optimal tests for autoregressive models based on autoregression rank scores locally asymptotically optimal tests based on autoregression rank scores are constructed for testing linear constraints on the structural parameters of ar processes such tests are asymptotically distribution free and do not require the estimation of nuisance parameters they constitute robust flexible and quite powerful alternatives to existing methods such as the classical correlogram based parametric tests the gaussian lagrange multiplier tests the optimal non gaussian and ranked residual tests described by kreiss as well as to the aligned rank tests of hallin and puri optimality requires a nontrivial extension of existing asymptotic representation results to the case of unbounded score functions such as the gaussian quantile function the problem of testing ar p 1 against ar p dependence is considered as an illustration asymptotic local powers and asymptotic relative efficiencies are explicitly computed in the special case of van der waerden scores the asymptotic relative efficiency with respect to optimal correlogram based procedures is uniformly larger than one

weak convergence of some classes of martingales with jumps this paper deals with weak convergence of stochastic integrals with respect to multivariate point processes the results are given in terms of an entropy condition for partitioning of the index set of the integrands which is a sort of l 2 bracketing we also consider valued martingale difference arrays and present natural generalizations of jain marcus s and ossiander s central limit theorems as an application the asymptotic behavior of log likelihood ratio random fields in general statistical experiments with parameters is derived

quantile autoregression commentary we consider quantile autoregression qar models in which the autoregressive coefficients can be expressed as monotone functions of a single scalar random variable the models can capture systematic influences of conditioning variables on the location scale and shape of the conditional distribution of the response and thus constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a location shift the models may be interpreted as a special case of the general random coefficient autoregression model with strongly dependent coefficients statistical properties of the proposed model and associated estimators are studied the limiting distributions of the autoregression quantile process are derived qar inference methods are also investigated empirical applications of the model to the u s unemployment rate short term interest rate and gasoline prices highlight the model s potential

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 new integrable equation valued on a cayley dickson algebra we introduce a new integrable equation valued on a cayley dickson c d algebra in the particular case in which the algebra reduces to a complex one the new interacting term in the equation cancels and the equation becomes the known korteweg de vries kdv equation for each c d algebra the equation has an infinite sequence of local conserved quantities we obtain a backlund transformation in the sense of walhquist estabrook for the equation for any cayley dickson algebra and relate it to a generalized gardner equation from this the infinite sequence of conserved quantities follows directly we give the explicit expression for the first few from the backlund transformation we get the lax pair and the one soliton and two soliton solutions generalizing the known solutions for the quaternion valued kdv equation from the gardner equation we obtain the generalized modified kdv equation which also has an infinite sequence of conserved quantities the new integrable equation is preserved under a subgroup of the automorphisms of the c d algebra in the particular case of the algebra of octonions the equation is invariant under

simple resampling methods for censored regression quantiles abstract powell journal of econometrics 25 1984 303 325 journal of econometrics 32 1986 143 155 considered censored regression quantile estimators the asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably the difficulty may be avoided by applying the bootstrap method hahn econometric theory 11 1995 105 121 calculation of the estimators however requires solving a nonsmooth and nonconvex minimization problem resulting in high computational costs in implementing the bootstrap we propose in this paper computationally simple resampling methods by convexfying powell s approach in the resampling stage a major advantage of the new methods is that they can be implemented by efficient linear programming simulation studies show that the methods are reliable even with moderate sample sizes

goodness of fit and related inference processes for quantile regression abstract we introduce a goodness of fit process for quantile regression analogous to the conventional r2 statistic of least squares regression several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated the asymptotic behavior of the inference processes is shown to be closely related to earlier p sample goodness of fit theory involving bessel processes the approach is illustrated with some hypothetical examples an application to recent empirical models of international economic growth and some monte carlo evidence

propagation dynamics for a spatially periodic integrodifference competition model abstract in this paper we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat an interesting feature of such a system is that multiple spreading speeds can be observed which biologically means different species may have different spreading speeds we show that the model system admits a single spreading speed and it coincides with the minimal wave speed of the spatially periodic traveling waves a set of sufficient conditions for linear determinacy of the spreading speed is also given

