inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

some asymptotic results for the systematic and stratified sampling of a finite population summary a sample mean has an asymptotically insignificant model bias under a broad set of functional relationships between the parameter of interest and an auxiliary size variable given a systematic sample from a size ordered list when based on randomly drawn samples within size strata this estimator of the population mean not only has an asymptotically insignificant model bias but is design consistent as well in addition there are more efficient estimation strategies that have insignificant model biases and may be design consistent

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

survey design under the regression superpopulation model abstract the construction of sample designs and estimators under a linear regression superpopulation model is considered the anticipated variance the variance of the predictor computed with respect to the sampling design and the superpopulation model is used as a criterion for evaluating probability designs and model unbiased predictors regression predictors that are model unbiased and design consistent are constructed

quantiles for counts this article studies the estimation of conditional quantiles of counts given the discreteness of the data some smoothness must be artificially imposed on the problem we show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques the performance and implementation of the estimators are illustrated by simulations and an application

two part multiple spell models for health care demand the demand for certain types of health care services depends on decisions of both the individual and the health care provider this paper studies the conditions under which it is possible to separately identify the parameters driving the two decision processes using only count data on the total demand it is found that the frequently used hurdle models may not be adequate to describe this type of demand especially when the assumption of a single illness spell per observation period is violated a test for the single spell hypothesis is developed and alternative modelling strategies are suggested including one that allows for correlated unobserved heterogeneity the results of the paper are illustrated with an application

regression rank scores and regression quantiles we show that regression quantiles which could be computed as solutions of a linear programming problem and the solutions of the corresponding dual problem which we call the regression rank scores generalize the duality of order statistics and of ranks from the location to the linear model noting this fact we study the regression quantile and regression rank score processes in the heteroscedastic linear regression model obtaining some new estimators and interesting comparisons with existing estimators

some basic information on information based complexity theory abstract a branch of complexity theory called information based complexity theory ibct produces an abundance of impressive results about the quest for approximate solutions to mathematical problems why then do most numerical analysts turn a cold shoulder to ibct close analysis of two papers representative of ibct s best efforts reveals a mixture of nice new observations misdirected examples and misleading theorems some elements in the framework of ibct erected to support a rigorous yet flexible theory make it difficult to judge whether a model is off target or reasonably realistic for instance a sharp distinction is made between information and algorithms restricted to this information yet the information itself usually comes from an algorithm and so the distinction clouds the issues and can lead to true but misleading inferences another troublesome aspect of ibct is a free parameter f the class of admissible problem instances whose membership fee is completely ignored in ascertaining the cost of solving the worst case in f sometimes this leads to unrealistic models we conclude that one s satisfaction with each result of ibct must be inversely proportional to what one knows about the problem the surprising results known to us pertain only to unnatural situations and ibct s genuinely new insights might serve us better if expressed in the conventional mode of error bounds and approximation theory

estimation and inference for distribution functions and quantile functions in treatment effect models abstract we propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions we show that these estimators converge weakly to zero mean gaussian processes a simulation method is proposed to approximate these limiting processes based on these results we construct tests for stochastic dominance relations between the potential outcomes monte carlo simulations are conducted to examine the finite sample properties of our tests we apply our test in an empirical example and find that a job training program had a positive effect on incomes

quantile regression under misspecification with an application to the u s wage structure quantile regression qr fits a linear model for conditional quantiles just as ordinary least squares ols fits a linear model for conditional means an attractive feature of ols is that it gives the minimum mean squared error linear approximation to the conditional expectation function even when the linear model is misspecified empirical research using quantile regression with discrete covariates suggests that qr may have a similar property but the exact nature of the linear approximation has remained elusive in this paper we show that qr minimizes a weighted mean squared error loss function for specification error the weighting function is an average density of the dependent variable near the true conditional quantile the weighted least squares interpretation of qr is used to derive an omitted variables bias formula and a partial quantile regression concept similar to the relationship between partial regression and ols we also present asymptotic theory for the qr process under misspecification of the conditional quantile function the approximation properties of qr are illustrated using wage data from the u s census these results point to major changes in inequality from 1990 to 2000

model based finite population correction for the horvitz thompson estimator summary this paper discusses a model based finite population correction term for estimating the model and design variances of the horvitz thompson estimator under the usual model suppose we want to estimate the variance of the estimate of a finite population mean yn y p yi n where lp denotes summation over the units in the population we use the horvitzthompson estimator yht xnn ls yi xi where is denotes summation over the units in the sample all the xi nin n are known and npi nxi nin is the probability of selecting unit i for the sample it is well known that this estimation strategy is design unbiased that is ep 9ht yn where ep denotes expectation with respect to the sampling design moreover it is model unbiased if the yi have the stochastic structure

