariance a class of shape invariant bound state problems which represent two level systems are introduced it is shown that the coupled channel hamiltonians obtained correspond to the generalization of the jaynes cummings hamiltonian

on global attractor for m laplacian parabolic equation with local and nonlocal nonlinearity abstract in this paper we study the long time behavior of solutions for m laplacian parabolic equation u t m u a x u u f 0 u k y u y t d y g x in 0 with the initial data u x 0 u 0 x l q q 1 and zero boundary condition in two cases for a x a 0 0 and a x 0 are considered we obtain the existence and l p estimate of global attractor a in l p for any p max 1 q the attractor a is in fact a bounded set in w 0 1 m l if a x a 0 0 in and a is bounded in w 0 1 m l p if a x 0 in

p laplacian with a concentrated nonlinear source abstract in this paper we consider the cauchy problem for the p laplacian with a concentrated nonlinear source we obtain the existence of the generalized solutions for the problem based on some a priori estimates on solutions

a new condition for the concavity method of blow up solutions to p laplacian parabolic equations abstract in this paper we consider an initial boundary value problem of the p laplacian parabolic equation u t x t div u x t p 2 u x t f u x t x t 0 u x t 0 x t 0 u x 0 u 0 0 x where p 2 and is a bounded domain of r n n 1 with smooth boundary the main contribution of this work is to introduce a new condition c p 0 u f s d s u f u u p u 0 for some 0 with 0 p 1 p p where 1 p is the first eigenvalue of p laplacian p and we use the concavity method to obtain the blow up solutions to the above equations in fact it will be seen that the condition c p improves the conditions ever known so far

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

asymptotics for panel quantile regression models with individual effects this paper studies panel quantile regression models with individual fixed effects we formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals n and the number of time periods t jointly go to infinity the estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature nevertheless due to the non smoothness of the objective function we had to impose a more restrictive condition on t to prove asymptotic normality than that usually found in the literature the finite sample performance of the estimator is evaluated by monte carlo simulations

global and blow up solutions to a p laplacian equation with nonlocal source this paper deals with a p laplacian equation ut div u p 2 u uq x t dx with null dirichlet boundary conditions in a bounded domain rn where p 2 q 1 under appropriate hypotheses we establish local theory of the solution and obtain that the solution either exists globally or blows up in finite time

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

the problem of dirichlet for evolution one dimensional p laplacian with nonlinear source in the present paper we consider the dirichlet problem for one dimensional p laplacian with nonlinear source we obtain new a priori estimates of a solution and of the gradient of a solution and formulate conditions guaranteeing the global solvability of this problem our consideration includes singular case as well

estimation of censored quantile regression for panel data with fixed effects this article investigates estimation of censored quantile regression qr models with fixed effects standard available methods are not appropriate for estimation of a censored qr model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity motivated by these limitations the article proposes estimators that are obtained by applying fixed effects qr to subsets of observations selected either parametrically or nonparametrically we derive the limiting distribution of the new estimators under joint limits and conduct monte carlo simulations to assess their small sample performance an empirical application of the method to study the impact of the 1964 civil rights act on the black white earnings gap is considered supplementary materials for this article are available online

global existence and blow up of solutions to an evolution p laplace system coupled via nonlocal sources abstract the aim of this paper is to investigate the behavior of positive solutions to the following system of evolution p laplace equations coupled via nonlocal sources u t u x p 1 1 u x x 0 a v m 1 t d x t in 0 a 0 t v t v x p 2 1 v x x 0 a u m 2 t d x t in 0 a 0 t with nonlinear boundary conditions u x x 0 0 u x x a u q 11 v q 12 x a v x x 0 0 v x x a u q 21 v q 22 x a and the initial data u 0 v 0 where p 1 p 2 1 m 1 m 2 q 11 q 12 q 21 q 22 0 under appropriate hypotheses the authors first prove a local existence result by a regularization method then the authors discuss the global existence and blow up of positive weak solutions by using a comparison principle

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

the extinction versus the blow up global and non global existence of solutions of source types of degenerate parabolic equations with a singular absorption abstract we consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term t u u x p 2 u x x u u 0 f u x t in i 0 t with the homogeneous zero boundary condition on i x 1 x 2 an open bounded interval in r through this paper we assume that p 2 and 0 1 to show the local existence result we prove first a sharp pointwise estimate for u x one of our main goals is to analyze conditions on which local solutions can be extended to the whole time interval t 0 the so called global solutions or by the contrary a finite time blow up 0 0 arises such that lim t 0 u t l i moreover we prove that any global solution must vanish identically after a finite time if provided that either the initial data or the source term is small enough finally we show that the condition f 0 x t 0 x t i 0 is a necessary and sufficient condition for the existence of solution of equations of this type

