on variable bandwidth selection in local polynomial regression the performances of data driven bandwidth selection procedures in local polynomial regression are investigated by using asymptotic methods and simulation the bandwidth selection procedures considered are based on minimizing prelimit approximations to the conditional mean squared error mse when the mse is considered as a function of the bandwidth h we first consider approximations to the mse that are based on taylor expansions around h 0 of the bias part of the mse these approximations lead to estimators of the mse that are accurate only for small bandwidths h we also consider a bias estimator which instead of using small h approximations to bias naively estimates bias as the difference of two local polynomial estimators of different order and we show that this estimator performs well only for moderate to large h we next define a hybrid bias estimator which equals the taylor expansion based estimator for small h and the difference estimator for moderate to large h we find that the mse estimator based on this hybrid bias estimator leads to a bandwidth selection procedure with good asymptotic and for our monte carlo examples finite sample properties

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

new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

local empirical likelihood inference for varying coefficient density ratio models based on case control data in this article we develop a varying coefficient density ratio model for case control studies the case and control samples come from two different distributions under the model assumption the ratio of the two densities is related to the linear combination of covariates with varying coefficients through a known function a special case is the exponential tilt model where the log ratio of the two densities is a linear function of covariates we propose a local empirical likelihood el approach to estimate the nonparametric coefficient functions under some regularity assumptions the proposed estimators are shown to be consistent and asymptotically normally distributed the sieve empirical likelihood ratio selr test statistic for detecting whether the varying coefficients are really constant and other related hypotheses is constructed and it follows approximately a chi squared distribution we introduce a modified bootstrap procedure to estimate the null distribution of the selr when sample size is s

local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

reducing variance in univariate smoothing a variance reduction technique in nonparametric smoothing is proposed at each point of estimation form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged the nearby points are chosen to maximize the variance reduction we study in detail the case of univariate local linear regression while the new estimator retains many advantages of the local linear estimator it has appealing asymptotic relative efficiencies bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation a simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes this technique is very general and has a wide range of applications

unexpected properties of bandwidth choice when smoothing discrete data for constructing a functional data classifier the data functions that are studied in the course of functional data analysis are assembled from discrete data and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed existing literature shows that this approach is effective and even optimal when using functional data methods for prediction or hypothesis testing however in the present paper we show that this approach is not effective in classification problems there a useful rule of thumb is that undersmoothing is often desirable but there are several surprising qualifications to that approach first the effect of smoothing the training data can be more significant than that of smoothing the new data set to be classified second undersmoothing is not always the right approach and in fact in some cases using a relatively large bandwidth can be more effective and third these perverse results are the consequence of very unusual properties of error rates expressed as functions of smoothing parameters for example the orders of magnitude of optimal smoothing parameter choices depend on the signs and sizes of terms in an expansion of error rate and those signs and sizes can vary dramatically from one setting to another even for the same classifier

convolutional autoregressive models for functional time series abstract functional data analysis has became an increasingly popular class of problems in statistical research however functional data observed over time with serial dependence remains a less studied area motivated by bosq 2000 who first introduced the functional autoregressive models we propose a convolutional functional autoregressive model where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions plus a noise process mimicking the vector autoregressive process it provides an intuitive and direct interpretation of the dynamics of a stochastic process instead of principal component analysis commonly used in functional data analysis we adopt a sieve estimation procedure based on b spline approximation of the convolution functions we establish convergence rate of the proposed estimator and investigate its theoretical properties the model building model validation and prediction procedures are also developed both simulated and real data examples are presented

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

efficient statistical inference procedures for partially nonlinear models and their applications motivated by an analysis of a real data set in ecology we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present we develop two new estimation procedures to estimate the parameters in the parametric component consistency and asymptotic normality of the resulting estimators are established we further propose an estimation procedure and a generalized f test procedure for the nonparametric component in the partially nonlinear models asymptotic properties of the newly proposed estimation procedure and the test statistic are derived finite sample performance of the proposed inference procedures are assessed by monte carlo simulation studies an application in ecology is used to illustrate the proposed methods

some inequalities for information divergence and related measures of discrimination inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics ergodic theory and other scientific fields we suggest new inequalities of this type often based on underlying identities as a consequence we obtain certain improvements of the well known pinsker inequality our study depends on two measures of discrimination called capacitory discrimination and triangular discrimination the discussion contains references to related research and comparison with other measures of discrimination e g ali silvey csiszar 1996 1966 divergences and in particular the hellinger distance