the conditional distribution of excess returns an empirical analysis abstract in this article we describe the cumulative distribution function of excess returns conditional on a broad set of predictors that summarize the state of the economy we do so by estimating a sequence of conditional logit models over a grid of values of the response variable our method uncovers higher order multidimensional structure that cannot be found by modeling only the first two moments of the distribution we compare two approaches to modeling one based on a conventional linear logit model and the other based on an additive logit the second approach avoids the curse of dimensionality problem of fully nonparametric methods while retaining both interpretability and the ability to let the data determine the shape of the relationship between the response variable and the predictors we find that the additive logit fits better and reveals aspects of the data that remain undetected by the linear logit the additive model retains its superiority even in out of sample prediction and portfolio s

quantile estimation with a complex survey design estimation of the finite population distribution function and related statistics such as the median and interquartile range is considered large sample properties of estimators constructed from stratified cluster samples and properties of large sample confidence intervals are established the results are obtained within the context of a sequence of finite populations generated from a superpopulation

generic inference on quantile and quantile effect functions for discrete outcomes quantile and quantile effect qe functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation existing inference methods for these functions

estimating a finite population mean from unequal probability samples abstract two approaches to estimating a finite population mean from unequal probability samples are contrasted in the prediction approach a model is specified for the population values and is used to predict the nonsampled values in the generalized regression approach the horvitz thompson estimator of the population mean is modified to allow the introduction of covariate information sarndal 1980 generalized regression estimates have the desirable property of asymptotic design consistency which is not always enjoyed by estimates in the prediction class however it is suggested that the prediction approach is the more principled method of estimation if asymptotic design consistency is a desirable property in a given application then only models that yield asymptotically design consistent prediction estimates should be used two classes of models with this property are suggested namely fixed and random effects models that allow a separate intercept for subclasses of the population indexed by the pr

conditional properties of some estimators in stratified sampling abstract the prediction properties of the stratified expansion estimator the separate and combined ratio estimators and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable several estimators of variance for each total estimator are considered including standard ones from probability sampling theory alternative choices derived from a superpopulation model and the jackknife the theory is tested in an empirical study using a real population earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties whether similar results hold for stratified samples and estimators has been the subject of some debate this article illustrates both theoretically and empirically that the use of stratifi

quantile treatment effects in the regression discontinuity design abstract we introduce a nonparametric estimator for local quantile treatment effects in the regression discontinuity rd design the procedure uses local distribution regression to estimate the marginal distributions of the potential outcomes we illustrate the procedure through monte carlo simulations and an application on the distributional effects of a universal pre k program in oklahoma we find that participation in a pre k program significantly raises the lower end and the middle of the distribution of test scores

network and panel quantile effects via distribution regression abstract this paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two way effects strictly exogenous covariates and possibly discrete outcome variables the method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators these fixed effects estimators are debiased to deal with the incidental parameter problem under asymptotic sequences where both dimensions of the data set grow at the same rate the confidence bands for the quantile functions and effects have correct joint coverage in large samples an empirical application to gravity models of trade illustrates the applicability of the methods to network data

misspecification testing in a class of conditional distributional models we propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates the test is based on the cramer von mises distance between an unrestricted estimate of the joint distribution function of the data and a restricted estimate that imposes the structure implied by the model the procedure is straightforward to implement is consistent against fixed alternatives has nontrivial power against local deviations of order n 1 2 from the null hypothesis and does not require the choice of smoothing parameters in an empirical application we use our test to study the validity of various models for the conditional distribution of wages in the united states

on the optimal solution of large linear systems the information based study of the optimal solution of largelinear systems is initiated by studying the case of krylovinformation among the algorithms that use krylov information areminimal residual conjugate gradient chebyshev and successiveapproximation algorithms a sharp lower bound on the number ofmatrix vector multiplications required to compute ana approximation is obtained for any orthogonally invariantclass of matrices examples of such classes include many ofpractical interest such as symmetric matrices symmetric positivedefinite matrices and matrices with bounded condition number itis shown that the minimal residual algorithm is within at most onematrix vector multiplication of the lower bound a similar resultis obtained for the generalized minimal residual algorithm thelower bound is computed for certain classes of orthogonallyinvariant matrices how the lack of certam properties symmetry positive definiteness increases the lower bound is shown aconjecture and a number of open problems are stated