exact solution of an n body problem in one dimension two comments we comment on a recent paper which presents two rather remarkable statements on the quantum mechanical one dimensional problem of n equal mass particles interacting via the potential we point out that the first statement concerning the bound state spectrum is the special case corresponding to the coulomb potential of a more general result valid for any radial potential v r while the second statement concerning the scattering regimes does not hold

conditional quantile regression models of melanoma tumor growth curves for assessing treatment effect in small sample studies tumor growth curves provide a simple way to understand how tumors change over time the traditional approach to fitting such curves to empirical data has been to estimate conditional mean regression functions which describe the average effect of covariates on growth however this method ignores the possibility that tumor growth dynamics are different for different quantiles of the possible distribution of growth patterns furthermore typical individual preclinical cancer drug study designs have very small sample sizes and can have lower power to detect a statistically significant difference in tumor volume between treatment groups in our work we begin to address these issues by combining several independent small sample studies of an experimental cancer treatment with differing study designs to construct quantile tumor growth curves for modeling we use a penalized fixed effects quantile regression with added study effects to control for study differences we demonstrate this approach using data from a series of small sample studies that investigated the effect of a naturally derived biological peptide p28 on tumor volumes in mice grafted with human melanoma cells we find a statistically significant quantile treatment effect on tumor volume trajectories and baseline values in particular the experimental treatment and a corresponding conventional chemotherapy had different effects on tumor growth by quantile the conventional treatment dacarbazine dtic tended to inhibit growth for smaller quantiles while the experimental treatment p28 produced slower rates of growth in the upper quantiles especially in the 95th quantile copyright 2014 john wiley sons ltd

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

blow up versus extinction in a nonlocal p laplace equation with neumann boundary conditions abstract this paper studies a fast diffusive p laplace equation with the nonlocal source u q u q d x in a bounded domain subject to homogeneous neumann boundary value condition a critical criterion is determined that the changing sign solutions blow up in finite time with q 1 and non positive initial energy associated and must be global for any initial energy if q 1 in particular the conditions are obtained under which the changing sign solutions vanish in finite time

support properties of solutions to a degenerate equation with absorption and variable density abstract in this paper we study the properties of solutions to a degenerate parabolic equation with variable density and absorption we first obtain a critical exponent which distinguishes the localization of solutions from the positivity of them when positivity prevails we obtain the other critical exponent with respect to the decay of the variable density which separates the global existence of interfaces from the disappearance of them moreover the long time behavior of interfaces is characterized

a complete characterization of nonlinear absorption for the evolution p laplacian equations to have positive or extinctive solutions this paper is concerned with long time behaviors of solutions to the initial boundary value problem of the evolution p laplacian equations with nonlinear absorption a long time behavior of solutions to these equations has been studied so far for particular types of nonlinear absorption term the purpose of this paper is to give a complete characterization of the nonlinear absorption term according to the parameter p in p laplacian operator and the growth of the nonlinear absorption term near the origin in order to determine whether the solution to the equations is extinctive or positive in addition we also give upper bounds for extinction times of solutions

liouville type results for a class of quasilinear parabolic problems the aim of this paper is to study the properties of positive solutions to the nonlinear diffusion equation with a nonlinear bistable source we show that there exists a universal a priori upper bound for all positive solutions moreover under some assumptions we prove the convergence of these solutions to a constant if t

some algebraically solvable three body problems in one dimension the three body problem in one dimension with a repulsive inverse square potential between every pair was solved by calogero after mapping the three body problem to that of a particle on a plane the known results of supersymmetric quantum mechanics are used to solve this problem as well as a number of new ones algebraically this general technique is applicable when the potential is separable in the radial and angular variables on the plane and its supersymmetric partner is shape invariant after discussing one example in detail an exhaustive list of such exactly solvable potentials is given

quantum dynamics of a two level system coupled to a shape invariant potential the quantum dynamics of a two level system coupled to a shape invariant potential is investigated shape invariant potentials share an integrability condition called shape invariance which identifies an underlying algebraic structure in general infinite dimensional that transforms the potential parameters such as strength range and diffuseness we determine the time evolution operator the density operator of the system and obtain the temporal behaviour of various dynamical variables by considering either pure or mixed initial states of the system constructed with the generalized coherent state of the shape invariant coupling potential we consider specific examples of shape invariant coupling potentials harmonic oscillator poschl teller and self similar potentials the results obtained for all dynamical variables exhibit rapid oscillations which periodically collapse and regenerate in different ways depending on the coupling potential nature

