a proposal for a residual autocorrelation test in linear models summary this note proposes a test of goodness of fit for time series models based on the sum of the squared residual partial autocorrelations the test statistic is asymptotically x2 its small sample performance is studied through a monte carlo experiment it appears sensitive to erroneous specifications especially when the fitted model understates the order of the moving average component residual analysis is a fundamental step in building empirical time series models when checking the adequacy of the model one usually tests for the absence of residual autocorrelation there is a number of tests designed for this purpose both in the time and frequency domains see for instance quenouille 1947 1949 bartlett 1954 box pierce 1970 ljung box 1978 ansley newbold 1979 godfrey 1979 in this paper a test based on residual partial autocorrelations is proposed which is particularly powerful in cases when the fitted model underestimates the order of the moving average component let x be a zero mean process generated by a arma model o b x 0 b at where b is the backshift operator b is a polynomial of order p 0 b is a polynomial of order q and a is a white noise let a atn be the residuals obtained after estimating the model a very popular goodness of fit test proposed by box pierce 1970 and improved by ljung box 1978 is based on the statistic m

nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates abstract allowing for the existence of irrelevant covariates we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data we estimate the conditional quantile regression function using the check function based kernel method and suggest a data driven cross validation cv approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates when the number of covariates is large we first use a screening method to remove the irrelevant covariates and then apply the cv criterion to those that survive the screening procedure simulations and an empirical application demonstrate the usefulness of the proposed methods

local linear regression smoothers and their minimax efficiencies in this paper we introduce a smooth version of local linear regression estimators and address their advantages the mse and mise of the estimators are computed explicitly it turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency they are not only efficient in rates but also nearly efficient in constant factors in the nonparametric regression context the asymptotic minimax lower bound is developed via the heuristic of the hardest onedimensional subproblem of donoho and liu connections of the minimax risk with the modulus of continuity are made the lower bound is also applicable for estimating conditional mean regression and conditional quantiles for both fixed and random design regression problems

nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

nonparametric inference of quantile curves for nonstationary time series the paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes using bahadur representation and gaussian approximation results for nonstationary time series simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type i error rates a wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the asymptotic results in particular our results can be used to test the trends of extremes of climate variables an important problem in understanding climate change our methodology is applied to the analysis of the maximum speed of tropical cyclone winds it was found that an inhomogeneous upward trend for cyclone wind speeds is pronounced at high quantile values however there is no trend in the mean lifetime maximum wind speed this example shows the effectiveness of the quantile regression technique

testing and estimation in marker set association study using semiparametric quantile regression kernel machine we consider quantile regression for partially linear models where an outcome of interest is related to covariates and a marker set e g gene or pathway the covariate effects are modeled parametrically and the marker set effect of multiple loci is modeled using kernel machine we propose an efficient algorithm to solve the corresponding optimization problem for estimating the effects of covariates and also introduce a powerful test for detecting the overall effect of the marker set our test is motivated by traditional score test and borrows the idea of permutation test our estimation and testing procedures are evaluated numerically and applied to assess genetic association of change in fasting homocysteine level using the vitamin intervention for stroke prevention trial data

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

estimation of stochastic volatility models via monte carlo maximum likelihood this paper discusses the monte carlo maximum likelihood method of estimating stochastic volatility sv models the basic sv model can be expressed as a linear state space model with log chi square disturbances the likelihood function can be approximated arbitrarily accurately by decomposing it into a gaussian part constructed by the kalman filter and a remainder function whose expectation is evaluated by simulation no modifications of this estimation procedure are required when the basic sv model is extended in a number of directions likely to arise in applied empirical research this compares favorably with alternative approaches the finite sample performance of the new estimator is shown to be comparable to the monte carlo markov chain mcmc method

local rank inference for varying coefficient models by allowing the regression coefficients to change with certain covariates the class of varying coefficient models offers a flexible approach to modeling nonlinearity and interactions between covariates this article proposes a novel estimation procedure for the varying coefficient models based on local ranks the new procedure provides a highly efficient and robust alternative to the local linear least squares method and can be conveniently implemented using existing r software package theoretical analysis and numerical simulations both reveal that the gain of the local rank estimator over the local linear least squares estimator measured by the asymptotic mean squared error or the asymptotic mean integrated squared error can be substantial in the normal error case the asymptotic relative efficiency for estimating both the coefficient functions and the derivative of the coefficient functions is above 96 even in the worst case scenarios the asymptotic relative efficiency has a lower bound 88 96

