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

multitask quantile regression under the transnormal model abstractwe consider estimating multitask quantile regression under the transnormal model with focus on high dimensional setting we derive a surprisingly simple closed form solution through rank based covariance regularization in particular we propose the rank based l1 penalization with positive definite constraints for estimating sparse covariance matrices and the rank based banded cholesky decomposition regularization for estimating banded precision matrices by taking advantage of the alternating direction method of multipliers nearest correlation matrix projection is introduced that inherits sampling properties of the unprojected one our work combines strengths of quantile regression and rank based covariance regularization to simultaneously deal with nonlinearity and nonnormality for high dimensional regression furthermore the proposed method strikes a good balance between robustness and efficiency achieves the oracle like convergence rate and provides the provable prediction interval und

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results

global existence to the vlasov poisson system and propagation of moments without assumption of finite kinetic energy we consider classical as well as weak solutions to the three dimensional vlasov poisson system without assuming finiteness of kinetic energy we prove global existence of classical solutions by assuming the initial datum is smooth enough and has a compact velocity spatial support which will be specified in theorem 1 1 we also establish some propagation results for low moments of weak solutions

to how many simultaneous hypothesis tests can normal student s t or bootstrap calibration be applied in the analysis of microarray data and in some other contemporary statistical problems it is not uncommon to apply hypothesis tests in a highly simultaneous way the number n say of tests used can be much larger than the sample sizes n to which the tests are applied yet we wish to calibrate the tests so that the overall level of the simultaneous test is accurate often the sampling distribution is quite different for each test so there may not be an opportunity to combine data across samples in this setting how large can n be as a function of n before level accuracy becomes poor here we answer this question in cases where the statistic under test is of student s t type we show that if either the normal or student t distribution is used for calibration then the level of the simultaneous test is accurate provided that log n increases at a strictly slower rate than n 1 3 as n diverges on the other hand if bootstrap methods are used for calibration then we may choose log n almost as large as

method of medians for lifetime data with weibull models the weibull family of distributions is frequently used in failure time models the maximum likelihood estimator is very sensitive to occurrence of upper and lower outliers especially when the hazard function is increasing we consider the method of medians estimator for the two parameter weibull model as an m estimator it has a bounded influence function and is highly robust against outliers it is easy to compute as it requires solving only one equation instead of a pair of equations as for most other m estimators furthermore no assumptions or adjustments are needed for the estimator when there are some possibly censored observations at either end of the sample about 16 per cent of the largest observations and 34 per cent of the smallest observations may be censored without affecting the calculations we also present a simple criterion to choose between the maximum likelihood estimator and the method of medians estimator to improve on the finite sample efficiency of the weibull model robust inference on the shape parameter is also considered the usefulness with contaminated or censored samples is illustrated by examples on three lifetime data sets a simulation study was carried out to assess the performance of the proposed estimator and the confidence intervals of a variety of contaminated weibull models

identifying risk factors for severe childhood malnutrition by boosting additive quantile regression we investigated the risk factors for childhood malnutrition in india based on the 2005 2006 demographic and health survey by applying a novel estimation technique for additive quantile regression ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects and as a consequence focus on average properties of the response the use of such a regression model for analyzing childhood malnutrition in developing or transition countries implies that the estimated effects describe the average nutritional status however it is of even greater interest to analyze quantiles of the response distribution such as the 5 or 10 quantile which relate to the risk of extreme malnutrition our investigation is based on a semiparametric extension of quantile regression models where different types of nonlinear effects are included in the model equation leading to additive quantile regression we addressed the variable selection and model c

propagation of moments and regularity for the 3 dimensional vlasov poisson system we prove that if the initial data has moments inv higher than three then the solution of vlasov poisson has also moments inv higher than three we deduce from this different regularity results on the local density the force field or the solution itself also we give a new uniqueness result and new regularity results for solutions satisfying only the energy andl bounds our proofs are based on a new representation formula and logarithmic estimates for the force field

