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

an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

algebraic and differential operator equations abstract explicit expressions for solutions of boundary value problems and cauchy problems related to the operator differential equation x n a n 1 x n 1 a 0 x 0 are given in terms of solutions of the algebraic operator equation x n a n 1 x n 1 a 0 0 a method for solving this algebraic equation is studied

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

estimating and testing a quantile regression model with interactive effects this paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables we provide conditions under which the slope parameter estimator is asymptotically gaussian monte carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate meth ods we discuss an approach to testing the model specification against a competing fixed effects specification the paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment the findings show that i a change in the gender composition of a class impacts differently low and high performing students ii while smaller classes are beneficial for low performers larger classes are beneficial for high performers iii reductions in class size do not seem to impact mean and median student performance iv the fixed effects specification is rejected in favor of the interactive effects specification

nonparametric specification tests for conditional duration models this paper deals with the testing of autoregressive conditional duration acd models by gauging the distance between the parametric density and hazard rate functions implied by the duration process and their non parametric estimates we derive the asymptotic justification using the functional delta method for fixed and gamma kernels and then investigate the finite sample properties through monte carlo simulations although our tests display some size distortion bootstrapping suffices to correct the size without compromising their excellent power we show the practical usefulness of such testing procedures for the estimation of intraday volatility patterns

tests of linear hypotheses and l 1 estimation statistics of a linear hypothesis in the standard linear model these test statistics which correspond to wald likelihood ratio and lagrange multiplier tests are shown to have the same limiting chi square behavior under mild regularity conditions on design and the distribution of errors the asymptotic theory of the tests is derived for a large class of error distributions thus in huber s 10 terminology we investigate the behavior of the likelihood ratio test under non standard conditions the asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly gaussian errors but may yield large efficiency gains in non gaussian situations the lagrange multiplier test seems particularly attractive from a computational standpoint we derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis extension of these results to hypotheses of the form r 8 r is a straightforward exercise when the density of the error distribution is strictly positive at the median all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null when the variance of the error distribution is bounded analogous results are well known for classical forms of the wald likelihood ratio and lagrange multipler tests based on least squares methods see for example silvey 18 and the discussion in section 4 below

permutation tests for least absolute deviation regression a permutation test based on proportionate reduction in sums of absolute deviations when passing from reduced to full parameter models is developed for testing hypotheses about least absolute deviation lad estimates of conditional medians in linear regression models sampling simulations demonstrated that the permutation test on full model lad estimates had greater relative power 1 06 1 43 than normal theory tests on least squares estimates for asymmetric chi square error distributions and symmetric double exponential error distributions for models with one n 35 and n 63 and three n 63 independent variables relative power was 77 84 for normal error distributions power simulations demonstrated the low sensitivity of lad estimates and permutation tests to outlier contamination and heteroscedasticity that was a linear function of x and increased sensitivity to heteroscedasticity that was a function of x2 for simple regression models three permutation procedures for testing partial models in multiple regression were compared permuting residuals from the reduced model permuting residuals from the full model and permuting the dependent variable permuting residuals from the reduced model maintained nominal error rates best under the null hypothesis for all error distributions and for correlated and uncorrelated independent variables power under the alternative hypotheses for this partial testing procedure was similar to full lad regression model tests four example applications of lad regression are provided

slowly oscillating solutions of cauchy problems with countable spectrum let u be a bounded slowly oscillating mild solution of an inhomogeneous cauchy problem u t au t f t on r or r where a is a closed operator such that ap a ir is countable and the carleman or laplace transform of f has a continuous extension to an open subset of the imaginary axis with countable complement it is shown that u is asymptotically almost periodic if u is totally ergodic or if x does not contain c 0 in the case of a problem on r similar results hold for second order cauchy problems and volterra equations