global existence and blow up solutions and blow up estimates for a non local quasilinear degenerate parabolic system this paper deals with p laplacian systems ut div u p 2 u a u 1 x t v 1 x t dx x t 0 vt div v q 2 v b u 2 x t v 2 x t dx x t 0 with null dirichlet boundary conditions in a smooth bounded domain rn where p q 1 i i 0 i 1 2 and a b 0 are positive constants we first get the non existence result for a related elliptic systems of non increasing positive solutions secondly by using this non existence result blow up estimates for above p laplacian systems with the homogeneous dirichlet boundary value conditions are obtained under br x rn x 0 then under appropriate hypotheses we establish local theory of the solutions and obtain that the solutions either exists globally or blow up in finite time

a study of new solvable few body problems we study new solvable few body problems consisting of generalizations of the calogero and the calogero marchioro wolfes three body problems by introducing non translationally invariant three body potentials after separating the radial and angular variables by appropriate coordinate transformations we provide eigensolutions of the schrodinger equation with the corresponding energy spectrum we found a domain of the coupling constant for which the irregular solutions are square integrable

extinction and non extinction for a p laplacian equation with nonlinear source abstract in this paper we deal with the extinction of solutions of the initial boundary value problem of the p laplacian equation u t div u p 2 u u q in a bounded domain of r n with n 2 for 1 p 2 we show that q p 1 is the critical exponent of extinction for the weak solution furthermore for 1 p 2 and q p 1 we prove that the extinction and non extinction of the solution depends strongly on the first eigenvalue of the problem div p 2 p 2 in 0

the blowup property of solutions to some diffusion equations with localized nonlinear reactions abstract in this paper we investigate the blowup property of solutions to the equation u t u u x 0 t where x0 is a fixed point in the domain we show that under certain conditions the solution blows up in finite time moreover we prove that the set of all blowup points is the whole region furthermore the growth rate of solutions near the blowup time is also derived finally the results are generalized to the following nonlocal reaction diffusion equation u t u u dx

connection between the spectrum and the moments of the ground state density in n dimensional space we show that a series of recurrent inequalities derived in n 3 have the same formal expressions in any dimension n 2 they are derived from the multipole sum rules and provide us with upper bounds for the moments of the ground state density depending only on the lowest multipole excitation energy these bounds are transformed into approximate recurrent relations by means of an empirical correction factor the 1 r potential and the harmonic oscillator play a key role in establishing this factor which is exact for these two potentials by construction for a large class of potentials we show that this factor tends to 1 as n in such cases at the large n limit the lowest state for each multipole excitation exhausts the sum rule it thus acquires the characteristics of the one phonon excitation typical of the harmonic oscillator

network and panel quantile effects via distribution regression abstract this paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two way effects strictly exogenous covariates and possibly discrete outcome variables the method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators these fixed effects estimators are debiased to deal with the incidental parameter problem under asymptotic sequences where both dimensions of the data set grow at the same rate the confidence bands for the quantile functions and effects have correct joint coverage in large samples an empirical application to gravity models of trade illustrates the applicability of the methods to network data

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

panel data quantile regression with grouped fixed effects abstract this paper introduces estimation methods for grouped latent heterogeneity in panel data quantile regression we assume that the observed individuals come from a heterogeneous population with a finite number of types the number of types and group membership is not assumed to be known in advance and is estimated by means of a convex optimization problem we provide conditions under which group membership is estimated consistently and establish asymptotic normality of the resulting estimators simulations show that the method works well in finite samples when t is reasonably large

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

a gradient estimate to a degenerate parabolic equation with a singular absorption term the global quenching phenomena we prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term we also show the global quenching phenomena for l1 initial datums moreover the free boundary problem is considered in this paper

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

hierarchical spline models for conditional quantiles and the demand for electricity abstract methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of koenker and bassett spline parameterizations of the conditional quantile functions are used the methods are illustrated by estimating hierarchical models for household electricity demand using data from the chicago metropolitan area the empirical results show that lower quantiles of demand base load vary only slightly across residential households this variability is difficult to explain using household characteristics however upper quantiles of the demand distribution vary considerably and are systematically related to household characteristics and appliance ownership the implications of analyzing mean demand behavior rather than various quantiles of the distribution of demand are also discussed

quantile regression for dynamic panel data with fixed effects abstract this paper studies a quantile regression dynamic panel model with fixed effects panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors to reduce the dynamic bias we suggest the use of the instrumental variables quantile regression method of chernozhukov and hansen 2006 along with lagged regressors as instruments in addition we describe how to employ the estimated models for prediction monte carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias and the empirical levels for prediction intervals are very close to nominal levels finally we illustrate the procedures with an application to forecasting output growth rates for 18 oecd countries