testing additivity in generalized nonparametric regression models with estimated parameters we develop several kernel based consistent tests of an hypothesis of additivity in nonparametric regression we allow for discrete covariates and parameters estimated from a semiparametric gmm criterion function the additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for nonparametric estimators the asymptotic distribution of the parameter estimators are found we also derive the asymptotic distribution of the additivity test statistics under a sequence of local alternatives we give a ranking of the different tests based on local asymptotic power the practical performance is investigated through simulations based on the data set used in linton and hardle 1996

misclassification of the dependent variable in a discrete response setting abstract misclassification of dependent variables in a discrete response model causes inconsistent coefficient estimates when traditional estimation techniques e g probit or logit are used a modified maximum likelihood estimator that corrects for misclassification is proposed a semiparametric approach which combines the maximum rank correlation estimator of han 1987 journal of econometrics 35 303 316 with isotonic regression allows for more general forms of misclassification than the maximum likelihood approach the parametric and semiparametric estimation techniques are applied to a model of job change with two commonly used data sets the current population survey cps and the panel study of income dynamics psid

the existence of solitary wave solutions of delayed camassa holm equation via a geometric approach abstract this paper is concerned with the camassa holm equation which is a model for shallow water waves we first establish the existence of solitary wave solutions for the equation without delay and then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system especially the geometric singular perturbation theory and invariant manifold theory according to the relationship between solitary wave and homoclinic orbit the camassa holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution it is proved that the equation with disturbance also possesses homoclinic orbit and there exists solitary wave solution of the delayed camassa holm equation

on a shallow water model with the coriolis effect abstract in the present study an asymptotic model for wave propagation in shallow water with the effect of the coriolis force is derived from the governing equation in two dimensional flows the transport equation theory is then applied to investigate the local well posedness and wave breaking phenomena for this model the nonexistence of the camassa holm type peaked solution and classification of various traveling wave solutions to the new system are also established moreover it is shown that all the symmetric waves to this model are traveling waves

on the global existence and wave breaking criteria for the two component camassa holm system considered herein is a two component camassa holm system modeling shallow water waves moving over a linear shear flow a wave breaking criterion for strong solutions is determined in the lowest sobolev space hs s 32 by using the localization analysis in the transport equation theory moreover an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this sobolev space hs

on a shallow water approximation to the green naghdi equations with the coriolis effect abstract we consider an asymptotic 1d in space rotation camassa holm r ch model which could be used to describe the propagation of long crested shallow water waves in the equatorial ocean regions with allowance for the weak coriolis effect due to the earth s rotation this model equation has similar wave breaking phenomena as the camassa holm equation it is analogous to the rotation green naghdi r gn equations with the weak earth s rotation effect modeling the propagation of wave allowing large amplitude in shallow water we provide here a rigorous justification showing that solutions of the r gn equations tend to associated solution of the r ch model equation in the camassa holm regime with the small amplitude and the larger wavelength furthermore we demonstrate that the r gn model equations are locally well posed in a sobolev space by the refined energy estimates

on the blow up rate and the blow up set of breaking waves for a shallow water equation we consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation blow up can occur only in the form of wave breaking i e the solution remains bounded but its slope becomes unbounded in finite time a quite detailed description of the wave breaking phenomenon is given there is at least a point in general depending on time where the slope becomes infinite exactly at breaking time the precise blow up rate is established and for a large class of initial data we also determine the blow up set

on prediction and the power transformation family summary the power transformation family is often used for transforming to a normal linear model the variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated compared to when the transformation parameter is known we consider prediction of future untransformed observations when the data can be transformed to a linear model when the transformation must be estimated the prediction error is not much larger than when the parameter is known

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

a nonlocal shallow water model with the weak coriolis and equatorial undercurrent effects abstract we derive a quasilinear nonlocal shallow water model equation for moderate amplitude equatorial waves with effects of the weak coriolis force and equatorial undercurrent this mathematical modeling is analogous to the camassa holm approximation of the two dimensional incompressible and rotational euler equations in the equatorial region moreover we investigate the influences and interactions of the weak coriolis force caused by the earth rotation vorticity and nonlocal higher nonlinearities on the wave breaking phenomena in certain cases by applying the method of characteristics and extremal property of the solution to the riccati type differential inequality we demonstrate that wave breaking phenomena occur only depending on a shape of wave initially in the local spacial point

rank estimators for monotonic index models we present a new class of rank estimators of scaled coefficients in semiparametric monotonic linear index models the estimators require no subjective bandwidth choices and have attractive computational properties we establish n consistency and asymptotic normality and provide the general form and consistent estimators of the asymptotic covariance matrix we also provide a generalization covering single equation multiple indices models satisfying certain monotonicity constraints an analogue of consistency when all explanatory variables are categorical is established and an application is presented

tame algebras and tits quadratic forms abstract we solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated tits integral quadratic forms and derive some consequences

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

non uniform continuity of the solution map to the rotation two component camassa holm system abstract studied in this paper is the rotation two component camassa holm system which can be considered as a model for the propagation of long crested shallow water waves in the equatorial ocean regions with the weak coriolis effect due to the earth s rotation it is shown that the data to solution map is not uniformly continuous on both the line and the circle in certain sobolev spaces depending on the effect of the coriolis force and stretching balance parameters the non uniform dependence result is established by using the method of approximate solutions with refined energy estimates

wave breaking analysis for the periodic rotation two component camassa holm system abstract in this paper we study the blow up phenomenon of the initial boundary value problem for the periodic rotation two component camassa holm r2ch system the results include a precise blow up criterion when 0 and two new blow up statements and the exact blow up rate for strong solutions of the system

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

on the rotation two component camassa holm system modelling the equatorial water waves abstract in this paper a modified two component camassa holm system with the effect of the coriolis force in the rotating fluid is derived which is a model in the equatorial water waves the effects of the coriolis force caused by the earth s rotation and nonlocal nonlinearities on blow up criteria and wave breaking phenomena are then investigated our refined analysis relies on the method of characteristics and conserved quantities and is proceeded with the riccati type differential inequality finally conditions which guarantee the permanent waves are obtained by using a method of the lyapunov function

on the bootstrap of the maximum score estimator this paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator the theory developed also applies to other estimators within a cube root convergence class for some single parameter estimators in this class the results suggest a simple method for inference based upon the bootstrap

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

identification of binary response models abstract this article studies identification of the threshold crossing model of binary response most research on binary response has considered specific estimators and tests the study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods it also clarifies the connections between reduced form and structural analyses of binary response data assume that the binary outcome z is determined by an observable random vector x and by an unobservable scalar u through a model z 1 x u 0 also assume that fu x the probability distribution of u conditional on x is continuous and strictly increasing given these maintained assumptions we investigate the identifiability of given the following restrictions on the distributions fu x x x mean independence quantile independence index sufficiency statistical independence and statistical independence with the distribution known we find that mean independence has n

a test for anchoring and yea saying in experimental consumption data we analyze experimental survey data with a random split into respondents who get an open ended question on the amount of total family consumption with follow up unfolding brackets of the form is consumption x or more for those who answer don t know or refuse and respondents who are immediately directed to unfolding brackets in both cases the entry point of the unfolding bracket sequence is randomized allowing for any type of selection into answering the open ended or bracket questions a nonparametric test is developed for errors in the answers to the first bracket question that are different from the usual reporting errors that will also affect open ended answers two types of errors are considered explicitly anchoring and yea saying data are collected in the 1995 wave of the assets and health dynamics survey which is representative of the population in the united states that is 70 years and older we reject the joint hypothesis of no anchoring and no yea saying once yea saying is take

on the wave breaking phenomena and global existence for the periodic rotation two component camassa holm system abstract considered herein is the periodic rotation two component camassa holm system which can be derived from the f plane governing equations for the geophysical water waves with a constant underlying current the nonlocal nonlinearities on blow up criteria and wave breaking phenomena are established finally a sufficient condition for global solutions is obtained by using a method of the lyapunov function

robust estimation of generalized linear models with measurement errors this paper considers consistent estimation of generalized linear models with covariate measurement errors in contrast to the previous approach of assuming that measurement errors are normally distributed we make no distributional assumptions on the latent variables or the measurement errors using the results of li j econometrics 110 2002 1 on the nonparametric identification and estimation of the distribution of the latent variables when replicate measurements are available we propose to maximize the criterion based on an asymptotically corrected likelihood we show that such an estimator is consistent we also evaluate the finite sample performance of our estimator through a monte carlo study

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

on the cauchy problem for the shallow water model with the coriolis effect abstract in this paper we are concerned with an asymptotic model for wave propagation in shallow water with the effect of the coriolis force we first establish the local well posedness in a range of the besov spaces as well as the local well posedness in the critical space then we study the gevrey regularity of the shallow water model by using a generalized cauchy kovalevsky theorem which implies that the shallow water model admits analytical solutions locally in time and globally in space moreover we obtain a precise lower bound of the lifespan and the continuity of the solution finally working with moderate weight functions that are commonly used in time frequency analysis some persistence results to the shallow water model are illustrated

partial identification of probability distributions with misclassified data abstract this paper addresses the problem of data errors in discrete variables when data errors occur the observed variable is a misclassified version of the variable of interest whose distribution is not identified inferential problems caused by data errors have been conceptualized through convolution and mixture models this paper introduces the direct misclassification approach the approach is based on the observation that in the presence of classification errors the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations in which the coefficient matrix is the matrix of misclassification probabilities formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities such information can have strong identifying power the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest a method for estimating the identification regions and construct their confidence sets is given and illustrated with an empirical analysis of the distribution of pension plan types using data from the health and retirement study

a model for multinomial response error applied to labor flows abstract a model for the response error associated with reported categorical data is developed the model is used to construct estimators for the interior cells of a two way table with marginals subject to independent response error the estimation procedure is applied to the month to month table of employment status obtained from the u s current population survey

misclassification in binary choice models abstract bias from misclassification of binary dependent variables can be pronounced we examine what can be learned from such contaminated data first we derive the asymptotic bias in parametric models allowing misclassification to be correlated with observables and unobservables simulations and validation data show that the bias formulas are accurate in finite samples and in most situations imply attenuation second we examine the bias in a prototypical application erroneously restricting the covariance of misclassification and covariates aggravates the bias for all estimators we examine estimators that relax this restriction perform well if a model of misclassification or validation data is available

the global gevrey regularity of the rotation two component camassa holm system abstract in this paper we study the rotation two component camassa holm system which is a model in the equatorial water waves with the effect of the coriolis force we establish the global gevrey regularity of the rotation two component camassa holm system in gevrey class g with 1 in time our obtained result improves considerably the recent result in 45

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

how robust is the evidence on the effects of college quality evidence from matching we estimate the effects of college quality using propensity score matching methods and the national longitudinal survey of youth 1979 cohort matching allows us to relax the linear functional form assumption implicit in regression based estimates we also examine the support problem by determining whether there are individuals attending low quality colleges similar to those attending high quality colleges and find that the support condition holds only weakly thus the linear functional form plays an important role in regression based estimates and matching estimates have large standard errors point estimates from regression and matching are similar for men but not women

learning kernel logistic regression in the presence of class label noise the classical machinery of supervised learning machines relies on a correct set of training labels unfortunately there is no guarantee that all of the labels are correct labelling errors are increasingly noticeable in email protected s classification tasks as the scale and difficulty of these tasks increases so much that perfect label assignment becomes nearly impossible several algorithms have been proposed to alleviate the problem of which a robust kernel fisher discriminant is a successful example however for classification discriminative models are of primary interest and rather curiously the very few existing label robust discriminative classifiers are limited to linear problems in this paper we build on the widely used and successful kernelising technique to introduce a label noise robust kernel logistic regression classifier the main difficulty that we need to bypass is how to determine the model complexity parameters when no trusted validation set is available we propose to adapt the multiple kernel learning approach for this new purpose together with a bayesian regularisation scheme empirical results on 13 benchmark data sets and two real world applications demonstrate the success of our approach

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results

prediction and power transformations when the choice of power is restricted to a finite set abstract we study the family of power transformations proposed by box and cox 1964 when the choice of the power parameter is restricted to a finite set r the behavior of the box cox procedure is as anticipated in two extreme cases when the true parameter is an element of r and when is far from r we study the case in which 0 is close to r finding that the resulting methods can be very different from unrestricted maximum likelihood and that inferences may depend on the design the values of the regression parameters and the distance of to r

on the curvature blow up phenomena for the fokas qiao xia li equation abstract we study the blow up phenomena of the strong solutions for the fokas qiao xia li fqxl equation with quadratic and cubic nonlinearities which include the celebrated camassa holm equation and the fokas olver rosenau qiao forq equation as its special case the fqxl equation models the unidirectional propagation of the shallow water waves over a flat bottom and describes the physics more accurately than its celebrated counterpart the gardner equation two kinds of conditions on the initial data including cases where the initial momentum density is not of one sign are formulated to guarantee finite time blow up for the strong solutions for this equation the first condition relies on the sign persistence property of the momentum density m the second condition is based on the full use of the conservation laws of the equation especially the conservation quantity h 2 u 0

on weakly non negative unit forms and tame algebras in this paper we consider integral quadratic forms q ip z of the form q x 2i x i jqijx xj and call them unit forms such a unit form q is said to be weakly non negative if q x q whenever jt2 0 that is whenever x o for i 1 n our main purpose is to formulate a criterion for weak non negativity of unit forms this question arises in various areas of representation theory in connection with the characterization of tame representation type in the representation theory of quivers 17 6 partially ordered sets 18 19 certain classes of bimodules 8 23 1 3 and certain classes of algebras 20 14 24 16 for each of these structures q there is a unit form qn naturally attached to q such that the weak non negativity of qn is an equivalent or at least a necessary condition for q to be of tame representation type a class of algebras for which tame representation type is equivalent to the weak non negativity of the associated unit form is described in the last section of this paper a general criterion for weak non negativity using determinants was given by zeldich 28 see also 21 another criterion was obtained by de la pena 21 our approach is similar to that in 11 where we gave a characterization of weakly positive unit forms based on the classification of the critical forms let us recall some notions given a unit form q ip tl and a non empty subset ix im of 1 n we denote by qt the quadratic form qd where d z it maps the cth natural basis vector ek onto eik such a unit form q is called the restriction of q to we call a unit form q on ip a hypercritical form if q is weakly non negative for every proper subset 1 n though q itself is not in these terms a unit form q is weakly non negative if and only if q admits no hypercritical restriction so we have to classify the hypercritical forms in 1 we show that they can be obtained by certain elementary transformations from the unit forms naturally attached to the hyperbolic graphs of fig 1 on p 50 in particular there are only finitely many hypercritical forms however their number is large by a simple process we reduce the problem to the classification of the stretched hypercritical forms in 2 we show that except for a few of them these are of the shape q x q x xn xn ixn where q q n d is critical in a similar way the unit forms attached to the hyperbolic graphs am dm em correspond to those