limiting distributions for l sb 1 regression estimators under general conditions it is well known that l 1 estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0 in this paper we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0

nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

normal forms in bl algebra and their contribution to universal approximation of functions this paper continues the investigation of approximating properties of generalized normal forms in fuzzy logic the problem is formalized and solved algebraically normal forms are considered in two variants infinite and finite it is proved that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any l valued function where l is a support set of any complete bl algebra the estimation of the quality of approximation is suggested moreover functions which can be precisely represented by the discrete normal forms are considered

goodness of fit and related inference processes for quantile regression abstract we introduce a goodness of fit process for quantile regression analogous to the conventional r2 statistic of least squares regression several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated the asymptotic behavior of the inference processes is shown to be closely related to earlier p sample goodness of fit theory involving bessel processes the approach is illustrated with some hypothetical examples an application to recent empirical models of international economic growth and some monte carlo evidence

wild bootstrap for quantile regression the existing theory of the wild bootstrap has focused on linear estimators in this note we broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators as most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression a simulation study on median regression is carried out to compare various bootstrap methods with a simple finite sample correction the wild bootstrap is shown to account for general forms of heteroscedasticity in a regression model with fixed design points

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

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

a note on bootstrapping the sample median efron 1979 1982 in his treatment of the bootstrap discusses its use for estimation of the asymptotic variance of the sample median in the sampling situation of independent and identically distributed random variables with common distribution function f having a positive derivative continuous in a neighborhood of the true median mu the natural conjecture that the bootstrap variance estimator converges almost surely to the asymptotic variance is shown by an example to be false unless a tail condition is imposed on f we prove that such strong convergence does hold under the fairly nonrestrictive condition that e lbrack mid x alpha rbrack 0

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

a conditional kolmogorov test this paper introduces a conditional kolmogorov test of model specification for parametric models with covariates regressors the test is an extension of the kolmogorov test of goodness of fit for distribution functions the test is shown to have power against 1 n local alternatives and all fixed alternatives to the null hypothesis a parametric bootstrap procedure is used to obtain critical values for the test

stability of dynamical systems with competitive controls the degenerate case abstract we study the stability of a dynamical system with two competitive controls to a general closed set the stability is proven to be equivalent to the continuity on such set of the value function of a differential game with maximum cost functional the existence of a suitably defined and continuous lyapunov function is proven to imply the stability our lyapunov function satisfies a differential inequality in the sense of the theory of viscosity solutions

a resampling method based on pivotal estimating functions summary suppose that under a semiparametric model setting one is interested in drawing inferences about a finite dimensi onal parameter vector based on an estimating function generally a consistent point estimator j for 0 the true value for j can be easily obtained by finding a root of the corresponding estimating equation to estimate the variance of ft however may involve complicated and subjective nonparametric functional estimates in this paper a general and simple resampling method for inferences about js0 based on pivotal estimating functions is proposed the new procedure is illustrated with the quantile and rank regression models for both cases our proposal can be easily and efficiently implemented with existing statistical software

cluster robust bootstrap inference in quantile regression models abstractin this article i develop a wild bootstrap procedure for cluster robust inference in linear quantile regression models i show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process the proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much smaller than the sample size an application to project star data is provided supplementary materials for this article are available online

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

discontinuous differential games and control systems with supremum cost abstract this paper concerns with the existence of a value for a zero sum two player differential game with supremum cost of the form c t 0 x 0 u v sup t 0 t h x t 0 x 0 u v under isaacs condition we characterize the value function as the unique solution in a suitable sense to a pde namely the hamilton jacobi isaacs equation as a byproduct we obtain a pde characterization of the value function for control system

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

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

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

identifying social interactions through conditional variance restrictions this paper proposes a new method for identifying social interactions using conditional variance restrictions the method provides a consistent estimate of the social multiplier when social interactions take the linear in means form manski 1993 when social interactions are not of the linear in means form the estimator under certain conditions continues to form the basis of a consistent test of the no social interactions null with correct large sample size the methods are illustrated using data from the tennessee class size reduction experiment project star the application suggests that differences in peer group quality were an important source of individual level variation in the academic achievement of project star kindergarten students

operations fitting triangular norm based biresiduation abstract given a t norm t and the corresponding biresiduation t an operation k fits the latter or shortly is fitting if t is respected by k in all its arguments in this paper the structure of fitting operations is investigated special attention is paid to the case of basic t norms the connection between the fitting property and the lipschitz property is stressed some examples are given

a generalization of zubov s method to perturbed systems a generalization of zubov s theorem on representing the domain of attraction via the solution of a suitable partial differential equation is presented for the case of perturbed systems with a singular fixed point for the construction it is necessary to consider solutions in the viscosity sense as a consequence maximal robust lyapunov functions can be characterized as viscosity solutions