a multistep protein lysate array quantification method and its statistical properties the protein lysate array is an emerging technology for quantifying the protein concentration ratios in multiple biological samples statistical inference for a parametric quantification procedure has been inadequately addressed in the literature mainly because the appropriate asymptotic theory involves a problem with the number of parameters increasing with the number of observations in this article we develop a multistep procedure for the sigmoidal models ensuring consistent estimation of the concentration levels with full asymptotic efficiency the results obtained in the article justify inferential procedures based on large sample approximations simulation studies and real data analysis are used in the article to illustrate the performance of the proposed method in finite samples the multistep procedure is convenient to work with asymptotically and is recommended for its statistical efficiency in protein concentration estimation and improved numerical stability by focusing on optimization of lower dimensional objective functions

sampling of generalized almost cyclostationary signals in this paper the problem of sampling a continuous time generalized almost cyclostationary gacs signal is addressed the class of such nonstationary signals includes as a special case the almost cyclostationary acs signals acs signals filtered by some linear time variant channels are further examples it is shown that the discrete time signal constituted by the samples of a gacs signal is a discrete time acs signal thus discrete time acs signals can arise not only from the sampling of continuous time acs signals but from the sampling of a wider class of nonstationary signals as well namely the continuous time gacs signals in the paper relationships between generalized cyclic statistics of a continuous time gacs signal and cyclic statistics of the discrete time acs signal constituted by its samples are derived the problem of aliasing in the domain of the cycle frequencies is considered and a condition assuring that the cyclic temporal moment function of the discrete time signal can be obtained by sampling that of the continuous time signal is determined finally it is shown that starting from the sampled signal the gacs or acs nature of the continuous time signal can be conjectured provided that the analysis parameters such as the sampling period padding factor and data record length are properly chosen

a general bahadur representation of m estimators and its application to linear regression with nonstochastic designs we obtain strong bahadur representations for a general class of m estimators that satisfies sigma i psi x i theta o delta n where the x i s are independent but not necessarily identically distributed random variables the results apply readily to m estimators of regression with nonstochastic designs more specifically we consider the minimum l p distance estimators bounded influence gm estimators and regression quantiles under appropriate design conditions the error ratesobtained for the first order approximations are sharp in these cases we also provide weaker and more easily verifiable conditions that suffice for an error rate that is suboptimal but strong enough for deriving the asymptotic distribution of m estimators in a wide variety of problems

sufficient moment and truncated moment conditions for the law of the iterated logarithm various sufficient conditions for the law of the iterated logarithm are given extending the main result of the author s previous paper 16 and kolmogoroff s law of iterated logarithm as a byproduct we give a unified approach to various old and new stability results

markov chain marginal bootstrap markov chain marginal bootstrap mcmb is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of m estimators of linear regression the mcmb method distinguishes itself from the usual bootstrap methods in two important aspects it involves solving only one dimensional equations for parameters of any dimension and produces a markov chain rather than a conditionally independent sequence it is designed to alleviate computational burdens often associated with bootstrap in high dimensional problems the validity of mcmb is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models

strong representations for lad estimators in linear models consider the standard linear modely i z i e i i 1 2 n where zi denotes theith row of ann x p design matrix p is an unknown parameter to be estimated andei are independent random variables with a common distribution functionf the least absolute deviation lad estimate tilde beta of is defined as any solution of the minimization problem sum limits i 1 n left y i z i tilde beta right inf left sum limits i 1 n left y i z i beta right beta in mathbb r p right