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

identification and estimation of triangular simultaneous equations models without additivity this paper uses control variables to identify and estimate models with nonseparable multidimensional disturbances triangular simultaneous equations models are considered with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable also for any control variable identification results are given for quantile average and policy effects bounds are given when a common support assumption is not satisfied estimators of identified objects and bounds are provided and a demand analysis empirical example is given

bi level path following for cross validated solution of kernel quantile regression we show how to follow the path of cross validated solutions to families of regularized optimization problems defined by a combination of a parameterized loss function and a regularization term a primary example is kernel quantile regression where the parameter of the loss function is the quantile being estimated even though the bi level optimization problem we encounter for every quantile is non convex the manner in which the optimal cross validated solution evolves with the parameter of the loss function allows tracking of this solution we prove this property construct the resulting algorithm and demonstrate it on real and artificial data this algorithm allows us to efficiently solve the whole family of bi level problems we show how it can be extended to cover other modeling problems like support vector regression and alternative in sample model selection approaches

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

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

a tukey nonadditivity type test for time series nonlinearity the past few years have seen a revived interest in the study of nonlinear stationary time series the most general form of a nonlinear stationary process is that referred to as a volterra expansion this is to a linear process what a higher order polynomial is to a linear function the so called bilinear model is a special case which is quite broad and is defined by a small number of parameters volterra expansions involve more than secondorder theory and require higher order cumulant spectra various tests for linearity have been proposed although none is totally satisfactory because of the similarity of volterra expansions to polynomials an analogue of tukey s 1949 one degree of freedom for nonadditivity test seems quite reasonable as a diagnostic for linearity versus a second order volterra expansion such a test would be time domain based and computationally less complex than the frequency domain based alternatives directly generalizable to higher order than second and possibly suggestive of a power transformation toward linearity

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

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

optimal smoothing in nonparametric conditional quantile derivative function estimation abstract marginal effect in nonparametric quantile regression is of special interest as it quantitatively measures how one unit change in explanatory variable heterogeneously affects dependent variable ceteris paribus at distinct quantiles in this paper we propose a data driven bandwidth selection procedure based on the gradient of an unknown quantile regression function our method delivers the bandwidth with the oracle property in the sense that it is asymptotically equivalent to the optimal bandwidth if the true gradient were known the results of monte carlo simulations are reported and the finite sample performance of our proposed method confirms our theoretical analysis an empirical application is also provided showing that our proposed method delivers more reasonable and reliable quantile derivative estimates than traditional cross validation method

nonparametric conditional quantile estimation a locally weighted quantile kernel approach abstract nonparametric conditional cumulative distribution function cdf estimation has emerged as a powerful tool having widespread potential application which has led to a literature on estimators of conditional quantile functions that are obtained via inversion of the nonparametrically estimated conditional cdf other nonparametric estimators of conditional quantiles that are based on an alternative characterization of the quantile i e as the function that minimizes the expectation of the check function have also appeared in the literature in this paper we propose a novel nonparametric approach relative to its inverse cdf based and the check function based peers our proposed estimator has a simple expression we also show that under certain conditions our estimator is more efficient in tail regions when the data has unbounded support our theoretical results underscore this property theoretical underpinnings are developed a method for data driven smoothing parameter selection is provided and monte carlo simulations and empirical examples are considered two empirical examples illustrate how the proposed approach can deliver more reasonable quantile and quantile derivative estimates than its inverse cdf based and the check function based counterparts particularly in tail regions

nonlinearity tests for time series summary this paper considers two nonlinearity tests for stationary time series the idea of tukey s one degree of freedom for nonadditivity test is generalized to the time series setting the case of concurrent nonlinearity is discussed in detail simulation results show that the proposed tests are more powerful than that of keenan 1985

inference on multiple correlation coefficients with moderately high dimensional data summary whenthemultiplecorrelationcoefficientisusedtomeasurehowstronglyagivenvariablecanbelinearly associated with a set of covariates it suffers from an upward bias that cannot be ignored in the presence of a moderately high dimensional covariate under an independent component model we derive an asymptotic approximation to the distribution of the squared multiple correlation coefficient that depends on a simple correction factor we show that this approximation enables us to construct reliable confidence intervals on the population coefficient even when the ratio of the dimension to the sample size is close to unity and the variables are non gaussian