nonparametric tests for conditional symmetry in dynamic models this article proposes omnibus tests for conditional symmetry around a parametric function in a dynamic context conditional moments may not exist or may depend on the explanatory variables test statistics are suitable functionals of the empirical process of residuals and explanatory variables whose limiting distribution under the null is nonpivotal the tests are implemented with the assistance of a bootstrap method which is justified assuming very mild regularity conditions on the specification of the center of symmetry and the underlying serial dependence structure finite sample properties are examined by means of a monte carlo experiment

a geometrical formulation of fermionic integrable systems a fermionic hamiltonian system is formulated on a supermanifold it is shown that if the system possesses a bi hamiltonian structure one can naturally define a lax equation associated with a 1 1 tensor on this supermanifold and this allows one to construct a set of conserved quantities furthermore if the corresponding nijenhuis tensor vanishes it is shown that all these conserved quantities would be in involution which is a sufficient condition for integrability of the system the fermionic extension of the kdv equation with a bi hamiltonian structure within this geometrical approach is studied

nonparametric estimation and inference on conditional quantile processes this paper presents estimation methods and asymptotic theory for the analysis of a nonparametrically specified conditional quantile process two estimators based on local linear regressions are proposed the first estimator applies simple inequality constraints while the second uses rearrangement to maintain quantile monotonicity the bandwidth parameter is allowed to vary across quantiles to adapt to data sparsity for inference the paper first establishes a uniform bahadur representation and then shows that the two estimators converge weakly to the same limiting gaussian process as an empirical illustration the paper considers a dataset from project star and delivers two new findings

a fully supersymmetric akns theory we construct a fully supersymmetric bihamiltonian theory in four superfields admitting zero curvature and lax formulation this theory is an extension of the classical akns which can be recovered as a reduction other supersymmetric theories are obtained as reductions of the susy akns namely a nonlinear schrodinger a modified kdv and the manin radul kdv the susy nonlinear schrodinger hierarchy is related to the one of roelofs and kersten we determine its bihamiltonian and lax formulation finally we show that the susy kdv s mentioned before are related through a susy miura map

on the nature of the gardner transformation it is shown that every higher korteveg de vries equation can be included in a one parameter family of integrable equations

a conditional kolmogorov test this paper introduces a conditional kolmogorov test of model specification for parametric models with covariates regressors the test is an extension of the kolmogorov test of goodness of fit for distribution functions the test is shown to have power against 1 n local alternatives and all fixed alternatives to the null hypothesis a parametric bootstrap procedure is used to obtain critical values for the test

travelling wave solutions of reduced super kdv equation a perspective from lame equation abstract reduced supersymmetric korteweg de vries super kdv equation is investigated in this paper with the help of an auxiliary lame equation and jacobi elliptic function travelling wave solutions of reduced super kdv equation are obtained in the form of jacobi elliptic periodic function meanwhile trigonal solutions and hyperbolic solutions are derived

markov chain marginal bootstrap markov chain marginal bootstrap mcmb is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of m estimators of linear regression the mcmb method distinguishes itself from the usual bootstrap methods in two important aspects it involves solving only one dimensional equations for parameters of any dimension and produces a markov chain rather than a conditionally independent sequence it is designed to alleviate computational burdens often associated with bootstrap in high dimensional problems the validity of mcmb is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

prolongation structures for supersymmetric equations the well known prolongation technique of wahlquist and estabrook 1975 for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the kdv equation of manin radul using the theory of kac moody lie superalgebras the explicit form of the resulting lie superalgebra is determined it is shown to be isomorphic to rmr cov c 2 sigma where rmr is an eight dimensional radical an auto backlund transformation is derived from the prolongation structure and the relationship with known solution methods of the skdv equation is analysed in addition it is indicated how a super position principle for the skdv equation can be obtained

estimation of semiparametric models when the criterion function is not smooth we provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated our results extend existing theories such as those of pakes and pollard 1989 andrews 1994a and newey 1994 we also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters we apply our results to two examples a hit rate and a partially linear median regression with some endogenous regressors