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

inference for censored quantile regression models in longitudinal studies we develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants we consider a semi parametric quantile regression model that makes no distributional assumptions our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit in such studies the focus is often on testing hypotheses about treatment equality to this end we propose a rank score test for large sample inference on a subset of the covariates we demonstrate the importance of accounting for both censoring and intra subject dependency and evaluate the performance of our proposed methodology in a simulation study we then apply the proposed inference procedures to data from an aids related clinical trial we conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable

on the lagrangian structure of transport equations the vlasov poisson system the vlasov poisson system is an important nonlinear transport equation used to describe the evolution of particles under their self consistent electric or gravitational field the existence of classical solutions is limited to dimensions d 3 under strong assumptions on the initial data whereas weak solutions are known to exist under milder conditions however in the setting of weak solutions it is unclear whether the eulerian description provided by the equation physically corresponds to a lagrangian evolution of the particles in this article we develop several general tools concerning the lagrangian structure of transport equations with nonsmooth vector fields and we apply these results to show that weak renormalized solutions of vlasov poisson are lagrangian and actually that the concepts of renormalized and lagrangian solutions are equivalent as a corollary we prove that finite energy solutions in dimension d 4 are transported by a global flow in particular they preserve all the natural casimir invariants and we obtain the global existence of weak solutions in any dimension under minimal assumptions on the initial data

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

regularity and propagation of moments in some nonlinear vlasov systems we introduce a new approach to prove the regularity of solutions to transport equations of the vlasov type our approach is mainly based on the proof of propagation of velocity moments as in a previous paper by lions and perthame 16 we combine it with moment lemmas which assert that locally in space velocity moments can be gained from the kinetic equation itself we apply our theory to two cases first to the vlasov poisson system and we solve a long standing conjecture namely the propagation of any moment larger than two next to the vlasov stokes system where we prove the same result for fairly singular kernels

a general framework for quantile estimation with incomplete data quantile estimation has attracted significant research interests in recent years however there has been only a limited literature on quantile estimation in the presence of incomplete data in this paper we propose a general framework to address this problem our framework combines the two widely adopted approaches for missing data analysis the imputation approach and the inverse probability weighting approach via the empirical likelihood method the proposed method is capable of dealing with many different missingness settings we mainly study three of them i estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates ii estimating the conditional quantile of a fully observed response while the covariates are partially available and iii estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables the proposed method allows multiple models for both the missingness probability and the data distribution the resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified the asymptotic distributions are established using the empirical process theory

the vlasov equation with infinite mass we show existence and uniqueness for the solutions to the vlasov equation for a positive smooth and short range potential in the case of unbounded mass

rank based estimates in the linear model with high breakdown point abstract an estimator in the linear model is defined by minimizing an objective function the derivative of which is a signed rank statistic the scores are generated from a function h 0 1 0 which is not necessarily nondecreasing as is usually assumed it is shown that this estimator can be chosen with a maximal breakdown point of 5 moreover strong consistency and asymptotic normality with convergence rate n 1 2 of the proposed estimator are proved under various regularity conditions because the objective function generally is not convex in the regression parameters the usual proofs of asymptotic normality do not carry over instead the proof is based on an asymptotic linearity result similar to that obtained by huber for m estimates and some moment estimates for signed rank statistics numerical examples illustrate the behavior of the estimator

m estimation of linear models with dependent errors we study asymptotic properties of m estimates of regression parameters in linear models in which errors are dependent weak and strong bahadur representations of the m estimates are derived and a central limit theorem is established the results are applied to linear models with errors being short range dependent linear processes heavy tailed linear processes and some widely used nonlinear time series

the vlasov poisson system with infinite mass and energy this paper deals with solutions to the vlasov poisson system with an infinite mass the solution to the poisson equation cannot be defined directly because the macroscopic density is constant at infinity to solve this problem we decompose the solution to the kinetic equation into a homogeneous function and a perturbation we are then able to prove an existence result in short time for weak solutions to the equation for the perturbation even though there are no a priori estimates by lack of positivity

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

on the 3 d vlasov poisson system with point charges global solutions with unbounded supports and propagation of velocity spatial moments abstract a new energy functional which is shown to decay to zero as time tends to infinite is introduced for the three dimensional vlasov poisson plasma in the presence of heavy point charges with repulsive interaction moreover a new kind of pointwise energy of a plasma particle relative to each point charge is also constructed and the variation of its root is shown to be controlled by the electrostatic fields based on those results we prove global existence and uniqueness of a classical solution possibly having infinite kinetic energy but with compact velocity spatial support specified in theorem 1 1 furthermore for the single point charge vlasov poisson plasma global existence and polynomial propagation of velocity spatial moments of weak solutions are also established