brief modified stochastic luenberger observers a modified stochastic luenberger observer mslo structure is proposed to recover the optimal performance of the coventional slo for obtaining full state estimates in linear discrete time stochastic systems the optimal mslo omslo which gives the mmse estimates is derived by using the general two stage kalman filter a reduced order form of the omslo is also proposed for systems having singular measurement noises the connection between the omslo and the optimal minimal order observer of leondes and novak is also shown

a powerful portmanteau test of lack of fit for time series a new portmanteau test for time series more powerful than the tests of ljung and box and monti is proposed the test is based on the mth root of the determinant of the mth autocorrelation matrix it is shown that the proposed statistic is a function of all of the squared multiple correlation coefficients of the regressions of the residuals on their lags when the number of lags goes from 1 to m it can also be written as a function of the first m partial autocorrelation coefficients the asymptotic distribution of the test statistic is a linear combination of chi squared distributions and can be approximated by a gamma distribution it is shown depending on the model and sample size that this test can be up to 50 more powerful than the ljung and box and monti tests the test is applied to the detection of several types of nonlinearity by using the autocorrelation matrix of the squared residuals and it is shown that in general the new test is more powerful than the test of mcleod and li an example

diagnostic testing of univariate time series models summary the portmanteau statistic for testing the adequacy of an autoregressive moving average model is based on the first m autocorrelations of the residuals from the fitted model this paper examines the properties of this test for various choices of m a modification which allows the use of small values of m is shown to result in a more powerful test the lagrange multiplier statistic godfrey 1979 and a test statistic examined by newbold 1980 are also discussed

new weighted portmanteau statistics for time series goodness of fit testing we exploit ideas from high dimensional data analysis to derive new portmanteau tests that are based on the trace of the square of the mth order autocorrelation matrix the resulting statistics are weighted sums of the squares of the sample autocorrelation coefficients that unlike many other tests appearing in the literature are numerically stable even when the number of lags considered is relatively close to the sample size the statistics behave asymptotically as a linear combination of chi squared random variables and their asymptotic distribution can be approximated by a gamma distribution the proposed tests are modified to check for nonlinearity and to check the adequacy of a fitted nonlinear model simulation evidence indicates that the proposed goodness of fit tests tend to have higher power than other tests appearing in the literature particularly in detecting long memory nonlinear models the efficacy of the proposed methods is demonstrated by investigating nonlinear effects in apple inc an

a semiparametric quantile panel data model with an application to estimating the growth effect of fdi abstract this paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant a three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated a simple and easily implemented procedure for making inferences is proposed monte carlo simulation is conducted to examine the finite sample performance of the proposed estimators finally using the cross country panel data we find a strong empirical evidence of the existence of the absorptive capacity hypothesis together with another new finding that fdi has much stronger growth effects for countries with fast economic growth than for those with slow economic growth

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

vector quantile regression an optimal transport approach we propose a notion of conditional vector quantile function and a vector quantile regression a conditional vector quantile function cvqf of a random vector y taking values in d given covariates z z taking values in k is a map u qy z u z which is monotone in the sense of being a gradient of a convex function and such that given that vector u follows a reference non atomic distribution fu for instance uniform distribution on a unit cube in d the random vector qy z u z has the distribution of y conditional on z z moreover we have a strong representation y qy z u z almost surely for some version of u the vector quantile regression vqr is a linear model for cvqf of y given z under correct specification the notion produces strong representation y u f z for f z denoting a known set of transformations of z where u u f z is a monotone map the gradient of a convex function and the quantile regression coefficients u u have the interpretations analogous to that of the standard scalar quantile regression as f z becomes a richer class of transformations of z the model becomes nonparametric as in series modelling a key property of vqr is the embedding of the classical monge kantorovich s optimal transportation problem at its core as a special case in the classical case where y is scalar vqr reduces to a version of the classical qr and cvqf reduces to the scalar conditional quantile function several applications to diverse problems such as multiple engel curve estimation and measurement of financial risk are considered

on possibilistic representations of fuzzy intervals it is acknowledged that a fuzzy interval has two equivalent representations given in terms of the so called left and right sides of the membership function lr representation or in terms of the lower and upper branches defining the endpoints of the cuts lu representation in this paper we suggest an additional representation of fuzzy intervals called acf representation using an average cumulative function instead of the membership function based on possibility theory we illustrate how to build the new representation and we state its basic properties the main result is that the average cumulative ac function can be uniquely defined for any fuzzy interval and it is possible to move from one representation to the others through appropriate transformations an interesting link can be established between acf representation and quantile functions with a possible statistical interpretation useful in real application we also recommend a parametric form of the ac function