integrable system constructed out of two interacting superconformal fields we consider an interaction between superconformal fields of the same gradation this entails the construction of a supersymmetric poisson tensor for these fields generating a new class of hamiltonian systems the lax representation is found for one of them by supersymmetrizing the lax operator for the hirota satsuma equation the supersymmetric equation is not reducible to the classical hirota satsuma case we show that our generalized system can be reduced to the the supersymmetric kdv equation a 4 surprisingly the integrals of motion are not reduced to integrals of motion of the supersymmetric kdv equation

regression rank scores and regression quantiles we show that regression quantiles which could be computed as solutions of a linear programming problem and the solutions of the corresponding dual problem which we call the regression rank scores generalize the duality of order statistics and of ranks from the location to the linear model noting this fact we study the regression quantile and regression rank score processes in the heteroscedastic linear regression model obtaining some new estimators and interesting comparisons with existing estimators

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

on the bihamiltonian structure of the supersymmetric kdv hierarchies a lie superalgebraic approach we give a lie superalgebraic interpretation of the bihamiltonian structure of known supersymmetric kdv equations we show that the loop algebra of a lie superalgebra carries a natural poisson pencil and we subsequently deduce the bihamiltonian structure of the supersymmetric kdv hierarchies by applying to loop superalgebras an appropriate reduction technique this construction can be regarded as a superextension of the drinfeld sokolov method for building a kdv type hierarchy from a simple lie algebra

quantile regression under misspecification with an application to the u s wage structure quantile regression qr fits a linear model for conditional quantiles just as ordinary least squares ols fits a linear model for conditional means an attractive feature of ols is that it gives the minimum mean squared error linear approximation to the conditional expectation function even when the linear model is misspecified empirical research using quantile regression with discrete covariates suggests that qr may have a similar property but the exact nature of the linear approximation has remained elusive in this paper we show that qr minimizes a weighted mean squared error loss function for specification error the weighting function is an average density of the dependent variable near the true conditional quantile the weighted least squares interpretation of qr is used to derive an omitted variables bias formula and a partial quantile regression concept similar to the relationship between partial regression and ols we also present asymptotic theory for the qr process under misspecification of the conditional quantile function the approximation properties of qr are illustrated using wage data from the u s census these results point to major changes in inequality from 1990 to 2000

bistable travelling waves in competitive recursion systems abstract this paper is devoted to the study of spatial dynamics for a class of discrete time recursion systems which describes the spatial propagation of two competitive invaders the existence and global stability of bistable travelling waves are established for such systems under appropriate conditions the methods involve the upper and lower solutions spreading speeds of monostable systems and the monotone semiflows approach

the quantilogram with an application to evaluating directional predictability abstract we propose a new diagnostic tool for time series called the quantilogram the tool can be used formally and we provide the inference tools to do this under general conditions and it can also be used as a simple graphical device we apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability the test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value we provide the distribution theory needed to conduct inference propose some model free upper bound critical values and apply our methods to s p500 stock index return data the empirical results suggest some directional predictability in returns the evidence is strongest in mid range quantiles like 5 10 and for daily data the evidence for predictability at the median is of comparable strength to the evidence around the mean and is strongest at the daily frequency

an adaptive rate optimal test of linearity for median regression models this article is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness we develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate the test does not require knowledge of the distribution of the model s random noise component and it permits conditional heteroscedasticity of unknown form the numerical performance and usefulness of the test are illustrated by the results of monte carlo experiments and an empirical example

riemann liouville integrals of fractional order and extended kp hierarchy an attempt to formulate the extensions of the kp hierarchy by introducing fractional order pseudo differential operators is given in the case of the extension with the half order pseudo differential operators a system analogous to the supersymmetric extensions of the kp hierarchy is obtained unlike the supersymmetric extensions no grassmannian variable appears in the hierarchy considered here more general hierarchies constructed by the 1 nth order pseudo differential operators their integrability and the reduction procedure are also investigated in addition to finding the new extensions of the kp hierarchy a brief introduction to the riemann liouville integral is provided to yield a candidate for the fractional order pseudo differential operators

