existence of infinitely many stationary solutions of the l 2 subcritical and critical nlse on compact metric graphs abstract we investigate the existence of stationary solutions for the nonlinear schrodinger equation on compact metric graphs in the l 2 subcritical setting we prove the existence of an infinite number of such solutions for every value of the mass in the critical regime the existence of infinitely many solutions is established if the mass is lower than a threshold value while global minimizers of the nls energy exist if and only if the mass is lower or equal to the threshold moreover the relation between this threshold and the topology of the graph is characterized the investigation is based on variational techniques and some new versions of gagliardo nirenberg inequalities

additive functional regression for densities as responses we propose and investigate additive density regression a novel additive functional regression model for situations where the responses are random distributions that can be viewed as random densiti

reference values obtained by kernel based estimation of quantile regressions in this paper we study the problem of estimating non parametrically a quantile regression curve as it applies to computing reference values we propose an automatic procedure that uses a symmetrized nearest neighbor kernel estimator of conditional distributions we also discuss ways of measuring the dispersion of quantile regression estimator one is based on the asymptotic distribution of such quantiles while the other relies on the bootstrap method the results of a small simulation study show that the methods of the paper perform rather well even in a situation where a good parametric solution is available as an example we analyze a small part of a data set that was collected to establish reference values for blood velocity in different parts of the umbilical cord of human fetuse as they grow toward birth

quantile smoothing splines summary although nonparametric regression has traditionally focused on the estimation of conditional mean functions nonparametric estimation of conditional quantile functions is often of substantial practical interest we explore a class of quantile smoothing splines defined as solutions to

a class of nonlinear schrodinger equations with concentrated nonlinearity abstract we consider the nonlinear schrodinger equation in dimension one with a nonlinearity concentrated in a finite number of points detailed results on the local existence of the solution in fractional sobolev spaces h are given we also prove the conservation of the l 2 norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space h 1 finally we prove the existence of blow up solutions for strongly attractive interaction

an adaptive composite quantile approach to dimension reduction sufficient dimension reduction li 1991 has long been a prominent issue in multivariate nonparametric regression analysis to uncover the central dimension reduction space we propose in this paper an adaptive composite quantile approach compared to existing methods 1 it requires minimal assumptions and is capable of revealing all dimension reduction directions 2 it is robust against outliers and 3 it is structure adaptive thus more efficient asymptotic results are proved and numerical examples are provided including a real data analysis

on the lack of bound states for certain nls equations on metric graphs abstract the purpose of this paper is to prove some results on the absence of bound states for certain nonlinear schrodinger equations on noncompact metric graphs with localized nonlinearity in particular we show how the topological and metric properties of graphs affect the existence nonexistence of bound states this work completes the discussion initiated in serra and tentarelli 2016 and tentarelli 2016

two stage rank estimation of quantile index models abstract this paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable this class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction thus allowing for very general forms of conditional heteroscedasticity a two stage approach is adopted to estimate the relevant parameters in the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in chaudhuri journal of multivariate analysis 39 1991a 246 269 annals of statistics 19 1991b 760 777 and cavanagh 1996 preprint in the second stage the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank based objective function the proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model

estimating conditional quantiles at the root of a regression function the robbins monro process x n 1 x n c n y n is a standard stochastic approximation method for estimating the root theta of an unknown regression function there is a vast literature on the convergence properties of x n to theta in practice one is also interested in the conditional distribution of the system under the sequential control when the control is set at theta or near theta this problem appears to have received no attention in the literature we introduce an estimator using methods of nonparametric conditional quantile estimation and derive its asymptotic properties

bound states of the nls equation on metric graphs with localized nonlinearities abstract we investigate the existence of multiple bound states of prescribed mass for the nonlinear schrodinger equation on a noncompact metric graph the main feature is that the nonlinearity is localized only in a compact part of the graph our main result states that for every integer k the equation possesses at least k solutions of prescribed mass provided that the mass is large enough these solutions arise as constrained critical points of the nls energy functional estimates for the energy of the solutions are also established

conditional empirical processes consider a sequence i xi yi i 1 of independent d 1 random vectors with common d f h text h left text x y right mathbb p left text x x y y right text left text x y right in mathbb r text d 1

a direct approach to inference in nonparametric and semiparametric quantile models we construct a generic confidence interval for a conditional quantile via the direct approach it avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile any conditional quantile estimator and any data structure provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator we also construct a generic confidence band for the conditional quantile function across a range of covariate values by using yang stute estimator and two semiparametric quantile functions we demonstrate the flexibility and simplicity of the direct approach the advantages of our new confidence intervals are borne out in a simulation study

regression rank scores estimation in anocova in semiparametric anocova mixed effects models the role of regression rank scores in robust estimation of fixed effects parameters as well as covariate regression functionals is critically appraised and the relevant asymptotic theory is presented

weak convergence of k nn density and regression estimators with varying k and applications on considere le probleme sous une condition de lissite du second ordre dans le cas unidimensionnel

reference curves based on non parametric quantile regression reference curves which take time into account such as those for age are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking classical methods are based on parametric fitting polynomial curves semi parametric methods are also widely used especially in europe here we propose a new methodology for the estimation of reference intervals for data sets based on non parametric estimation of conditional quantiles the derived methods should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale as an example we analyse a data set collected to establish reference curves for biophysical properties of the skin of healthy french women the results are compared to those obtained with royston s polynomial parametric method and the semi parametric lms approach

the matrix logarithmic covariance model abstract a flexible method is introduced to model the structure of a covariance matrix c and study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix a the matrix exponential transformation c exp a is a positive definite matrix because there is no constraint on the possible values of the upper triangular elements on a any possible structure of interest can be imposed on them the method presented here is not intended to replace the existing special models available for a covariance matrix but rather to provide a broad range of further structures that supplements existing methodology maximum likelihood estimation procedures are used to estimate the parameters and the large sample asymptotic properties are obtained a simulation study and two real life examples are given to illustrate the method introduced

computing kernel smoothed conditional quantiles from many observations abstract quantiles of a variable y conditional on another variable x when plotted against x can be a useful descriptive tool these plots give a quick impression of the functional form of the relation between x and the location spread and shape of the conditional distribution of y if several y are observed for each x then sample quantiles could be calculated for each x the resulting quantile plot may be quite noisy however and smoothing across x may be desired this article presents an algorithm that calculates kernel smoothed conditional quantiles with a cross validation choice of bandwidth for x it is computationally feasible for large data sets when x assumes a small number of values since it requires only one pass through the full data set the cross validation does not require a pass through the data because of simplifications arising from the l 1 loss function being based on absolute values the technique is illustrated by plotting the conditional quantiles of the net wealth of a sample of

uniqueness and non uniqueness of prescribed mass nls ground states on metric graphs abstract we consider the problem of uniqueness of ground states of prescribed mass for the nonlinear schrodinger energy with power nonlinearity on noncompact metric graphs we first establish that the lagrange multiplier appearing in the nls equation is constant on the set of ground states of mass up to an at most countable set of masses then we apply this result to obtain uniqueness of ground states on two specific noncompact graphs finally we construct a graph that admits at least two ground states with the same mass having different lagrange multipliers our proofs are based on careful variational arguments and rearrangement techniques and hold both for the subcritical range p 2 6 and in the critical case p 6

semiparametrically efficient inference based on signs and ranks for median restricted models since the pioneering work of koenker and bassett 1978 econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest contrary to the traditional models where the noise is assumed to have mean zero median restricted models enjoy a rich group invariance structure in this paper we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models these procedures are based on residual signs and ranks and therefore insensitive to possible misspecification of the underlying innovation density yet semiparametrically efficient at correctly specified densities this latter combination is a definite advantage of these procedures over classical quasi likelihood methods the techniques we propose can be applied without additional technical difficulties to both cross sectional and time series models they do not require any explicit tangent space calculation nor any projections on these

on average derivative quantile regression for fixed 0 1 the quantile regression function gives the th quantile x in the conditional distribution of a response variable y given the value x x of a vector of covariates it can be used to measure the effect of covariates not only in the center of a population but also in the upper and lower tails a functional that summarizes key features of the quantile specific relationship between x and y is the vector of weighted expected values of the vector of partial derivatives of the quantile function x in a nonparametric setting can be regarded as a vector of quantile specific nonparametric regression coefficients in survival analysis models e g cox s proportional hazard model proportional odds rate model accelerated failure time model and in monotone transformation models used in regression analysis gives the direction of the parameter vector in the parametric part of the model can also be used to estimate the direction of the parameter vector in semiparametric single index models popular in econometrics we show that under suitable regularity conditions the estimate of obtained by using the locally polynomial quantile estimate of chaudhuri 1991a is n 1 2 consistent and asymptotically normal with asymptotic variance equal to the variance of the influence function of the functional we discuss how the estimate of can be used for model diagnostics and in the construction of a link function estimate in general single index models

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

nls ground states on metric graphs with localized nonlinearities abstract we investigate the existence of ground states for the focusing subcritical nls energy on metric graphs with localized nonlinearities in particular we find two thresholds on the measure of the region where the nonlinearity is localized that imply respectively existence or nonexistence of ground states in order to obtain these results we adapt to the context of metric graphs some classical techniques from the calculus of variations

bivariate quantile smoothing splines it has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample we introduce bivariate quantile smoothing splines which belong to the space of bilinear tensor product splines as nonparametric estimators for the conditional quantile functions in a two dimensional design space the estimators can be computed by using standard linear programming techniques and can further be used as building blocks for conditional quantile estimations in higher dimensions for moderately large data sets we recommend penalized bivariate b splines as approximate solutions we use real and simulated data to illustrate the methodology proposed

efficient bias corrected nonparametric spectral estimation summary we consider estimation of a spectral density at a particular frequency a linear model is developed based on the local second order behaviour of kernel spectral estimates and a second stage estimate is derived from this model the estimate is shown to be asymptotically more efficient than the kernel estimate with the optimal but unknown bandwidth whenever the smoothing parameter is chosen so that it oversmooths the kernel estimate a small sample simulation study shows good characteristics of the second stage estimate practical implementation is discussed through examples

kernel and nearest neighbor estimation of a conditional quantile let x 1 z 1 x 2 z 2 x n z n be iid as x z and for 0 p 1 let p x denote the conditional p quantile of z given x x i e p z p x x x p kernel and near est neighbor estimators of p x are proposed in order to study the asymptotics of these estimates bahadur type representations of the sample conditional quantiles are obtained these representations are used to examine the important issue of choosing the smoothing parameter by a local approach for a fixed x based on weak convergence of these estimators the results lead to asymptotic linear models which motivate certain estimators