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

goodness of fit statistics for age specific reference intervals the age specific reference interval is a commonly used screening tool in medicine it involves estimation of extreme quantile curves such as the 5th and 95th centiles of a reference distribution of clinically normal individuals it is crucial that models used to estimate such intervals fit the data extremely well however few procedures to assess goodness of fit have been proposed in the literature and even fewer have been evaluated systematically here we consider procedures based on the distribution of the z scores standardized residuals from a model and on pearson chi 2 statistics for observed and expected counts in groups defined by age and the estimated reference centile curves two of the procedures q and grid tests are mainly inferential whereas the third permutation bands and b tests is essentially graphical we obtain approximations to the null distributions of several relevant test statistics and examine their size and power for a range of models based on real data sets we recommend q tests in all situations where z scores are available since they are general simple to calculate and usually have the highest power among the three classes of test considered for the cases considered the grid tests are always inferior to the q and b tests

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

a quantile correlated random coefficients panel data model abstract we propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data specifically we extend the correlated random coefficients representation of linear quantile regression e g koenker 2005 section 2 6 we show that panel data allows the econometrician to i introduce dependence between the regressors and the random coefficients and ii weaken the assumption of comonotonicity across them i e to enrich the structure of allowable dependence between different coefficients we adopt a fixed effects approach leaving any dependence between the regressors and the random coefficients unmodeled we motivate different notions of quantile partial effects in our model and study their identification for the case of discretely valued covariates we present analog estimators and characterize their large sample properties when the number of time periods t exceeds the number of random coefficients p identification is regular and our estimates are n consistent when t p our identification results make special use of the subpopulation of stayers units whose regressor values change little over time in a way which builds on the approach of graham and powell 2012 in this just identified case we study asymptotic sequences which allow the frequency of stayers in the population to shrink with the sample size one purpose of these discrete bandwidth asymptotics is to approximate settings where covariates are continuously valued and as such there is only an infinitesimal fraction of exact stayers while keeping the convenience of an analysis based on discrete covariates when the mass of stayers shrinks with n identification is irregular and our estimates converge at a slower than n rate but continue to have limiting normal distributions we apply our methods to study the effects of collective bargaining coverage on earnings using the national longitudinal survey of youth 1979 nlsy79 consistent with prior work e g chamberlain 1982 vella and verbeek 1998 we find that using panel data to control for unobserved worker heterogeneity results in sharply lower estimates of union wage premia we estimate a median union wage premium of about 9 percent but with in a more novel finding substantial heterogeneity across workers the 0 1 quantile of union effects is insignificantly different from zero whereas the 0 9 quantile effect is of over 30 percent our empirical analysis further suggests that on net unions have an equalizing effect on the distribution of wages

quantile regression in reproducing kernel hilbert spaces in this article we consider quantile regression in reproducing kernel hilbert spaces which we call kernel quantile regression kqr we make three contributions 1 we propose an efficient algorithm that computes the entire solution path of the kqr with essentially the same computational cost as fitting one kqr model 2 we derive a simple formula for the effective dimension of the kqr model which allows convenient selection of the regularization parameter and 3 we develop an asymptotic theory for the kqr model

design of reduced order optimal estimators directly in the frequency domain the frequency domain design of optimal reduced order estimators caiman filters for continuous time linear time invariant systems containing 0 k m noise free output measurements is considered in a direct frequency domain approach to state feedback and estimation the states of a system do not appear explicitly and therefore we here focus our attention mainly on the frequency domain characteristics of the optimal filter by suitably modifying known time domain results a simple polynomial matrix equation can be derived from which the optimal filter parameters are obtained by spectral factorization the equivalence between the time and the frequency domain results is established with the aid of a non minimal representation of reduced order observers