statistical inference for conditional quantiles in nonlinear time series models abstract this paper studies the statistical properties of a two step conditional quantile estimator in nonlinear time series models with unspecified error distribution the asymptotic distribution of the quasi maximum likelihood estimators and the filtered empirical percentiles is derived three applications of the asymptotic result are considered first we construct an interval estimator of the conditional quantile without any distributional assumptions second we develop a specification test for the error distribution finally using the specification test we propose methods for estimating the tail index of the error distribution that supports the construction of a new estimator for the conditional quantile at the extreme tail the asymptotic results and their applications are illustrated by simulations and real data analyses in which our methods for analyzing daily and intraday financial return series have been adopted

lack of fit tests for quantile regression models the paper novelly transforms lack of fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates accordingly by applying some successful two sample test statistics in the literature two tests are constructed to check the lack of fit for low and high dimensional quantile regression models the low dimensional test works well when the number of covariates is moderate whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size the null distribution of the high dimensional test has an explicit form and the p values or critical values can then be calculated directly the finite sample performance of the tests proposed is examined by simulation studies and their usefulness is further illustrated by two real examples

specification analysis of linear quantile models this paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels these tests may be applied to assess the validity of post estimation inferences regarding the effect of conditioning variables on the distribution of outcomes we show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure monte carlo evidence and an application to the empirical analysis of age earnings curves are included

fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation the fermionic covariant prolongation structure theory is investigated we extend the fermionic covariant prolongation structure technique to the multidimensional super nonlinear evolution equation and present the fermionic covariant fundamental equations determining the prolongation structure furthermore we investigate a 2 1 dimensional super nonlinear schrodinger equation and analyze its integrability by means of this prolongation structure technique we derive its lax representation and backlund transformation moreover we present a solution of this multidimensional super integrable equation

nonparametric model checks for time series this paper studies a class of tests useful for testing the goodness of fit of an autoregressive model these tests are based on a class of empirical processes marked by certain residuals the paper first gives their large sample behavior under null hypotheses then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free consistency of these tests is also discussed briefly

an operator valued extension of the super korteweg de vries equations an extension of the super korteweg de vries kdv integrable system in terms of operator valued functions is obtained following the ideas of gardner a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented the approach is applied to the above described system and infinitely many conserved quantities are constructed in a particular case they reduce to the corresponding conserved quantities of super kdv

specification tests of parametric dynamic conditional quantiles this article proposes omnibus specification tests of parametric dynamic quantile models in contrast to the existing procedures we allow for a flexible specification where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data generating process since the null limit distribution of tests is not pivotal we propose a subsampling approximation of the asymptotic critical values a monte carlo study shows that the asymptotic results provide good approximations for small sample sizes finally an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk

integrable fermionic extensions of the garnier system and the anharmonic oscillator we first derive a fermionic extension of the garnier system by applying the method of binary nonlinearization of spectral problem to the supersymmetric kdv equation of kupershmidt and then a fermionic extension of the anharmonic oscillator by a simple reduction the integrable properties of resulting systems such as lax representations corresponding r matrices and conversed integrals of motion are established

bootstrap methods for median regression models the least absolute deviations lad estimator for a median regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the lad objective function is not smooth this paper overcomes this problem by smoothing the objective function the smoothed estimator is asymptotically equivalent to the standard lad estimator with bootstrap critical values the rejection probabilities of symmetrical t and x 2 tests based on the smoothed estimator are correct through o n under the null hypothesis where 1 but can be arbitrarily close to 1 in contrast first order asymptotic approximations make errors of size o n these results also hold for symmetrical t and x 2 tests for censored median regression models

fitting an error distribution in some heteroscedastic time series models this paper addresses the problem of fltting a known distribution to the innovation distribution in a class of stationary and ergodic time series models the asymptotic null distribution of the usual kolmogorov smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution to overcome the dependence on the underlying model parameters we propose that tests be based on a vector of certain weighted residual empirical processes under the null hypothesis and under minimal moment conditions this vector of processes is shown to converge weakly to a vector of independent copies of a gaussian process whose covariance function depends only on the fltted distribution and not on the model under certain local alternatives the proposed test is shown to have nontrivial asymptotic power the monte carlo critical values of this test are tabulated when fltting standard normal and double exponential distributions the results obtained are shown to be applicable to garch and arma garch models the often used models in econometrics and flnance a simulation study shows that the test has satisfactory size and power for flnite samples at these models the paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions a result of independent interest