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

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

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

on the asymptotics of constrained m estimation limit theorems for an m estimate constrained to lie in a closed subset of r d are given under two different sets of regularity conditions a consistent sequence of global optimizers converges under chernoff regularity of the parameter set a n consistent sequence of local optimizers converges under clarke regularity of the parameter set in either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value limit theorems for the optimal value are also obtained agreeing with chernoff s result in the case of maximum likelihood with global optimizers

solving second order matrix differential equations with regular singular points avoiding the increase of the problem dimension in this paper we propose a method for solving second order matrix differential systems of the form t 2x ta t x b t x 0 where a and b are analytic matrix functions in a neighborhood of t 0 series solutions of the problem are constructed without increasing the problem dimension by introducing the concept of a fundamental set of solutions of the above equation an analogous result to the frobenius theorem to solve the corresponding scalar equation is presented

analytic solutions of coupled second order delay differential equations abstract in this paper initial value problems for systems of second order delay differential equations with variable coefficients are treated by means of a combined use of the method of steps and the method of frobenius the analytic solution of the problem is constructed

tractable bayesian variable selection beyond normality abstractbayesian variable selection often assumes normality but the effects of model misspecification are not sufficiently understood there are sound reasons behind this assumption particularly for large p ease of interpretation analytical and computational convenience more flexible frameworks exist including semi or non parametric models often at the cost of some tractability we propose a simple extension that allows for skewness and thicker than normal tails but preserves tractability it leads to easy interpretation and a log concave likelihood that facilitates optimization and integration we characterize asymptotically parameter estimation and bayes factor rates under certain model misspecification under suitable conditions misspecified bayes factors induce sparsity at the same rates than under the correct model however the rates to detect signal change by an exponential factor often reducing sensitivity these deficiencies can be ameliorated by inferring the error distribution a simp

intersection bounds estimation and inference we develop a practical and novel method for inference on intersection bounds namely bounds defined by either the infimum or supremum of a parametric or nonparametric function or equivalently the value of a linear programming problem with a potentially infinite constraint set we show that many bounds characterizations in econometrics for instance bounds on parameters under conditional moment inequalities can be formulated as intersection bounds our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters and also applies to models with inequalities that are nonseparable in parameters since analog estimators for intersection bounds can be severely biased in finite samples routinely underestimating the size of the identified set we also offer a median bias corrected estimator of such bounds as a by product of our inferential procedures we develop theory for large sample inference based on the strong approximation of a sequence of series or kernel based empirical processes by a sequence of penultimate gaussian processes these penultimate processes are generally not weakly convergent and thus are non donsker our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes our construction also provides new adaptive inequality moment selection methods we provide conditions for the use of nonparametric kernel and series estimators including a novel result that establishes strong approximation for any general series estimator admitting linearization which may be of independent interest

explicit solution of systems of second order differential difference equations abstract in this paper systems of second order differential difference equations are studied by using the concept of co solution of certain associated algebraic matrix equations an explicit solution of initial value problems for second order differential difference systems is constructed

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

asymptotic inference for the constrained quantile regression process abstract i investigate the asymptotic distribution of linear quantile regression coefficient estimates when the parameter lies on the boundary of the parameter space in order to allow for inferences made across many conditional quantiles i provide a uniform characterization of constrained quantile regression estimates as a stochastic process over an interval of quantile levels to do this i pose the process of estimates as solutions to a parameterized family of constrained optimization problems parameterized by quantile level a uniform characterization of the dual solution to these problems the so called regression rankscore process is also derived which can be used for score type inference in quantile regression the asymptotic behavior of quasi likelihood ratio wald and regression rankscore processes for inference when the null hypothesis asserts that the parameters lie on a boundary follows from the features of the constrained solutions

testing functional inequalities abstract this paper develops tests for inequality constraints of nonparametric regression functions the test statistics involve a one sided version of l p type functionals of kernel estimators 1 p drawing on the approach of poissonization this paper establishes that the tests are asymptotically distribution free admitting asymptotic normal approximation in particular the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives furthermore we establish conditions under which the tests have nontrivial local power against pitman local alternatives some results from monte carlo simulations are presented

a noncommutative version of the bispectral problem we consider a matrix valued version of the bispectral problem involving a block tridiagonal doubly infinite matrix and a first order differential operator with matrix coefficients we give a set of necessary conditions that the coefficients need to satisfy and solve these equations under a variety of conditions the situations discussed here should make it plain that while the corresponding problem in the scalar case is relatively trivial and devoid of any interest the noncommutative version of the problem is much richer and subtle the results here should be useful for instance in the study of a noncommutative version of the nonlinear toda lattice