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

on additive conditional quantiles with high dimensional covariates we investigate the estimation of the conditional quantile when many covariates are involved in particular we model the conditional quantile of a response as a nonlinear additive function of relevant covariates for this setup we propose a nonparametric smoother to estimate the unknown functions the estimator provides direct computation of the nonlinear functions because it does not require any iteration the estimator allows fast and routine data analysis on the theoretical front we also show asymptotic properties of the estimator including mean squared error and limiting distribution the theory confirms that for moderate dimension of the covariates the estimator escapes the curse of dimensionality problem both simulated and real data examples are provided to illustrate the methodology

time varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories a recurring objective in longitudinal studies on aging and longevity has been the investigation of the relationship between age at death and current values of a longitudinal covariate trajectory that quantifies reproductive or other behavioral activity we propose a novel technique for predicting age at death distributions for situations where an entire covariate history is included in the predictor the predictor trajectories up to current time are represented by time varying functional principal component scores which are continuously updated as time progresses and are considered to be time varying predictor variables that are entered into a class of time varying functional regression models that we propose we demonstrate for biodemographic data how these methods can be applied to obtain predictions for age at death and estimates of remaining lifetime distributions including estimates of quantiles and of prediction intervals for remaining lifetime estimates and predictions are obtained for individual subjects based on their observed behavioral trajectories and include a dimension reduction step that is implemented by projecting on a single index the proposed techniques are illustrated with data on longitudinal daily egg laying for female medflies predicting remaining lifetime and age at death distributions from individual event histories observed up to current time

preadjusted non parametric estimation of a conditional distribution function summary the paper deals with non parametric estimation of a conditional distribution function we suggest a method of preadjusting the original observations non parametrically through location and scale to reduce the bias of the estimator we derive the asymptotic properties of the estimator proposed a simulation study investigating the finite sample performances of the estimators discussed is provided and reveals the gain that can be achieved it is also shown how the idea of the preadjusting opens the path to improved estimators in other settings such as conditional quantile and density estimation and conditional survival function estimation in the case of censored data

application of nonparametric quantile regression to body mass index percentile curves from survey data increasing rates of overweight among children in the u s stimulated interest in obtaining national percentile curves of body size to serve as a benchmark in assessing growth development in clinical and population settings in 2000 the u s centers for disease control and prevention cdc developed conditional percentile curves for body mass index bmi for ages 2 20 years the 2000 cdc bmi for age curves are partially parametric and only partially incorporated the survey sample weights in the curve estimation as a result they may not fully reflect the underlying pattern of bmi for age in the population this motivated us to develop a nonparametric double kernel based method and automatic bandwidth selection procedure we include sample weights in the bandwidth selection conduct median correction to reduce small sample smoothing bias and rescale the bandwidth to make it scale invariant using this procedure we re estimate the national percentile bmi for age curves and the prevalence of high bmi children in the u s

semiparametric quantile regression estimation in dynamic models with partially varying coefficients national science foundation of china 71131008 70871003 70971113 university of north carolina at charlotte chinese ministry of education minjiang scholarship from fujian province china xiamen university boston college

local asymptotics for quantile smoothing splines quantile smoothing splines were introduced by koenker ng and portnoy as natural and appealing estimates of conditional quantiles of response variables the natural setting for the problem considers minimization of a weighted combination of a fit penalty and a roughness penalty over the space of functions whose derivatives have bounded variation although this space is not traditional shen has shown recently that the quantile smoothing splines do indeed converge at the usual optimal rate n 2 5 in various norms here local asymptotic results are obtained by establishing bahadur representations for local parameters of the splines these are used to obtain local rates of convergence to establish uniform convergence rates to provide local distribution theory for quantile b splines and to expand the fit measure in order to analyze an information criterion for determining the smoothing parameter examples of using derivatives of the smoothing splines for estimating jump functions are also presented

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

variable bandwidth and local linear regression smoothers in this paper we introduce an appealing nonparametric method for estimating the mean regression function the proposed method combines the ideas of local linear smoothers and variable bandwidth hence it also inherits the advantages of both approaches we give expressions for the conditional mse and mise of the estimator minimization of the mise leads to an explicit formula for an optimal choice of the variable bandwidth moreover the merits of considering a variable bandwidth are discussed in addition we show that the estimator does not have boundary effects and hence does not require modifications at the boundary the performance of a corresponding plug in estimator is investigated simulations illustrate the proposed estimation method

quantile regression inference with adaptive control of size abstractregression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors this article develops a new estimate of the asymptotic var

inference for single index quantile regression models with profile optimization single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients we consider a pseudo profile likelihood approach to estimation and testing for single index quantile regression models we establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation moreover we propose a score test for the index coefficient based on the gradient of the pseudo profile likelihood and employ a penalized procedure to perform consistent model selection and model estimation simultaneously we also use monte carlo studies to support our asymptotic results and use an empirical example to illustrate the proposed method