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

on the law of the iterated logarithm for independent banach space valued random variables in this paper we establish some general forms of the law of the iterated logarithm for independent random variables xn with banach space values where xn is not necessarily identically distributed our results include the kolmogorov law of the iterated logarithm lil in both finite and infinite dimensional cases and they improve the wittmann lil as well as extend it to the vector setting the ledoux talagrand lil for an i i d sequence is also a simple corollary of our results

monotone b spline smoothing abstract estimation of growth curves or item response curves often involves monotone data smoothing methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated built on the ideas of koenker ng and portnoy and ramsay we propose monotone b spline smoothing based on l 1 optimization this method inherits the desirable properties of spline approximations and the computational efficiency of linear programs the constrained fit is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence through applications to some real and simulated data we show that the method is useful in a variety of applications the basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems

estimation in a semiparametric model for longitudinal data with unspecified dependence structure this paper considers an extension of m estimators in semiparametric models for independent observations to the case of longitudinal data we approximate the nonparametric function by a regression spline and any m estimation algorithm for the usual linear models can then be used to obtain consistent estimators of the model and valid largesample inferences about the regression parameters without any specification of the error distribution and the covariance structure included as special cases are the analysis of the conditional mean and median functions for longitudinal data

the vlasov poisson system with infinite kinetic energy and initial data in lp r6 abstract in this paper the global existence of weak solutions to the three dimensional vlasov poisson system with infinite kinetic energy and initial data in l p r 6 is studied the propagation of low moments in the velocity variables is also proved

higher order infinitesimal robustness using the von mises expansion we study the higher order infinitesimal robustness of a general m functional and characterize its second order properties we show that second order robustness is equivalent to the boundedness of both the estimator s estimating function and its derivative with respect to the parameter it implies at the same time i variance robustness and ii robustness of higher order saddlepoint approximations to the estimator s finite sample density the proposed construction of second order robust m estimators is fairly general and potentially useful in a variety of relevant settings besides the theoretical contributions we discuss the main computational issues and provide an algorithm for the implementation of second order robust m estimators finally we illustrate our theory by monte carlo simulation and in a real data estimation of the maximal losses of nikkei 225 index returns our findings indicate that second order robust estimators can improve on other widely applied robus

a strongly consistent information criterion for linear model selection based on m estimation in this paper a linear model selection procedure based on m estimation is proposed which includes many classical model selection criteria as its special cases it is shown that the proposed criterion is strongly consistent under certain mild conditions for instance without assuming normality of the distribution of the random errors the results from a simulation study are also presented

multiple imputation in quantile regression summary we propose a multiple imputation estimator for parameter estimation in a quantile regression model when some covariates are missing at random the estimation procedure fully utilizes the entire dataset to achieve increased efficiency and the resulting coefficient estimators are root n consistent and asymptotically normal to protect against possible model misspecification we further propose a shrinkage estimator which automatically adjusts for possible bias the finite sample performance of our estimator is investigated in a simulation study finally we apply our methodology to part of the eating at american s table study data investigating the association between two measures of dietary intake

segmented model selection in quantile regression using the minimum description length principle this article proposes new model fitting techniques for quantiles of an observed data sequence including methods for data segmentation and variable selection the main contribution however is in providing a means to perform these two tasks simultaneously this is achieved by matching the data with the best fitting piecewise quantile regression model where the fit is determined by a penalization derived from the minimum description length principle the resulting optimization problem is solved with the use of genetic algorithms the proposed fully automatic procedures are unlike traditional break point procedures not based on repeated hypothesis tests and do not require unlike most variable selection procedures the specification of a tuning parameter theoretical large sample properties are derived empirical comparisons with existing break point and variable selection methods for quantiles indicate that the new procedures work well in practice

