nonparametric estimates of regression quantiles and their local bahadur representation let x y be a random vector such that x is d dimensional y is real valued and y theta x varepsilon where x and varepsilon are independent and the alpha th quantile of varepsilon is 0 alpha is fixed such that 0 0 and set r p m 2p d where m is a nonnegative integer smaller than p let t theta denote a derivative of theta of order m it is proved that there exists a pointwise estimate hat t n of t theta based on a set of i i d observations x 1 y 1 cdots s n y n that achieves the optimal nonparametric rate of convergence n r under appropriate regularity conditions further a local bahadur type representation is shown to hold for the estimate hat t n and this is used to obtain some useful asymptotic results

infinitely many solutions and least energy solutions for klein gordon maxwell systems with general superlinear nonlinearity abstract this paper is concerned with the following klein gordon maxwell system u v x u 2 u f x u x r 3 u 2 x r 3 where 0 is a constant v c r 3 r f c r 3 r r and f is superlinear at infinity using some weaker superlinear conditions instead of the common super cubic conditions on f we prove that the above system has 1 infinitely many solutions when v x is coercive and sign changing 2 a least energy solution when v x is positive periodic these results improve the related ones in the literature

on the distribution of a studentized quantile la variance asymptotique du quantile d echantillon depend de la valeur de la densite de population et du quantile de la population on considere l estimateur de siddiqui bloch gastwinth

singularly perturbed critical choquard equations abstract in this paper we study the semiclassical limit for the singularly perturbed choquard equation e 2 u v x u e 3 r 3 q y g u y x y d y q x g u in r 3 where 0 3 e is a positive parameter v q are two continuous real function on r 3 and g is the primitive of g which is of critical growth due to the hardy littlewood sobolev inequality under suitable assumptions on g we first establish the existence of ground states for the critical choquard equation with constant coefficients next we establish existence and multiplicity of semi classical solutions and characterize the concentration behavior by variational methods

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

positive solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x u p 1 u x r 3 k x u 2 x r 3 with p 3 5 assuming that a r 3 r and k r 3 r are nonnegative functions such that lim x a x a 0 lim x k x 0 and satisfying suitable assumptions but not requiring any symmetry property on them we prove the existence of positive solutions

optimal control of serial inventory systems with fixed replenishment intervals we consider a single item periodic review serial inventory production system with linear inventory holding and penalty costs to facilitate shipment consolidation and capacity planning we assume that the system has implemented fixed replenishment intervals each stage is allowed to order only at given equidistant times further for each stage except the most downstream one the replenishment interval is assumed to be an integer multiple of the replenishment interval of the next downstream stage this reflects the fact that the further upstream in a supply chain the higher setup times and costs tend to be and thus larger batches are desired our model with fixed replenishment intervals is a direct generalization of the serial model of clark and scarf 1960 for this generalized model we prove the optimality of base stock policies we derive newsboy equations for the optimal base stock levels and we describe an efficient exact solution procedure for the case with mixed erlang demands finally we present extensions to assembly systems and to systems with a modified fill rate constraint instead of backorder costs

iterated smoothed bootstrap confidence intervals for population quantiles this paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap t confidence intervals for population quantiles and establishes the optimal kernel bandwidths at various stages of the smoothing procedures the conventional smoothed bootstrap and bootstrap t methods have been known to yield one sided coverage errors of orders o n 1 2 and o n 2 3 respectively for intervals based on the sample quantile of a random sample of size n we sharpen the latter result to o n 5 6 with proper choices of bandwidths at the bootstrapping and studentization steps we show further that calibration of the nominal coverage level by means of the iterated bootstrap succeeds in reducing the coverage error of the smoothed bootstrap percentile interval to the order o n 2 3 and that of the smoothed bootstrap t interval to o n 58 57 provided that bandwidths are selected of appropriate orders simulation results confirm our asymptotic findings suggesting that the iterated smoothed bootstrap t method yields the most accurate coverage on the other hand the iterated smoothed bootstrap percentile method interval has the advantage of being shorter and more stable than the bootstrap t intervals

ground state solutions for generalized quasilinear schrodinger equations with variable potentials and berestycki lions nonlinearities by introducing some new tricks we prove that the following generalized quasilinear schrodinger equation div g2 u u g u g u u 2 v x u f u x rn admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a minimax characterization of the ground state energy our results improve and complement the previous ones in the literature by introducing some new tricks we prove that the following generalized quasilinear schrodinger equation div g2 u u g u g u u 2 v x u f u x rn admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a minimax characterization of the ground state energy our results improve and complement the previous ones in the literature

on nonlocal choquard equations with hardy littlewood sobolev critical exponents abstract we consider the following nonlinear choquard equation with dirichlet boundary condition u u 2 x y d y u 2 2 u f u in where is a smooth bounded domain of r n 0 n 3 0 n and 2 is the critical exponent in the sense of the hardy littlewood sobolev inequality under suitable assumptions on different types of nonlinearities f u we are able to prove some existence and multiplicity results for the equation by variational methods

ground state solutions for a class of choquard equations with potential vanishing at infinity abstract this paper is dedicated to studying the following nonlinear choquard equation u v x u r n q y f u y x y d y q x f u u d 1 2 r n where n 3 0 n v c r n 0 q c r n 0 f c r r and f t 0 t f s d s by combining the non nehari manifold approach with some new inequalities we prove that the above equation has a ground state solution in the case when v x 0 as x where the strict monotonicity condition on f is not required moreover by using perturbation method we obtain the existence of a least energy solution in the zero mass case i e v 0 where f satisfies the condition that f t 0 0 for some t 0 r instead of the usual ambrosetti rabinowitz type condition these results extend the ones in alves figueiredo and yang 2015 1 and some related literature

normalized solutions for schrodinger poisson equations with general nonlinearities abstract in this paper we prove the existence of normalized solutions to the following schrodinger poisson equation u x 1 u 2 u f u u x r 3 r where f c r r satisfies more general conditions which cover the case f u u q 2 u with q 3 10 3 10 3 6 especially some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently

fractional order statistic approximation for nonparametric conditional quantile inference abstract using and extending fractional order statistic theory we characterize the o n 1 coverage probability error of the previously proposed hutson 1999 confidence intervals for population quantiles using l statistics as endpoints we derive an analytic expression for the n 1 term which may be used to calibrate the nominal coverage level to get o n 3 2 log n 3 coverage error asymptotic power is shown to be optimal using kernel smoothing we propose a related method for nonparametric inference on conditional quantiles this new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations code is provided for both unconditional and conditional inference

bounded state solution of degenerate kirchhoff type problem with a critical exponent abstract in the present paper we investigate the following degenerate kirchhoff type problem b r n u 2 d x u v x u u 2 2 u in r n u d 1 2 r n where b is a positive constant v l n 2 r n is a given nonnegative function and 2 is the critical exponent quite a few papers have been published about the degenerate kirchhoff type problem with a critical exponent moreover this degenerate problem in r n n 5 has never been considered so far we obtain some sufficient conditions on the existence of bounded state solution for this degenerate problem as to the cases where n 5 it is the first time to consider the degenerate problem

improved quantile inference via fixed smoothing asymptotics and edgeworth expansion to estimate a sample quantile s variance the quantile spacing method involves smoothing parameter m when m n the corresponding studentized test statistic is asymptotically n 0 1 holding m fixed instead the asymptotic distribution contains the edgeworth expansion term capturing the variance of the quantile spacing consequently the fixed m distribution is more accurate than the standard normal under both asymptotic frameworks a testing optimal m is proposed to maximize power subject to size control in simulations the new method controls size better than similar methods while maintaining good power throughout are results for two sample quantile treatment effect inference code is available online

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

existence and concentration of ground state solutions for a critical nonlocal schrodinger equation in r2 we study the following singularly perturbed nonlocal schrodinger equation e2 u v x u e 2 1 x f u f u inr2 where v x is a continuous real function on r2 f s is the primitive of f s 0 2 and e is a positive parameter assuming that the nonlinearity f s has critical exponential growth in the sense of trudinger moser we establish the existence and concentration of solutions by variational methods

smoothed empirical likelihood confidence intervals for quantiles standard empirical likelihood confidence intervals for quantiles are identical to sign test intervals they have relatively large coverage error of size n 1 2 even though they are two sided intervals we show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order n 1 and may be bartlett corrected to produce intervals with an error of order only n 2 necessary and sufficient conditions on the smoothing parameter in order for these sizes of error to be attained are derived the effects of smoothing on the positions of endpoints of the intervals are analysed and shown to be only of second order

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

uniform confidence bands for functions estimated nonparametrically with instrumental variables abstract this paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables we show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed the asymptotic normality result holds in both mildly and severely ill posed cases we present methods to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values monte carlo experiments illustrate the finite sample performance of the uniform confidence band

optimal and heuristic echelon r nq t policies in serial inventory systems with fixed costs this paper studies a periodic review serial inventory system in which echelon r nq t policies are implemented under such a policy each stage reviews its inventory in every t period and orders according to an echelon r nq policy two types of fixed costs are considered one is associated with each order batch q and the other is incurred for each inventory review the objective is to find the policy parameters such that the average total cost per period is minimized this paper provides a method for obtaining heuristic and optimal policy parameters the heuristic is based on minimizing lower and upper bounds on the total cost function these total cost bounds which are separable functions of the policy parameters are obtained in two steps first we decompose the total cost into costs associated with each stage which include a penalty cost for holding inadequate stock second we construct lower and upper bounds for the penalty cost by regulating downstream policy parameters to find the optimal solution we further construct cost bounds for each echelon a subsystem that includes a stage and all of its downstream stages by regulating holding and backorder cost parameters the echelon lower bound cost functions as well as the stage cost bounds generate bounds for the optimal solution in a numerical study we find that the heuristic is near optimal when the ratio of the fixed cost to the holding cost at the most downstream stage is large we also find that changing the optimal batch sizes may not affect the optimal reorder intervals or equivalently the delivery schedules under some conditions

ground state solutions of pohozaev type and nehari type for a class of nonlinear choquard equations abstract in this paper we study the autonomous choquard equation u u i f u f u in r n where n 3 0 n i is a riesz potential and f c r r satisfies the general berestycki lions conditions in sec 2 combining constrained variational method with deformation lemma we obtain a ground state solution of pohozaev type for the above equation in sec 3 using non nehari manifold method we prove that the above equation has a ground state solution of nehari type the results improve some ones in 12

kernel smoothing to improve bootstrap confidence intervals summary some studies of the bootstrap have assessed the effect of smoothing the estimated distribution that is resampled a process usually known as the smoothed bootstrap generally the smoothed distribution for resampling is a kernel estimate and is often rescaled to retain certain characteristics of the empirical distribution typically the effect of such smoothing has been measured in terms of the mean squared error of bootstrap point estimates the reports of these previous investigations have not been encouraging about the efficacy of smoothing in this paper the effect of resampling a kernel smoothed distribution is evaluated through expansions for the coverage of bootstrap percentile confidence intervals it is shown that under the smooth function model proper bandwidth selection can accomplish a first order correction for the one sided percentile method with the objective of reducing the coverage error the appropriate bandwidth for one sided intervals converges at a rate of n 4 rather than the familiar n 115 for kernel density estimation applications of this same approach to bootstrap t and two sided intervals yield optimal bandwidths of order n 112 these bandwidths depend on moments of the smooth function model and not on derivatives of the underlying density of the data the relationship of this smoothing method to both the accelerated bias correction and the bootstrap t methods provides some insight into the connections between three quite distinct approximate confidence intervals

groundstates of nonlinear choquard equations existence qualitative properties and decay asymptotics we consider a semilinear elliptic problem delta u u i alpha ast abs u p abs u p 2 u quad text in r n where i alpha is a riesz potential and p 1 this family of equations includes the choquard or nonlinear schr odinger newton equation for an optimal range of parameters we prove the existence of a positive groundstate solution of the equation we also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point finally we derive the decay asymptotics at infinity of the groundstates