a nonparametric circular linear multivariate regression model with a rule of thumb bandwidth selector the purpose of this paper is to propose a nonparametric circular linear multivariate regression model using a kernel weighted local linear method the case of several linear regressors and one circular regressor is considered we extend results on the asymptotic bias and variance of the linear multivariate variable to the case of circular linear multivariate variable the rule of thumb selector is used to establish the optimal bandwidths for the nonparametric model the suitability of the model is judged from the coefficient of determination one simulation experiment and one real problem concerning wind energy are used to study the power performance of the nonparametric model

how far are automatically chosen regression smoothing parameters from their optimum abstract we address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation call the optimal bandwidth the minimizer of the average squared error we consider several automatically selected bandwidths that approximate the optimum how far are the automatically selected bandwidths from the optimum the answer is studied theoretically and through simulations the theoretical results include a central limit theorem that quantifies the convergence rate and gives the differences asymptotic distribution the convergence rate turns out to be excruciatingly slow this is not too disappointing because this rate is of the same order as the convergence rate of the difference between the minimizers of the average squared error and the mean average squared error in some simulations by john rice the selectors considered here performed quite differently from each other we anticipated that these differences would be reflected in differ

bandwidth selection for kernel density estimation the problem of automatic bandwidth selection for a kernel density estimator is considered it is well recognized that the bandwidth estimate selected by the least squares cross validation is subject to large sample variation this difficulty limits the application of the cross validation estimate based on characteristic functions an important expression for the cross validation bandwidth estimate is obtained the expression clearly points out the source of variation to stabilize the variation a simple bandwidth selection procedure is proposed it is shown that the stabilized bandwidth selector gives a strongly consistent estimate of the optimal bandwidth under commonly used smoothness conditions the stabilized bandwidth estimate has a faster convergence rate than the convergence rate of the cross validation estimate for sufficiently smooth density functions it is shown that the stabilized bandwidth estimate is asymptotically normal with a relative convergence rate n 1 2 instead of the rate n 1 10 of the cross validation estimate a plug in estimate and an adjusted plug in estimate are also proposed and their asymptotic distributions are obtained it is noted that the plug in estimate is asymptotically efficient the adjusted plug in bandwidth estimate and the stabilized bandwidth estimate are shown to be asymptotically equivalent the simulation results verify that the proposed procedures perform much better than the cross validation for finite samples

nonparametric regression analysis for group testing data group testing is a procedure used to reduce the cost and increase the speed of large screening studies in which infection or contamination of individuals is detected by a test carried out on a sample of for example blood urine or water instead of testing the sample of each individual the method involves pooling samples of groups of several individuals and testing those pooled samples we construct a nonparametric procedure for estimating the conditional probability of contamination given an explanatory variable when the observations are pooled data of this type we investigate asymptotic theoretical properties of the estimator and establish its consistency the procedure requires selecting an important smoothing parameter and we suggest a way to do this automatically from the data we illustrate the numerical performance of the method on some simulated examples and on data from the national health and nutrition examination survey we discuss extensions of the procedure to cases where the test is im

on optimal data based bandwidth selection in kernel density estimation a bandwidth selection method is proposed for kernel density estimation this is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth but with two important modifications the result is a bandwidth selector with the by nonparametric standards extremely fast asymptotic rate of convergence of n where n denotes sample size comparison is given to other bandwidth selection methods and small sample impact is investigated

adaptively varying coefficient spatiotemporal models we propose an adaptive varying coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time the model is capable of catching possible non linearity both in space and in time and non stationarity in space by allowing the auto regressive coefficients to vary with both spatial location and an unknown index variable we suggest a two step procedure to estimate both the coefficient functions and the index variable which is readily implemented and can be computed even for large spatiotemporal data sets our theoretical results indicate that in the presence of the so called nugget effect the errors in the estimation may be reduced via the spatial smoothing the second step in the estimation procedure proposed the simulation results reinforce this finding as an illustration we apply the methodology to a data set of sea level pressure in the north sea

new local estimation procedure for a non parametric regression function for longitudinal data this paper develops a new estimation of nonparametric regression functions for clustered or longitudinal data we propose to use cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously we further prove that the proposed estimator is as asymptotically efficient as if the covariance matrix were known a monte carlo simulation study is conducted to examine the finite sample performance of the proposed procedure and to compare the proposed procedure with the existing ones based on our empirical studies the newly proposed procedure works better than the naive local linear regression with working independence error structure and the efficiency gain can be achieved in moderate sized samples our numerical comparison also shows that the newly proposed procedure outperforms some existing ones a real data set application is also provided to illustrate the proposed estimation procedure

smooth optimum kernel estimators near endpoints summary kernel estimators for smooth curves like density spectral density or regression functions require modifications when estimating near endpoints of the support both for practical and asymptotic reasons the construction of such boundary kernels as solutions of a variational problem is addressed and representations in orthogonal polynomials are given including explicit solutions for the most important cases based on explicit formulae for certain functionals of the kernels it is shown that local bandwidth variation might be indicated near boundaries various bandwidth variation schemes are discussed and

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

a simple root n bandwidth selector the asymptotically best bandwidth selectors for a kernel density estimator currently require the use of either unappealing higher order kernel pilot estimators or related fourier transform methods the point of this paper is to present a methodology which allows the fastest possible rate of convergence with the use of only nonnegative kernel estimators at all stages of the selection process the essential idea is derived through careful study of factorizations of the pilot bandwidth in terms of the original bandwidth

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 crossvalidation method for estimating conditional densities summary we extend the idea of crossvalidation to choose the smoothing parameters of the double kernel local linear regression for estimating a conditional density our selection rule optimises the estimated conditional density function by minimising the integrated squared error we also discuss three other bandwidth selection rules an ad hoc method used by fan et al 1996 a bootstrap method of hall et al 1999 for bandwidth selection in the estimation of conditional distribution functions modified by bashtannyk hyndman 2001 to cover conditional density functions and finally a simple approach proposed by hyndman yao 2002 the performance of the new approach is compared with these three methods by simulation studies and our method performs outstandingly well the method is illustrated by an application to estimating the transition density and the value at risk of treasury bill 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

a flexible and fast method for automatic smoothing abstract the choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators the optimal choice depends on the data at hand a data driven bandwidth selection close to the optimal one would make these curve estimators objective more reliable and easier to use minimizing residual mean squared error criteria such as cross validation have been frequently proposed to estimate the optimal smoothing parameter empirical and theoretical evidence indicates that cross validation rules and related methods lead to rather variable estimated optimal bandwidths the method presented here builds on estimating the asymptotically optimal bandwidth from the data since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula such selection rules are called plug in estimators the functional that quantifies bias is approximated by the integrated squared second derivative of the regre

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

comparison of data driven bandwidth selectors abstract this article compares several promising data driven methods for selecting the bandwidth of a kernel density estimator the methods compared are least squares cross validation biased cross validation and a plug in rule the comparison is done by asymptotic rate of convergence to the optimum and a simulation study it is seen that the plug in bandwidth is usually most efficient when the underlying density is sufficiently smooth but is less robust when there is not enough smoothness present we believe the plug in rule is the best of those currently available but there is still room for improvement

estimation in partially linear models with missing covariates the partially linear model y xt z has been studied extensively when data are completely observed in this article we consider the case where the covariate x is sometimes missing with missingness probability depending on y z new methods are developed for estimating and our methods are shown to outperform asymptotically methods based only on the complete data asymptotic efficiency is discussed and the semiparametric efficient score function is derived justification of the use of the nonparametric bootstrap in this context is sketched the proposed estimators are extended to a working independence analysis of longitudinal clustered data and applied to analyze an aids clinical trial dataset the results of a simulation experiment are also given to illustrate our approach

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on variance estimation in nonparametric regression a simple explicit estimator of variance in nonparametric regression is suggested based on the mean square of a sequence of residuals the estimator is valid for general error distributions has elementary bias and variance properties and is optimal to both first and second orders

parameter estimation for differential equation models using a framework of measurement error in regression models differential equation de models are widely used in many scientific fields including engineering physics and biomedical sciences the so called forward problem the problem of simulations and predictions of state variables for given parameter values in the de models has been extensively studied by mathematicians physicists engineers and other scientists however the inverse problem the problem of parameter estimation based on the measurements of output variables has not been well explored using modern statistical methods although some least squares based approaches have been proposed and studied in this article we propose parameter estimation methods for ordinary differential equation ode models based on the local smoothing approach and a pseudo least squares psls principle under a framework of measurement error in regression models the asymptotic properties of the proposed psls estimator are established we also compare the psls method to the corresponding simulation extrapolation

efficient local estimation for time varying coefficients in deterministic dynamic models with applications to hiv 1 dynamics recently deterministic dynamic models have become very popular in biomedical research and other scientific areas examples include modeling human immunodeficiency virus hiv dynamics pharmacokinetic pharmacodynamic analysis tumor cell kinetics and genetic network modeling in this article we propose estimation methods for the time varying coefficients in deterministic dynamic systems that are usually described by a set of differential equations three two stage local polynomial estimators are proposed and their asymptotic normality is established an alternative approach a discretization method that is widely used in stochastic diffusion models is also investigated we show that the discretization method that uses the simple euler discretization approach for the deterministic dynamic model does not achieve the optimal convergence rate compared with the proposed two stage estimators we use monte carlo simulations to study the finite sample performance and use a real data application to hiv dynamic

on fractile transformation of covariates in regression the need for comparing two regression functions arises frequently in statistical applications comparison of the usual regression functions is not very meaningful in situations where the distributions and the ranges of the covariates are different for the populations for instance in econometric studies the prices of commodities and people s incomes observed at different time points may not be on comparable scales due to inflation and other economic factors in this article we describe a method of standardizing the covariates and estimating the transformed regression function which then become comparable we develop smooth estimates of the fractile regression function and study its statistical properties analytically as well as numerically we also provide a few real examples that illustrate the difficulty in comparing the usual regression functions and motivate the need for the fractile transformation our analysis of the real examples leads to new and useful statistical conclusions that are missed b

an automatic bandwidth selector for kernel density estimation summary to select a proper bandwidth is a critical step in kernel density estimation it is well known that the bandwidth selected by cross validation has a large variability this difficulty limits the applicability of cross validation to reduce the variability we suggested modifying the sample characteristic function beyond some cut off frequency in estimating the bias term of the mean integrated squared error it is proposed to select the cut off frequency by a generalization of cross validation for smooth density functions the asymptotic distribution of the bandwidth estimator based on the estimated cut off frequency is obtained the proposed bandwidth estimator has a relative convergence rate n which is much faster than the rate n 1110 for the bandwidth estimate selected by cross validation a modification which reduces the chance of selecting a large cut off frequency is also suggested in simulation studies the advantages of the proposed procedures are clearly demonstrated the procedures are also applied to some data sets

novel and simple non parametric methods of estimating the joint and marginal densities we introduce very simple non parametric methods that overcome key limitations of the existing literature on both the joint and marginal density estimation in doing so we do not assume any form of the marginal distribution or joint distribution a priori furthermore our method circumvents the bandwidth selection problems we compare our method to the kernel density method

testing for covariate effects in the fully nonparametric analysis of covariance model traditional inference questions in the analysis of covariance mainly focus on comparing different factor levels by adjusting for the continuous covariates which are believed to also exert a significant effect on the outcome variable testing hypotheses about the covariate effects although of substantial interest in many applications has received relatively limited study in the semiparametric nonparametric setting in the context of the fully nonparametric analysis of covariance model of akritas et al we propose methods to test for covariate main effects and covariate factor interaction effects the idea underlying the proposed procedures is that covariates can be thought of as factors with many levels the test statistics are closely related to some recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large the limiting normal distributions are established under the null hypotheses and local alternatives by asymptotically approximating a new class

estimation of fish abundance indices based on scientific research trawl surveys summary the fish abundance index over an ocean region is defined here to be the integral of expected catch per unit effort cpue approximated by the sum of expected cpue over grid squares when trawl surveys are done within grid squares selected according to a probability sampling design several other sources of variation such as the fish population dynamics and the catching process are also involved in such situations model assisted methods for estimating abundance assessed under both design and model perspectives have some advantages over purely design based methods such as the horvitz thompson ht estimator or purely model based prediction approaches this article develops model assisted empirical likelihood el methods via loglinear regression and nonparametric smoothing the methods are applied to grid surveys of the grand bank region carried out annually by fishery products international from 1996 through 2002 the ht and el methods produce similar point estimates of abundance indices simulation results however indicate that the el estimator under local linear smoothing is associated with smaller standard errors

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

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

multivariate functional coefficient regression models for nonlinear vector time series data summary vector time series data are widely found in practice in this paper we propose a multivariate functional coefficient regression model with heteroscedasticity for modeling such data the local linear smoother is employed to estimate the unknown coefficient matrices asymptotic normality 10 of the proposed estimators is established and bandwidth selection is considered to deal with cointegration widely observed in financial markets we propose an error corrected multivariate functional coefficient model simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well analysis of united states interest rates illustrates the proposed methodology 15

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