lagrangian solutions to the vlasov poisson system with l1 density the recently developed theory of lagrangian flows for transport equations with low regularity coefficients enables to consider non bv vector fields we apply this theory to prove existence and stability of global lagrangian solutions to the repulsive vlasov poisson system with only integrable initial distribution function with finite energy these solutions have a well defined lagrangian flow an a priori estimate on the smallness of the superlevels of the flow in three dimensions is established in order to control the characteristics

the optimal discovery procedure a new approach to simultaneous significance testing summary the neyman pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known this result has played a major role in the development of significance testing strategies that are used in practice most of the work extending single testing strategies to multiple tests has focused on formulating and estimating new types of significance measures such as the false discovery rate these methods tend to be based on p values that are calculated from each test individually ignoring information from the other tests i show here that one can improve the overall performance of multiple significance tests by borrowing information across all the tests when assessing the relative significance of each one rather than calculating p values for each test individually the optimal discovery procedure is introduced which shows how to maximize the number of expected true positive results for each fixed number of expected false positive results the optimality that is achieved by this procedure is shown to be closely related to optimality in terms of the false discovery rate the optimal discovery procedure motivates a new approach to testing multiple hypotheses especially when the tests are related as a simple example a new simultaneous procedure for testing several normal means is defined this is surprisingly demonstrated to outperform the optimal single test procedure showing that a method which is optimal for single tests may no longer be optimal for multiple tests connections to other concepts in statistics are discussed including stein s paradox shrinkage estimation and the bayesian approach to hypothesis testing

semilinear high dimensional model for normalization of microarray data a theoretical analysis and partial consistency normalization of microarray data is essential for removing experimental biases and revealing meaningful biological results motivated by a problem of normalizing microarray data a semilinear in slide model slim has been proposed to aggregate information from other arrays slim is generalized to account for across array information resulting in an even more dynamic semiparametric regression model this model can be used to normalize microarray data even when there is no replication within an array we demonstrate that this semiparametric model has a number of interesting features the parametric component and the nonparametric component that are of primary interest can be consistently estimated the former having a parametric rate and the latter having a nonparametric rate whereas the nuisance parameters cannot be consistently estimated this is an interesting extension of the partial consistent phenomena which itself is of theoretical interest the asymptotic normality for the parametric component

compressive temporal higher order cyclostationary statistics the application of nonlinear transformations to a cyclostationary signal for the purpose of revealing hidden periodicities has proven to be useful for applications requiring signal selectivity and noise tolerance the fact that the hidden periodicities referred to as cyclic moments are often compressible in the fourier domain motivates the use of compressive sensing cs as an efficient acquisition protocol for capturing such signals in this paper we consider the class of temporal higher order cyclostationary statistics thocs estimators when cs is used to acquire the cyclostationary signal assuming compressible cyclic moments in the fourier domain we develop a theoretical framework for estimating thocs using the low rate nonuniform sampling protocol from cs and illustrate the performance of this framework using simulated data

classical solutions to the fokker planck bgk equation with infinite energy abstract we consider the bgk equation perturbed by fokker planck operator which is important in the kinetic theory of rarefied gases this model equation which we call the fokker planck bgk equation has many physical features that the fokker planck boltzmann equation possesses by establishing a new moments lemma and l bounds for macroscopic quantities without the boundedness of energy we get several global existence and uniqueness results to the cauchy problem of the fokker planck bgk equation under various circumstances with infinite energy

asymptotic distributions of principal components based on robust dispersions algebraically principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability an attractive alternative in robust principal component analysis is to replace the classical variability measure i e variance by a robust dispersion measure this projection pursuit approach was first proposed in li chen 1985 as a method of constructing a robust scatter matrix recent unpublished work of c croux and a ruiz gazen provided the influence functions of the resulting principal components the present paper focuses on the asymptotic distributions of robust principal components in particular we obtain the asymptotic normality of the principal components that maximise a robust dispersion measure we also explain the need to use a dispersion functional with a continuous influence function