evaluation of a three step method for choosing the number of bootstrap repetitions abstract this paper provides a variety of monte carlo simulations that evaluate the finite sample performance of the three step method for choosing the number of bootstrap repetitions suggested by andrews and buchinsky econometrica 67 2000 23 51 the simulations cover bootstrap standard errors confidence intervals tests and p values three commonly used econometric applications are considered linear regression binary probit and quantile regression in brief we find that the three step method works very well in all of the contexts examined here we also find that the number of bootstrap repetitions commonly used in econometric applications is much less than needed to achieve accurate bootstrap quantities

inference with dependent data using cluster covariance estimators this paper presents a novel way to conduct inference using dependent data in time series spatial and panel data applications our method involves constructing t and wald statistics utilizing a cluster covariance matrix estimator cce we then use an approximation that takes the number of clusters groups as xed and the number of observations per group to be large and calcu late limiting distributions of the t and wald statistics this approximation is analogous to xed b asymptotics of kiefer and vogelsang 2002 2005 kv for heteroskedasticity and autocorrelation consistent inference but in our case yields standard t and f distributions where the number of groups essentially plays the role of sample size we provide simulation evidence that demonstrates our procedure outperforms conventional inference procedures and performs comparably to kv

generalized extensionality of fuzzy relations in this work we investigate a relationship between extensionality and continuity of fuzzy relations we found conditions when extensionality implies continuity and vice versa

differential games and zubov s method in this paper we provide generalizations of zubov s equation to differential games without the isaacs condition we show that both generalizations of zubov s equation which we call the min max and max min zubov equation respectively possess unique viscosity solutions which characterize the respective controllability domains as a consequence we show that under the usual isaacs condition the respective controllability domains as well as the local controllability assumptions coincide

a three step method for choosing the number of bootstrap repetitions this paper considers the problem of choosing the number of bootstrap repetitions b for bootstrap standard errors confidence intervals confidence regions hypothesis tests p values and bias correction for each of these problems the paper provides a three step method for choosing b to achieve a desired level of accuracy accuracy is measured by the percentage deviation of the bootstrap standard error estimate confidence interval length test s critical value test s p value or bias corrected estimate based on b bootstrap simulations from the corresponding ideal bootstrap quantities for which b the results apply quite generally to parametric semiparametric and nonparametric models with independent and dependent data the results apply to the standard nonparametric iid bootstrap moving block bootstraps for time series data parametric and semiparametric bootstraps and bootstraps for regression models based on bootstrapping residuals monte carlo simulations show that the proposed methods work very well

bootstrap standard error estimates for linear regression standard errors of parameter estimates are widely used in empirical work the bootstrap often can provide a convenient means of estimating standard errors the conditions under which bootstrap standard error estimates are theoretically justified have not received much attention however this article establishes conditions for the consistency of the moving blocks bootstrap estimators of the variance of the least squares estimator in linear dynamic models with dependent data we discuss several applications of this result in particular the use of bootstrap standard error estimates for bootstrapping studentized statistics a simulation study shows that inference based on bootstrap standard error estimates may be considerably more accurate in small samples than inference based on closed form asymptotic estimates

sibling and parent offspring correlation estimation with variable family size abstract a method for estimating intrafamilial correlations under variable family sizes involving weightings of paired data points is introduced classical methods of intrafamilial correlation estimation and those in current use are outlined and critically analyzed extensions of the proposed estimation method to more general data structures are delineated

on the number of bootstrap simulations required to construct a confidence interval abstract the purpose of this document is to make two points about the effect of the number of bootstrap simulations b on percentile t bootstrap confidence intervals the first point concerns coverage probability the second distance of the simulated critical point form the true critical point derived with b infinity in both cases the author has in mind applications to smooth statistics such as the studentized mean of a sample drawn from a continuous distribution he indicates the change that have to be made if the distribution of the statistic is not smooth additional keywords exponentive functions

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

a differential game with two players and one target we study a two player differential game in which one of the players wants the state of the system to reach an open target while the other player wants the state of the system to avoid this target we show that the victory domains of the players form a partition of the complement of the target one of them can be characterized by the mean of geometrical conditions as a discriminating domain finally we show that the common boundary of the victory domains enjoys a semipermeability property

control lyapunov functions and zubov s method for finite dimensional nonlinear control systems we study the relation between asymptotic null controllability and control lyapunov functions it is shown that control lyapunov functions clfs may be constructed on the domain of asymptotic null controllability as viscosity solutions of a first order pde that generalizes zubov s equation the solution is also given as the value function of an optimal control problem from which several regularity results may be obtained

value functions for differential games and control systems with discontinuous terminal cost this paper deals with mayer s problem for control systems and differential games with discontinuous terminal cost there are two main results in the paper the first one says that the value function for control systems can be characterized as the unique solution in suitable sense to the hamilton jacobi bellman equation without any regularity assumptions on the terminal cost for differential games satisfying isaacs s minmax condition the second main result says that the value function is the unique solution to the hamilton jacobi isaacs equation when the terminal cost is semicontinuous this allows to prove the existence of the value under isaacs s condition this paper extends some results already well known in the continuous case

mi algebras the existing arithmetics of fuzzy numbers usually stemming from the cut arithmetic do not preserve some of the important properties of the standard arithmetics of real numbers although one cannot expect a generalization of standard arithmetic to perfectly preserve all its properties the most important properties should be preserved at least in a weakened form we present a novel framework for arithmetics of extensional fuzzy numbers that more or less preserves all the important algebraic properties of the arithmetic of real numbers and thus seems to be an important seed for further investigations on this topic the suggested approach to arithmetics of extensional fuzzy numbers is demonstrated by many examples and besides its algebraic properties it is also shown to carry some desirable practical properties the investigation leads to novel algebraic structures mi algebras mi monoids mi groups mi fields that abstract the discussed properties the main idea of these structures is based on a set of pseudoidentities that complements the only commonly used identity element in a monoid group structure these pseudoidentities are elements that generalize the identity like behavior and allow us to weaken the standard forms of algebraic properties that are highly desirable to preserve at least in a weakened form appropriate properties of suggested mi structures are introduced and demonstrated by a number of practical examples

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

differential games of generalized pursuit and evasion differential games of generalized pursuit and evasion are studied by comparing them with differential games of fixed duration for which a theory already has been established it is shown that if the isaacs condition holds and the data satisfy reasonable hypotheses then the games have values which are continuous functions of the initial time and state if the data satisfy appropriate lipschitz conditions then the value is lipschitz continuous and satisfies the isaacs equation at all points of differentiability of the value

fuzzy transform as an additive normal form in this paper we recall a class of approximating formulas since they arose as a generalization of classical normal forms we denote them by the same term moreover we will show that the fuzzy transform f transform introduced in perfilieva i fuzzy approach to solution of differential equations with imprecise data application to reef growth problem in r v demicco g j klir eds fuzzy logic in geology academic press amsterdam 2003 pp 275 300 chapter 9 perfilieva i fuzzy transforms in j f peters a skowron eds transactions on rough sets ii rough sets and fuzzy sets lecture notes in computer science vol 3135 2004 pp 63 81 as an approximation method for continuous functions can be viewed as a particular case of normal form therefore the results valid for normal forms may be applied to f transforms as well

pursuit evasion problems and viscosity solutions of isaacs equations the dirichlet problem for first order hamilton jacobi equations arising in differential games of pursuit and evasion is studied local and global sub and superoptimality principles are stated for respectively viscosity sub and supersolutions these results are applied to obtain a general existence theorem and to prove the existence of the value of the game the main application concerns the problem of stability terminability of a dynamical system with two competitive controls and the opposite one of evadability from a general closed set the approach used in this paper allows lyapunov functions satisfying the usual condition in the weak sense of viscosity solutions

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

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

approximation of extensional fuzzy relations over a residuated lattice we investigate a relationship between extensionality of fuzzy relations and their lipschitz continuity on generalized metric spaces the duality of these notions is shown and moreover two particular applications of the extensionality property in the field of approximation are given

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

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

two guidelines for bootstrap hypothesis testing two guidelines for nonparametric bootstrap hypothesis testing are highlighted the first recommends that resampling be done in a way that reflects the null hypothesis even when the true hypothesis is distant from the null the second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction violation of the first guideline can seriously reduce the power of a test sometimes this reduction is spectacular since it is most serious when the null hypothesis is grossly in error the second guideline is of some importance when the conclusion of a test is equivocal it has no direct bearing on power but improves the level accuracy of a test

detecting differential expressions in genechip microarray studies a quantile approach in this article we consider testing for differentially expressed genes in genechip studies by modeling and analyzing the quantiles of gene expression through probe level measurements by developing a robust rank score test for linear quantile models with a random effect we propose a reliable test for detecting differences in certain quantiles of the intensity distributions by using a genomewide adjustment to the test statistic to account for within array correlation we demonstrate that the proposed rank score test is highly effective even when the number of arrays is small our empirical studies with real experimental data show that detecting differences in the quartiles for the probe level data is a valuable complement to the usual mixed model analysis based on gaussian likelihood the methodology proposed in this article is a first attempt to develop inferential tools for quantile regression in mixed models