supersymmetric euler equations associated to the n 3 neveu schwarz algebra we give a systematic study about supersymmetric euler equations on the smooth dual nsreg n of the neveu schwarz algebra ns n for n 3 let a be the inertia operator and c1 c2 r we will show that the n 2 supersymmetric euler equation with a c1 c2d2 is local bi super hamiltonian with the freezing point c1 c2 nsreg 2 which is similar to that of the virasoro algebra ns 0 and the n 3 supersymmetric euler equation with a c2d3 1 is local bi super hamiltonian with the freezing point 0 c2 nsreg 3 which is similar to that of the n 1 neveu schwarz algebra ns 1

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

autoregression quantiles and related rank scores processes this paper develops extensions of the regression quantiles of koenker and bassett 1978 to autoregression it generalizes several results of jureckova 1992a and gutenbrunner and jureckova 1992 in linear regression to autoregression models in particular it gives the asymptotic uniform linearity of linear rank scores statistics based on residuals suitable in autoregression it also discusses the two types of l statistics appropriate in autoregression

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

spreading speeds and traveling waves for abstract monostable evolution systems abstract this paper is devoted to the development of the theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure under appropriate assumptions we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the dirichlet boundary condition a reaction diffusion model with a quiescent stage a porous medium equation in a tube and a lattice system in a periodic habitat

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

testing multivariate economic restrictions using quantiles the example of slutsky negative semidefiniteness abstract this paper is concerned with testing a core economic restriction negative semidefiniteness of the slutsky matrix we consider a system of nonseparable structural equations with infinite dimensional unobservables and employ quantile regression methods because they allow us to utilize the entire distribution of the data difficulties arise because the restriction involves several equations while the quantile is a univariate concept we establish that we may use quantiles of linear combinations of the dependent variable develop a new empirical process based test that applies kernel quantile estimators and investigate its finite and large sample behavior finally we apply all concepts to canadian microdata

n 4 super kdv hierarchy in n 4 and n 2 superspaces we present the results of further analysis of the integrability properties of the n 4 supersymmetric korteweg de vries kdv equation deduced earlier by two of us f delduc and e ivanov phys lett b 309 312 1993 as a hamiltonian flow on n 4 su 2 superconformal algebra in the harmonic n 4 superspace to make this equation and the relevant hamiltonian structures more tractable we reformulate it in the ordinary n 4 and further in n 2 superspaces in n 2 superspace it is represented by a coupled system of evolution equations for a general n 2 superfield and two chiral and antichiral superfields and involves two independent real parameters a and b we construct a few first bosonic conserved charges in involution of dimensions from 1 to 6 and show that they exist only for the following choices of the parameters i a 4 b 0 ii a 2 b 6 iii a 2 b 6 the same values are needed for the relevant evolution equations including n 4 kdv itself to be bi hamiltonian we demonstrate that the above three options are related via su 2 transformations and actually amount to the su 2 covariant integrability condition found in the harmonic superspace approach our results provide a strong evidence that the unique n 4 su 2 super kdv hierarchy exists upon reduction to n 2 kdv the above three possibilities cease to be equivalent they give rise to the a 4 and a 2 n 2 kdv hierarchies which thus prove to be different truncations of the single n 4 su 2 kdv one

on an abstract competition model and applications is a map such that the coordinates of f x x2 represent the population or population densities which have evolved from the state xi x2 at a fixed time later setting yi y2 f x x2 it is natural to suppose that an increase in x coupled with a decrease in x2 results in an increase in y and a decrease in y2 and symmetrically a decrease in x1 coupled with an increase in x2 results in a decrease in yr and an increase in yz we define an order in e x e2 as follows if x xi e e x2 xi e e x1 i xi and xi i x2 then we write x1 7 1 5 4 9 x

predictive density and conditional confidence interval accuracy tests abstract this paper outlines testing procedures for assessing the relative out of sample predictive accuracy of multiple conditional distribution models the tests that are discussed are based on either the comparison of entire conditional distributions or the comparison of predictive confidence intervals we also briefly survey existing related methods in the area of predictive density evaluation including methods based on the probability integral transform and the kullback leibler information criterion the procedures proposed in this paper are similar in many ways to andrews 1997 a conditional kolmogorov test econometrica 65 1097 1128 conditional kolmogorov test and to white s 2000 a reality check for data snooping econometrica 68 1097 1126 reality check in particular a predictive density test is outlined that involves comparing square approximation errors associated with models i i 1 n by constructing weighted averages over u of e f i u z t i f 0 u z t 0 2 where f 0 and f i are true and model i distributions u u and u is a possibly unbounded set on the real line a conditional confidence interval version of this test is also outlined and appropriate bootstrap procedures for obtaining critical values when predictions used in the formation of the test statistics are obtained via rolling and recursive estimation schemes are developed an empirical illustration comparing alternative predictive models for u s inflation is given for the predictive confidence interval test

misspecification testing in a class of conditional distributional models we propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates the test is based on the cramer von mises distance between an unrestricted estimate of the joint distribution function of the data and a restricted estimate that imposes the structure implied by the model the procedure is straightforward to implement is consistent against fixed alternatives has nontrivial power against local deviations of order n 1 2 from the null hypothesis and does not require the choice of smoothing parameters in an empirical application we use our test to study the validity of various models for the conditional distribution of wages in the united states

a new n 2 supersymmetric korteweg de vries equation there are two known integrable n 2 space supersymmetric extensions of the kdv equation both can be written as hamiltonian systems with a common poisson structure which corresponds to the n 2 supersymmetric form of the second kdv structure by analyzing the conservation laws of the one parameter family of equations that share this hamiltonian structure one finds that a third system is singled out by the existence of nontrivial conservation laws it is conjectured to be integrable

on n 3 super korteweg de vries equation a one parameter family is constructed of n 3 supersymmetric and so 3 symmetric extensions of the korteweg de vries kdv equation as a hamiltonian flow on a n 3 superconformal algebra and it is argued that it is nonintegrable for any choice of the parameter then a modified n 3 super kdv equation is proposed which possesses the higher order conserved quantities and so is a candidate for an integrable system upon reduction to n 2 it yields the recently discussed would be integrable version of the n 2 super kdv equation in the bosonic core it contains a coupled system of the kdv type equation and a three component generalization of the mkdv equation a hamiltonian formulation of the new n 3 super kdv equation as a flow on some contraction of the direct sum of two n 3 superconformal algebras is given

on the bi hamiltonian structures of the skdv the first and the second hamiltonian structures of the supersymmetric kdv equation are derived following the conventional approach of gel fand and dickey in particular it is shown that the nonlocal nature of the first bracket is a direct consequence of the constrained nature of the lax operator

an interior point algorithm for nonlinear quantile regression abstract a new algorithm for computing quantile regression estimates for problems in which the response function is nonlinear in parameters is described the nonlinear l 1 estimation problem is a special median case the algorithm is closely related to recent developments on interior point methods for solving linear programs performance of the algorithm on a variety of test problems including the censored linear quantile regression problem of powell 1986 is reported

integrability of the n 3 super kdv equation we obtain the lax pair for the n 3 supersymmetric and so 3 symmetric extensions of kdv equation by using the prolongation structure technique hence its integrability is proved

supersymmetric extension of the scalar born infeld equation in this paper a supersymmetric extension of the scalar born infeld equation is constructed through a superspace formalism which involves the addition of one independent fermionic grassmann variable to the existing bosonic spacetime coordinates the bosonic scalar field is replaced by a fermionic superfield which is composed of two component fields one bosonic and one fermionic the resulting equation is invariant under a space supersymmetric transformation and in its most general form involves four arbitrary parameters for a certain specific case the lie superalgebra of symmetries was identified and the one dimensional subalgebras were systematically classified into splitting and non splitting conjugate classes a number of group invariant solutions were obtained including polynomial solutions solutions by radicals and solitary waves including bumps kinks and doubly periodic solutions