enhanced quantile normalization of microarray data to reduce loss of information in gene expression profiles in microarray experiments removal of systematic variations resulting from array preparation or sample hybridization conditions is crucial to ensure sensible results from the ensuing data analysis for example quantile normalization is routinely used in the treatment of both oligonucleotide and cdna microarray data even though there might be some loss of information in the normalization process we recognize that the ideal normalization if it ever exists would aim to keep the maximal amount of gene profile information with the lowest possible noise with this objective in mind we propose a valuable enhancement to quantile normalization and demonstrate through three affymetrix experiments that the enhanced normalization can result in better performance in detecting and ranking differentially expressed genes across experimental conditions

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

detecting case control expression quantitative trait loci using locally most powerful or maximin robust rank tests in testing genome wide gene expression quantitative trait loci efficiency robust statistical methods and their computational convenience are most relevant for this purpose we propose to use a modified locally most powerful rank test for the analysis of case control expression data this modified rank test statistic is computationally simple robust for non normally distributed expression data and asymptotically locally most powerful it depends on the specification of a location distribution form for data but is not sensitive to misspecifications when such a location distribution form cannot be specified we apply gastwirth s maximin efficiency robust rank test to gene expression data to maximize the worst pitman asymptotic relative efficiency among a family of location distributions we conduct simulation studies to assess their performance and use an application to real data for illustration copyright 2011 john wiley sons ltd

bayesian empirical likelihood for quantile regression bayesian inference provides a flexible way of combining data with prior information however quantile regression is not equipped with a parametric likelihood and therefore bayesian inference for quantile regression demands careful investigation this paper considers the bayesian empirical likelihood approach to quantile regression taking the empirical likelihood into a bayesian framework we show that the resultant posterior from any fixed prior is asymptotically normal its mean shrinks toward the true parameter values and its variance approaches that of the maximum empirical likelihood estimator a more interesting case can be made for the bayesian empirical likelihood when informative priors are used to explore commonality across quantiles regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas e g high or low percentile levels through empirical likelihood the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains by using an mcmc algorithm in the computation we avoid the daunting task of directly maximizing empirical likelihood the finite sample performance of the proposed method is investigated empirically where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels a theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method

an enhanced quantile approach for assessing differential gene expressions due to the small number of replicates in typical gene microarray experiments the performance of statistical inference is often unsatisfactory without some form of information sharing across genes in this article we propose an enhanced quantile rank score test eqrs for detecting differential expression in genechip studies by analyzing the quantiles of gene intensity distributions through probe level measurements a measure of sign correlation delta plays an important role in the rank score tests by sharing information across genes we develop a calibrated estimate of delta which reduces the variability at small sample sizes we compare the eqrs test with four other approaches for determining differential expression the gene specific quantile rank score test the quantile rank score test assuming a common delta a modified t test using summarized probe set level intensities and the mack skillings rank test on probe level data the proposed eqrs is shown to be favorable for preserving false discovery rates and for being robust against outlying arrays in addition we demonstrate the merits of the proposed approach using a genechip study comparing gene expression in the livers of mice exposed to chronic intermittent hypoxia and of those exposed to intermittent room air

measurement errors in quantile regression models abstract this paper develops estimation and inference for quantile regression models with measurement errors we propose an easily implementable semiparametric two step estimator when repeated measures for the covariates are available building on recent theory on z estimation with infinite dimensional parameters consistency and asymptotic normality of the proposed estimator are established we also develop statistical inference procedures and show the validity of a bootstrap approach to implement the methods in practice monte carlo simulations assess the finite sample performance of the proposed methods we apply the methods to the investment equation model using a firm level data with repeated measures of investment demand tobin s q we document strong heterogeneity in the sensitivity of investment to tobin s q and cash flow across the conditional distribution of investment the cash flow sensitivity is relatively larger at the lower part of the distribution providing evidence that these firms are more exposed to and dependent on fluctuations in internal finance