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

tauberian theorems for the laplace stieltjes transform let a 0 oo c be a function of locally bounded variation with a 0 0 whose laplace stieltjes transform g z fo e z da t is absolutely convergent for re z 0 let e be the singular set of g in ir and suppose that 0 e various estimates for lim supt la t g o l are obtained in particular a t g 0 as t oo if i e is null ii sup sup e aysda s oo yee t o o iii lim lim sup sup a s a t 0 610 t oo t 6 s t this result contains tauberian theorems for laplace transforms power series and dirichlet series

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

wald criteria for jointly testing equality and inequality restrictions on montre comment le test de wald s applique a des ensembles de restrictions d egalite et d inegalite et on presente la distribution pour de grands echantillons du test sous l hypothese nulle

asymptotically almost periodic solutions of evolution equations in banach spaces abstract tile linear abstract evolution equation u t au t t t r is considered where a d a e e is the generator of a strongly continuous semigroup of operators in the banach space e starting from analogs of kadets and loomis theorems for vector valued almost periodic functions we show that if a i r is countable and r e is asymptotically almost periodic then every bounded and uniformly continuous solution u to is asymptotically almost periodic provided e tu t has uniformly convergent means for all a i r related results on eberlein weakly asymptotically almost periodic periodic asymptotically periodic and c0 solutions of as well as on the discrete case of solutions of difference equations are included

the local nature of hypothesis tests involving inequality constraints in nonlinear models this paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis the paper is organized around a lemma which characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test we then present two examples which illustrate several implications of this lemma we also discuss the impact of these properties on the empirical implementation and interpretation of these test procedures

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

inference based on conditional moment inequalities in this paper we propose an instrumental variable approach to constructing confidence sets cs s for the true parameter in models defined by conditional moment inequalities equalities we show that by properly choosing instrument functions one can transform conditional moment inequalities equalities into unconditional ones without losing identification power based on the unconditional moment inequalities equalities we construct cs s by inverting cramer von mises type or kolmogorov smirnov type tests critical values are obtained using generalized moment selection gms procedures we show that the proposed cs s have correct uniform asymptotic coverage probabilities new methods are required to establish these results because an infinite dimensional nuisance parameter affects the asymptotic distributions we show that the tests considered are consistent against all fixed alternatives and typically have power against n 1 2 local alternatives to some but not all sequences of distributions in the null hypothesis monte carlo simulations for five different models show that the methods perform well in finite samples

a unified approach to likelihood inference on stochastic orderings in a nonparametric context abstract for data in a two way contingency table with ordered margins we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities this leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log likelihood ratio tests the usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases in particular for each of these three orderings we determine the transformation required to apply the estimation algorithm we then consider testing the hypothesis that the rows are identically distributed against the alternative that they are stochastically ordered as well as testing each stochastic order against an u

confidence sets for partially identified parameters that satisfy a finite number of moment inequalities this paper proposes a computationally simple way to construct confidence sets for a parameter of interest in models comprised of moment inequalities building on results from the literature on multivariate one sided tests i show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities the associated test statistic has an asymptotic chi bar square distribution and can be inverted to construct an asymptotic confidence set for the parameter of interest even if that parameter is only partially identified critical values for the test are easily computed and a monte carlo study demonstrates implementation and finite sample performance

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

testing multivariate economic restrictions using quantiles the example of slutsky negative semidefiniteness abstract this paper is concerned with testing a core economic restriction negative semidefiniteness of the slutsky matrix we consider a system of nonseparable structural equations with infinite dimensional unobservables and employ quantile regression methods because they allow us to utilize the entire distribution of the data difficulties arise because the restriction involves several equations while the quantile is a univariate concept we establish that we may use quantiles of linear combinations of the dependent variable develop a new empirical process based test that applies kernel quantile estimators and investigate its finite and large sample behavior finally we apply all concepts to canadian microdata

bent line quantile regression with application to an allometric study of land mammals speed and mass summary quantile regression which models the conditional quantiles of the response variable given covariates usually assumes a linear model however this kind of linearity is often unrealistic in real life one situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates to analyze such data we propose a bent line quantile regression model we derive its parameter estimates prove that they are asymptotically valid given the existence of a change point and discuss several methods for testing the existence of a change point in bent line quantile regression together with a power comparison by simulation an example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests

an improved bootstrap test of stochastic dominance we propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling the method admits prospects involving infinite as well as finite dimensional unknown parameters so that the variables are allowed to be residuals from nonparametric and semiparametric models the proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions this paper also characterizes the set of probabilities so that the asymptotic size is exactly equal to the nominal level uniformly as our simulation results show these characteristics of our tests lead to an improved power property in general the improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test s limiting distribution

least absolute error estimation in the presence of serial correlation abstract in this paper we consider some aspects of least absolute error estimation applied to a regression model with serially correlated errors in addition to the estimation itself we study an estimator of the asymptotic covariance matrix of the estimator a generalized version of the estimator analogous to gls and the properties of several tests for serial correlation both the theoretical and small sample properties are analyzed the latter through a monte carlo experiment

stability of individual elements under one parameter semigroups let t t t o be a c0 semigroup on a banach space x with generator a and let x e x if a a n ir is empty and t 4 t t x is uniformly continuous then iit t xii 0 as t oo if the semigroup is sun reflexive a a n ir is countable pa a n ir is empty and t 4 t t x is uniformly weakly continuous then t t x 0 weakly as t oo questions of almost periodicity and of stabilization of contraction semigroups on hilbert space are also discussed

when uniform weak convergence fails empirical processes for dependence functions via epi and hypographs for copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube the empirical copula process does not converge weakly with respect to the supremum distance this makes it hard to verify asymptotic properties of inference procedures for such copulas to resolve the issue a new metric for locally bounded functions is introduced and the corresponding weak convergence theory is developed convergence with respect to the new metric is related to epi and hypoconvergence and is weaker than uniform convergence still for continuous limits it is equivalent to locally uniform convergence whereas under mild side conditions it implies lp convergence even in cases where uniform convergence fails weak convergence with respect to the new metric is established for empirical copula and tail dependence processes no additional assumptions are needed for tail dependence functions and for copulas the assumptions reduce to existence and continuity of the partial derivatives almost everywhere on the unit cube the results are applied to obtain asymptotic properties of minimum distance estimators goodness of fit tests and resampling procedures

tauberian theorems and stability of solutions of the cauchy problem let f r x be a bounded strongly measurable function with values in a banach space x and let ie be the singular set of the laplace transform f in ir suppose that e is countable and 0 e i uf s u du 0 uniformly for s 0 as 0 for each in e it is shown that t 0 e i uf u du f i 0 as t for each in r e in particular f t 0 if f is uniformly continuous this result is similar to a tauberian theorem of arendt and batty it is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on buc r x and it implies several results concerning stability of solutions of cauchy problems

explicit solutions for second order operator differential equations with two boundary value conditions ii abstract boundary value problems for second order operator differential equations with two boundary value conditions are studied explicit expressions of the solutions in terms of data problems are given by means of the application of algebraic techniques analogous expressions to the ones known for the scalar case are obtained

exact and approximate solutions of second order including function delay differential equations with variable coefficients by means of the method of steps and the method of power series the exact solution of the initial value problem for coupled second order delay differential equations with variable coefficients is constructed then in a bounded domain a finite analytic solution with error bounds is provided

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

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