local linear quantile regression abstract in this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting two such estimators are considered one is based on localizing the characterization of a regression quantile as the minimizer of e pp y a x x where p is the appropriate check function the other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters rather than one our aim is to present fully operational versions of both approaches and to show that each works quite well although either might be used in practice we have a particular preference for the second our automatic smoothing parameter selection method is novel the main regression quantile smoothing parameters are chosen by rule of thumb adaptations of state of the art methods for smoothing parameter selection for regression mean estimation the techniques are illustrated by application to two datasets and compared in simulations

conditional minimum volume predictive regions for stochastic processes abstract motivated by interval region prediction in nonlinear time series we propose a minimum volume mv predictor for a strictly stationary process the mv predictor varies with respect to the current position in the state space and has the minimum lebesgue measure among all regions with the nominal coverage probability we have established consistency convergence rates and asymptotic normality for both coverage probability and lebesgue measure of the estimated mv predictor under the assumption that the observations are from a strong mixing process applications with both real and simulated datasets illustrate the proposed methods

an approach to multivariate covariate dependent quantile contours with application to bivariate conditional growth charts multivariate quantile contours are useful in numerous applications and have been studied in different contexts however no easy solutions exist when dynamic and conditional quantile contours are needed without strong distributional assumptions in this article we propose a new form of bivariate quantile contours and a two stage estimation procedure to take time effect into account the proposed procedure relies on quantile regression for longitudinal data and is flexible to include potentially important covariates as necessary in addition we propose a visual model assessment tool and discuss a practical guideline for model selection the performance of the proposed methodology is demonstrated by a simulation study as well as an application to joint height weight screening of young children in the united states we construct bivariate growth charts by a nested sequence of age dependent and covariate varying quantile contours of height and weight and use it to locate an individual subject s percentile

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

state estimation for linear systems with observations partially corrupted by noise abstract this paper exploits the fact that any row vector of the observability matrix applied for transforming the state converts the latter to the new state component in the form of some derivative of the output component using the same but appropriately chosen vectors for transforming the system with the observation not fully corrupted by white noise we can accurately determine some state components these vectors create the basis for the l dimensional subspace of transformation vectors to the new accurately determinable state components using this basis the state transformation is constructed which in one step converts the singular linear filtering problem to a nonsingular one with state dimension decreased by l

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

bootstrapping the portmanteau tests in weak auto regressive moving average models this paper uses a random weighting rw method to bootstrap the critical values for the ljung box monti portmanteau tests and weighted ljung box monti portmanteau tests in weak arma models unlike the existing methods no user chosen parameter is needed to implement the rw method as an application these four tests are used to check the model adequacy in power garch models simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests a real example on s p 500 index illustrates the merits of our testing procedure as one extension work the block wise rw method is also studied

quantile regression with varying coefficients quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean the regression methodology is well developed for linear models but less so for nonparametric models we consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines the proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm the proposed rao score type test that assesses the model against a linear model is also easy to implement we provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic empirical results are also provided including an application of the methodology to forced expiratory volume fev data

quasi likelihood estimation in semiparametric models abstract suppose the expected value of a response variable y may be written h x t where x and t are covariates each of which may be vector valued is an unknown parameter vector is an unknown smooth function and h is a known function in this article we outline a method for estimating the parameter of this type of semiparametric model using a quasi likelihood function algorithms for computing the estimates are given and the asymptotic distribution theory for the estimators is developed the generalization of this approach to the case in which y is a multivariate response is also considered the methodology is illustrated on two data sets and the results of a small monte carlo study are presented

further results on the finite sample distribution of monti s portmanteau test for the adequacy of an arma p q model this note investigates the finite sample performance of monti s test paying special attention to its estimated sizes and empirical powers our simulation results indicate that i the test size can be affected by the choice of the number of residual partial autocorrelations m and ii the empirical powers of the monti and the ljung box tests are similar in the cases of both seasonal and non seasonal data if m is properly chosen

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

quantile regression forests random forests were introduced as a machine learning tool in breiman 2001 and have since proven to be very popular and powerful for high dimensional regression and classification for regression random forests give an accurate approximation of the conditional mean of a response variable it is shown here that random forests provide information about the full conditional distribution of the response variable not only about the conditional mean conditional quantiles can be inferred with quantile regression forests a generalisation of random forests quantile regression forests give a non parametric and accurate way of estimating conditional quantiles for high dimensional predictor variables the algorithm is shown to be consistent numerical examples suggest that the algorithm is competitive in terms of predictive power