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

prediction of functional status for the elderly based on a new ordinal regression model the functional mobility of the elderly is a very important factor in aging research and prognostic information is valuable in making clinical and health care policy decisions we develop a predictive model for the functional status of the elderly based on data from the second longitudinal study of aging lsoa ii the functional status is an ordinal response variable the ordered probit model has been moderately successful in analyzing such data however its reliance on the normal distribution for its latent variable hinders its accuracy and potential in this paper we focus on the prediction of conditional quantiles of the functional status based on a more general transformation model the proposed estimation procedure does not rely on any parametric specification of the conditional distribution functions aiming to reduce model misspecification errors in the prediction cross validation within the lsoa ii data shows that our prediction intervals are more informative than those from the ordered probit

sub nyquist cyclostationary detection for cognitive radio cognitive radio requires efficient and reliable spectrum sensing of wideband signals in order to cope with the sampling rate bottleneck new sampling methods have been proposed that sample below the nyquist rate however such techniques decrease the signal to noise ratio snr deteriorating the performance of subsequent energy detection cyclostationary detection which exploits the periodic property of communication signal statistics absent in stationary noise is a natural candidate for this setting in this paper we consider cyclic spectrum recovery from sub nyquist samples in order to achieve both efficiency and robustness to noise to that end we propose a structured compressed sensing algorithm which extends orthogonal matching pursuit to account for the structure imposed by cyclostationarity next we derive a lower bound on the sampling rate required for perfect cyclic spectrum recovery in the presence of stationary noise in particular we show that the cyclic spectrum can be reconstructed from samples obtained at 4 5 of the nyquist rate without any sparsity constraints on the signal if the signal of interest is sparse then the sampling rate may be further reduced to 8 5 of the landau rate once the cyclic spectrum is recovered we estimate the number of transmissions that compose the input signal along with their carrier frequencies and bandwidths simulations show that cyclostationary detection outperforms energy detection in low snrs in the sub nyquist regime this was already known in the nyquist regime but is even more pronounced at sub nyquist sampling rates

on rank estimators in increasing dimensions abstract the family of rank estimators including han s maximum rank correlation han 1987 as a notable example has been widely exploited in studying regression problems for these estimators although the linear index is introduced for alleviating the impact of dimensionality the effect of large dimension on inference is rarely studied this paper fills this gap via studying the statistical properties of a larger family of m estimators whose objective functions are formulated as u processes and may be discontinuous in increasing dimension set up where the number of parameters p n in the model is allowed to increase with the sample size n first we find that often in estimation as p n n 0 p n n 1 2 rate of convergence is obtainable second we establish bahadur type bounds and study the validity of normal approximation which we find often requires a much stronger scaling requirement than p n 2 n 0 third we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent and show that the step size in implementing the covariance estimator has to be adjusted with respect to p n all theoretical results are further backed up by simulation studies

asymptotic distributions of the maximal depth estimators for regression and multivariate location we derive the asymptotic distribution of the maximal depth regression estimator recently proposed in rousseeuw and hubert the estimator is obtained by maximizing a projection based depth and the limiting distribution is characterized through a max min operation of a continuous process the same techniques can be used to obtain the limiting distribution of some other depth estimators including tukey s deepest point based on half space depth results for the special case of two dimensional problems have been available but the earlier arguments have relied on some special geometric properties in the low dimensional space this paper completes the extension to higher dimensions for both regression and multivariate location models

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

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

global weak solutions of vlasov maxwell systems we study here the vlasov maxwell system in its classical and relativistic form we prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data the main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset

adaptive l estimation for linear models asymptotically efficient adaptive estimators for the slope parameters of the linear regression model are constructed based upon the regression quantile statistics suggested by koenker and bassett the estimators are natural analogues of the adaptive l estimators of location of sacks but employ kernel density type estimators of the optimal l estimator weight function

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

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