concentration and compactness in nonlinear schrodinger poisson system with a general nonlinearity in this paper we use a concentration and compactness argument to prove the existence of a nontrivial non radial solution to the nonlinear schrodinger poisson equations in r3 assuming on the nonlinearity the general hypotheses introduced by berestycki and lions

existence of semiclassical ground state solutions for a generalized choquard equation abstract in this paper we study a generalized quasilinear choquard equation e p p u v x u p 2 u e n r n q y f u y x y q x f u in r n where p is the p laplacian operator 1 p n v and q are two continuous real functions on r n 0 n f s is the primate function of f s and e is a positive parameter under suitable assumptions on p and f we establish a new concentration behavior of solutions for the quasilinear choquard equation by variational methods the results are also new for the semilinear case p 2

existence of groundstates for a class of nonlinear choquard equations we prove the existence of a nontrivial solution h n to the nonlinear choquard equation i in n where i is a riesz potential under almost necessary conditions on the nonlinearity in the spirit of berestycki and lions this solution is a groundstate if moreover is even and monotone on 0 then is of constant sign and radially symmetric

confidence intervals for partially identified parameters recently a growing body of research has studied inference in settings where parameters of interest are partially identified in many cases the parameter is real valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data for this case confidence intervals cis have been proposed that cover the entire identification region with fixed probability here we introduce a conceptually different type of confidence interval rather than cover the entire identification region with fixed probability we propose cis that asymptotically cover the true value of the parameter with this probability however the exact coverage probabilities of the simplest version of our new cis do not converge to their nominal values uniformly across different values for the width of the identification region to avoid the problems associated with this we modify the proposed ci to ensure that its exact coverage probabilities do converge uniformly to their nominal values we motivate this modified ci through exact results for the gaussian case

ground state solutions of schrodinger poisson systems with variable potential and convolution nonlinearity abstract in the present paper we consider the following nonlinear schrodinger poisson system with convolution nonlinearity u v x u u i f u f u x r 3 u 2 x r 3 where 0 3 i r 3 r is the riesz potential v c r 3 0 f c r r and f t 0 t f s d s satisfies lim t f t t with min 2 6 4 by using some new analytic techniques and new inequalities we prove the above system admits a ground state solution under mild assumptions on v and f in particular our results cover and improve the existing ones for the schrodinger poisson system which can be considered as the limited problem when 0

analysis of a two echelon inventory control system with complete redistribution this paper examines a two level distribution system consisting of a central warehouse cw supplying several branch warehouses bw s which in turn supply normally distributed customer demands in a periodic review environment the cw replenishes system inventory using a base stock replenishment policy and a predetermined order cycle of h time periods i e every h periods the cw orders enough from an outside supplier to bring the systemwide inventory position to a certain level to be determined based on a given minimum level of customer service upon receipt of this order the cw allocates it entirely to the bw s so as to minimize the expected total units short at the bw s this simple allocation scheme may of course lead to out of balance bw inventories towards the end of the cw s order cycle hence redistribution during the cycle should be considered the redistribution treated here is a complete redistribution of all bw inventories one period before the end of the order cycle approximate formulas are derived which allow for a comparison of the system wide inventories appropriate to each of two allocation schemes 1 the simple allocation scheme only and 2 the simple allocation scheme with total redistribution one period before the end of the order cycle limited computational tests indicate the magnitude of the improvements possible with total redistribution and the sensitivities of these improvements to model parameters

calibrated interpolated confidence intervals for population quantiles beran hall s 1993 simple linear interpolation provides a very convenient approach for constructing nonparametric confidence intervals for population quantiles based on a random sample of size n we show that the coverage error of the interpolated interval which is of order o n 1 can be improved upon by calibrating the nominal coverage level three distinct methods of calibration are considered the analytical and monte carlo methods succeed in reducing the order of coverage error to o n 3 2 while the smoothed bootstrap method reduces it further to o n 25 14 we provide guidelines for practical implementation of the calibration methods their performance is compared with the simple linear interpolated interval in a simulation study which confirms superiority of the calibrated intervals

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