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

a simple solution to the singular linear minimum variance estimation problem a simple expression is obtained for the transfer function matrix of the minimum variance estimator for the states of a linear stationary continuous time right invertible system whose output is measured perfectly using the s domain approach it is shown that the optimal estimator first finds the driving noise input that achieves when applied on the minimum phase image model of the system an output spectrum which is identical to the measurement spectrum this input is then applied on a state space representation of the minimum phase image to produce the optimal estimate

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

a unified solution to the singular and nonsingular linear minimum variance estimation problem a unified solution is derived for the transfer function matrix of the minimum variance estimator of the state of a linear continuous time system with noisy or noise free measurements for the noisy measurement case the kalman bucy filter standard equations are used to give the general format of the transfer function the kalman bucy gain using the spectral factorization on the algebraic in the s plane is derived and substituted in the transfer function expression the singular case is then shown to be a special case of the noisy measurement estimator

non crossing non parametric estimates of quantile curves in this paper a new nonparametric estimate of conditional quantiles is proposed that avoids the problem of crossing quantile curves calculated for various p 2 0 1 the method uses an initial estimate of the conditional distribution function in a flrst step and solves the problem of inversion and monotonization with respect to p 2 0 1 simultaneously it is demonstrated that the new estimates are asymptotically normal distributed and asymptotically flrst order equivalent to quantile estimates obtained by local constant or local linear smoothing of the conditional distribution function the performance of the new procedure is illustrated by means of a simulation study and some comparisons with the currently available procedures which are similar in spirit with the proposed method are presented

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

quantile regression in partially linear varying coefficient models semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony in this paper we study a class of marginal partially linear quantile models with possibly varying coefficients the functional coefficients are estimated by basis function approximations the estimation procedure is easy to implement and it requires no specification of the error distributions the asymptotic properties of the proposed estimators are established for the varying coefficients as well as for the constant coefficients we develop rank score tests for hypotheses on the coefficients including the hypotheses on the constancy of a subset of the varying coefficients hypothesis testing of this type is theoretically challenging as the dimensions of the parameter spaces under both the null and the alternative hypotheses are growing with the sample size we assess the finite sample performance of the proposed method by monte carlo simulation studies and demonstrate its value by the analysis of an aids data set where the modeling of quantiles provides more comprehensive information than the usual least squares approach

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

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

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

estimation of conditional densities and sensitivity measures in nonlinear dynamical systems using locally polynomial regression we develop nonparametric estimators for the conditional density function and its square root and their partial derivatives two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed one of which relates fisher information with initial value sensitivity in dynamical systems we propose estimators for these and show asymptotic normality for one of them we further propose a simple method for choosing the bandwidth the methods are illustrated by simulation of two well known models in dynamical systems

graphical exploration of covariate effects on survival data through nonparametric quantile curves kaplan meier curves provide an effective means of presenting the distributional pattern in a sample of survival data however in order to assess the effect of a covariate a standard scatterplot is often difficult to interpret because of the presence of censored observations several authors have proposed a running median as an effective way of indicating the effect of a covariate this article proposes a form of kernel estimation employing double smoothing that can be applied in a simple and efficient manner to construct an estimator of a percentile of the survival distribution as a function of one or two covariates permutations and bootstrap samples can be used to construct reference bands that help identify whether particular features of the estimates indicate real features of the underlying curve or whether this may be due simply to random variation the techniques are illustrated on data from a study of kidney transplant patients

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

on quantile regression in reproducing kernel hilbert spaces with the data sparsity constraint for spline regressions it is well known that the choice of knots is crucial for the performance of the estimator as a general learning framework covering the smoothing splines learning in a reproducing kernel hilbert space rkhs has a similar issue however the selection of training data points for kernel functions in the rkhs representation has not been carefully studied in the literature in this paper we study quantile regression as an example of learning in a rkhs in this case the regular squared norm penalty does not perform training data selection we propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation we demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations and have comparable performance in other cases compared to that of the traditional squared norm penalty therefore the data sparsity method can serve as a competitive alternative to the squared norm penalty method some theoretical properties of our proposed method using the data sparsity constraint are obtained both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint