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

nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates abstract allowing for the existence of irrelevant covariates we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data we estimate the conditional quantile regression function using the check function based kernel method and suggest a data driven cross validation cv approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates when the number of covariates is large we first use a screening method to remove the irrelevant covariates and then apply the cv criterion to those that survive the screening procedure simulations and an empirical application demonstrate the usefulness of the proposed methods

perturbation free measurement of the harmonics to noise ratio in voice signals using pitch synchronous harmonic analysis the measurement of the harmonics to noise ratio hnr in speech signals gives an indication of the aperiodicity of the speech waveform this may be due to the presence of jitter shimmer additive noise waveshape change or some unknown combination of these factors in order to estimate the hnr as a measure of the additive noise component only the contaminating effects of the other contributory components must first be removed a pitch synchronous harmonic analysis is proposed to overcome this problem the procedure takes advantage of the time scale compression frequency expansion property of the fourier series in order to eliminate jitter and shimmer successive spectra are added by harmonic number as opposed to frequency location and perturbation is removed due to the fact that the relative heights of the harmonic components remain the same for scaled signals the technique is examined on synthetically generated voice signals a discussion of the results is given in terms of human voice signals characterization of jitter vocal tract filtering effects perturbation mechanisms nonlinear dynamics and the possibility of developing the method for use with inverse filtering strategies

model free forward screening via cumulative divergence feature screening plays an important role in the analysis of ultrahigh dimensional data due to complicated model structure and high noise level existing screening methods often suffer from model

an adaptive composite quantile approach to dimension reduction sufficient dimension reduction li 1991 has long been a prominent issue in multivariate nonparametric regression analysis to uncover the central dimension reduction space we propose in this paper an adaptive composite quantile approach compared to existing methods 1 it requires minimal assumptions and is capable of revealing all dimension reduction directions 2 it is robust against outliers and 3 it is structure adaptive thus more efficient asymptotic results are proved and numerical examples are provided including a real data analysis

trace pursuit a general framework for model free variable selection abstractwe propose trace pursuit for model free variable selection under the sufficient dimension reduction paradigm two distinct algorithms are proposed stepwise trace pursuit and forward trace pursuit stepwise trace pursuit achieves selection consistency with fixed p forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality the screening consistency property of forward trace pursuit based on sliced inverse regression is established finite sample performances of trace pursuit and other model free variable selection methods are compared through numerical studies supplementary materials for this article are available online

score test variable screening variable screening has emerged as a crucial first step in the analysis of high throughput data but existing procedures can be computationally cumbersome difficult to justify theoretically or inapplicable to certain types of analyses motivated by a high dimensional censored quantile regression problem in multiple myeloma genomics this paper makes three contributions first we establish a score test based screening framework which is widely applicable extremely computationally efficient and relatively simple to justify secondly we propose a resampling based procedure for selecting the number of variables to retain after screening according to the principle of reproducibility finally we propose a new iterative score test screening method which is closely related to sparse regression in simulations we apply our methods to four different regression models and show that they can outperform existing procedures we also apply score test screening to an analysis of gene expression data from multiple myeloma patients using a censored quantile regression model to identify high risk genes

global asymptotic stability beyond 3 2 type stability for a logistic equation with piecewise constant arguments abstract in this paper a logistic equation with multiple piecewise constant arguments is investigated in detail we generalize the approach in two papers k uesugi y muroya e ishiwata on the global attractivity for a logistic equation with piecewise constant arguments j math anal appl 294 2 2004 560 580 and y muroya e ishiwata n guglielmi global stability for nonlinear difference equations with variable coefficients j math anal appl 334 1 2007 232 247 and establish a new condition for the global stability of the equation their results are given as one of the special cases moreover we improve the 3 2 type stability condition under several dominance assumptions on the coefficients of the equation some examples and numerical simulations are also presented all of these examples show that there are several conditions for the global stability of the equation depending on the coefficients on the delay terms of the equation beyond the 3 2 type stability condition

parsimonious covariate selection with censored outcomes summary a new objective methodology is proposed to select the parsimonious set of important covariates that are associated with a censored outcome variable y the method simplifies to accommodate uncensored outcomes covariate selection proceeds in an iterated forward manner and is controlled by the pre chosen upper bound for the number of covariates to be selected and the global false selection rate and level a sequence of working regression models for the event y y given a covariate set is fit among subjects not censored before y and the corresponding process through y of conditional prediction error estimated the direction and magnitude of covariate effects can arbitrarily change with y the newly proposed adequacy measure for the covariate set is the slope coefficient resulting from a regression with no intercept between the baseline prediction error process for the intercept only model and that process corresponding to the covariate set under quite general conditions on the censoring variable the methods are shown to asymptotically control the false selection rate at the nominal level while consistently ranking covariate sets which permits recruitment of all important covariates from those available with probability tending to 1 a simulation study confirms these analytical results and compares the proposed methods to recent competitors two real data illustrations are provided

martingale difference correlation and its use in high dimensional variable screening in this article we propose a new metric the so called martingale difference correlation to measure the departure of conditional mean independence between a scalar response variable v and a vector predictor variable u our metric is a natural extension of distance correlation proposed by szekely rizzo and bahirov which is used to measure the dependence between v and u the martingale difference correlation and its empirical counterpart inherit a number of desirable features of distance correlation and sample distance correlation such as algebraic simplicity and elegant theoretical properties we further use martingale difference correlation as a marginal utility to do high dimensional variable screening to screen out variables that do not contribute to conditional mean of the response given the covariates further extension to conditional quantile screening is also described in detail and sure screening properties are rigorously justified both simulation results and real data illustrations demonstr

model selection via bayesian information criterion for quantile regression models bayesian information criterion bic is known to identify the true model consistently as long as the predictor dimension is finite recently its moderate modifications have been shown to be consistent in model selection even when the number of variables diverges those works have been done mostly in mean regression but rarely in quantile regression the best known results about bic for quantile regression are for linear models with a fixed number of variables in this article we investigate how bic can be adapted to high dimensional linear quantile regression and show that a modified bic is consistent in model selection when the number of variables diverges as the sample size increases we also discuss how it can be used for choosing the regularization parameters of penalized approaches that are designed to conduct variable selection and shrinkage estimation simultaneously moreover we extend the results to structured nonparametric quantile models with a diverging number of covariates we illustrate o

sure independence screening in generalized linear models with np dimensionality ultrahigh dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research among others fan and lv 2008 propose an independent screening framework by ranking the marginal correlations they showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with gaussian covariates and responses in this paper we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models we show that the proposed methods with fan and lv 2008 as a very special case also possess the sure screening property with vanishing false selection rate the conditions under which that the independence learning possesses a sure screening is surprisingly simple this justifies the applicability of such a simple method in a wide spectrum we quantify explicitly the extent to which the dimensionality can be reduced by independence screening which depends on the interactions of the covariance matrix of covariates and true parameters simulation studies are used to illustrate the utility of the proposed approaches in addition we supported in part by grant nsf grants dms 0714554 and dms 0704337 the bulk of the work was conducted when rui song was a postdoctoral research fellow at princeton university the authors would like to thank the associate editor and two referees for their constructive comments that improve the presentation and the results of the paper ams 2000 subject classifications primary 68q32 62j12 secondary 62e99 60f10

correcting the use of ensemble averages in the calculation of harmonics to noise ratios in voice signals a correcting formula for the estimation of harmonics to noise ratios hnr based on ensemble averaging techniques is derived the original method yields a biased approximation which is more accurate as the number of averaged pulses n increases however the method treats gradual waveform changes incorrectly as noise which is worsened for large values of n the obtained formula allows the use of as few averaged pulses as desired while allowing the complete removal of the bias from the estimate of hnr

survival analysis with quantile regression models quantile regression offers great flexibility in assessing covariate effects on event times thereby attracting considerable interests in its applications in survival analysis but currently available methods often require stringent assumptions or complex algorithms in this article we develop a new quantile regression approach for survival data subject to conditionally independent censoring the proposed martingale based estimating equations naturally lead to a simple algorithm that involves minimizations only of l1 type convex functions we establish uniform consistency and weak convergence of the resultant estimators we develop inferences accordingly including hypothesis testing second stage inference and model diagnostics we evaluate the finite sample performance of the proposed methods through extensive simulation studies an analysis of a recent dialysis study illustrates the practical utility of our proposals

lack of fit tests for quantile regression models the paper novelly transforms lack of fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates accordingly by applying some successful two sample test statistics in the literature two tests are constructed to check the lack of fit for low and high dimensional quantile regression models the low dimensional test works well when the number of covariates is moderate whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size the null distribution of the high dimensional test has an explicit form and the p values or critical values can then be calculated directly the finite sample performance of the tests proposed is examined by simulation studies and their usefulness is further illustrated by two real examples

variable screening via quantile partial correlation abstractin quantile linear regression with ultrahigh dimensional data we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors specifically we first employ quantile partial correlation for screening and then we apply the extended bayesian information criterion ebic for best subset selection our proposed method can successfully select predictors when the variables are highly correlated and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response theoretical results show that the proposed algorithm can yield the sure screening set by controlling the false selection rate model selection consistency can be achieved theoretically in practice we proposed using ebic for best subset selection so that the resulting model is screening consistent simulation studies demonstrate that the proposed algorithm performs well and an empirical example is present

model free feature screening for ultrahigh dimensional discriminant analysis this work is concerned with marginal sure independence feature screening for ultrahigh dimensional discriminant analysis the response variable is categorical in discriminant analysis this enables us to use the conditional distribution function to construct a new index for feature screening in this article we propose a marginal feature screening procedure based on empirical conditional distribution function we establish the sure screening and ranking consistency properties for the proposed procedure without assuming any moment condition on the predictors the proposed procedure enjoys several appealing merits first it is model free in that its implementation does not require specification of a regression model second it is robust to heavy tailed distributions of predictors and the presence of potential outliers third it allows the categorical response having a diverging number of classes in the order of o n with some 0 we assess the finite sample property of the proposed procedure by mont

conditional quantile screening in ultrahigh dimensional heterogeneous data summary to accommodate the heterogeneity that is often present in ultrahigh dimensional data we propose a conditional quantile screening method which enables us to select features that contribute to the conditional quantile of the response given the covariates the method can naturally handle censored data by incorporating a weighting scheme through redistribution of the mass to the right moreover it is invariant to monotone transformation of the response and requires substantially weaker conditions than do alternative methods we establish sure independent screening properties for both the complete and the censored response cases we also conduct simulations to evaluate the finite sample performance of the proposed method and compare it with existing approaches

the fused kolmogorov filter a nonparametric model free screening method a new model free screening method called the fused kolmogorov filter is proposed for high dimensional data analysis this new method is fully nonparametric and can work with many types of covariates and response variables including continuous discrete and categorical variables we apply the fused kolmogorov filter to deal with variable screening problems emerging from a wide range of applications such as multiclass classification nonparametric regression and poisson regression among others it is shown that the fused kolmogorov filter enjoys the sure screening property under weak regularity conditions that are much milder than those required for many existing nonparametric screening methods in particular the fused kolmogorov filter can still be powerful when covariates are strongly dependent on each other we further demonstrate the superior performance of the fused kolmogorov filter over existing screening methods by simulations and real data examples

persistence contractivity and global stability in logistic equations with piecewise constant delays abstract we establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium n 1 a i 0 m b i of the following differential equation with piecewise constant arguments dn t dt n t r t 1 an t i 0 m b i n n i n t n 0 1 2 n 0 n 0 0 and n j n j 0 j 1 2 m where r t is a nonnegative continuous function on 0 r t 0 i 0mbi 0 bi 0 i 0 1 2 m and a i 0mbi 0 these new conditions depend on a b0 and i 1mbi and hence these are other type conditions than those given by so and yu hokkaido math j 24 1995 269 286 and others in particular in the case m 0 and r t r 0 we offer necessary and sufficient conditions for the persistence and contractivity of solutions we also investigate the following differential equation with nonlinear delay terms dx t dt x t r t 1 ax t g x t x t 1 x t m t 0 x k k 0 0 k m and 0 0 where r t is a nonnegative continuous function on 0 r t 0 1 ax g x x x 0 has a unique solution x 0 and g x0 x1 xm c1 0 0 0

feature screening via distance correlation learning this article is concerned with screening features in ultrahigh dimensional data analysis which has become increasingly important in diverse scientific fields we develop a sure independence screening procedure based on the distance correlation dc sis the dc sis can be implemented as easily as the sure independence screening sis procedure based on the pearson correlation proposed by fan and lv however the dc sis can significantly improve the sis fan and lv established the sure screening property for the sis based on linear models but the sure screening property is valid for the dc sis under more general settings including linear models furthermore the implementation of the dc sis does not require model specification e g linear model or generalized linear model for responses or predictors this is a very appealing property in ultrahigh dimensional data analysis moreover the dc sis can be used directly to screen grouped predictor variables and multivariate response variables we establish

quantile adaptive model free variable screening for high dimensional heterogeneous data we introduce a quantile adaptive framework for nonlinear variable screening with high dimensional heterogeneous data this framework has two distinctive features 1 it allows the set of active variables to vary across quantiles thus making it more flexible to accommodate heterogeneity 2 it is model free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest under appropriate conditions on the quantile functions without requiring the existence of any moments the new procedure is shown to enjoy the sure screening property in ultra high dimensions furthermore the quantile adaptive framework can naturally handle censored data arising in survival analysis we prove that the sure screening property remains valid when the response variable is subject to random right censoring numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantile specific information from heteroscedastic data

locally weighted censored quantile regression censored quantile regression offers a valuable supplement to cox proportional hazards model for survival analysis existing work in the literature often requires stringent assumptions such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels moreover some of the work uses recursive algorithms making it challenging to derive asymptotic normality to overcome these drawbacks we propose a new locally weighted censored quantile regression approach that adopts the redistribution of mass idea and employs a local reweighting scheme its validity only requires conditional independence of the survival time and the censoring variable given the covariates and linearity at the particular quantile level of interest our method leads to a simple algorithm that can be conveniently implemented with r software applying recent theory of m estimation with infinite dimensional parameters we establish the consistency and asymptotic normality of the pr

the product limit estimator and the bootstrap some asymptotic representations the product limit estimator and its quantile process are represented as i i d mean processes with a remainder of ordern 3 4 logn 3 4 a s corresponding bootstrap versions of these representations are given which can help one visualize how the bootstrap procedure operates in this set up

temporal and spectral estimations of harmonics to noise ratio in human voice signals the quantity harmonic to noise ratio hnr has been used to estimate the level of noise in human voice signals hnr estimation can be accomplished in two ways 1 on a time domain basis in which hnr is computed directly from the acoustic waveform and 2 on a frequency domain basis in which hnr is computed from a transformed representation of the waveform an algorithm for computing hnr in the frequency domain was modified and tested in the work described here the modifications were designed to reduce the influence of spectral leakage in the computation of harmonic energy and to remove the necessity of spectral baseline shifting prescribed in one existing algorithm g de krom j speech hear res 36 254 266 1993 frequency domain estimations of hnr based on this existing algorithm and our modified algorithm were compared to time domain estimations on synthetic signals and human pathological voice samples results indicated a highly significant linear correlation between frequency and time domain estimations of hnr for our modified approach

testing for marginal linear effects in quantile regression this paper develops a new marginal testing procedure to detect the presence of significant predictors associated with the conditional quantiles of a scalar response the idea is to fit the marginal quantile regression on each predictor one at a time and then base the test on the t statistics associated with the most predictive predictors a resampling method is devised to calibrate this test statistic which has non regular limiting behavior due to the selection of the most predictive variables asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified even though a fixed dimension is assumed to derive the asymptotic results the proposed test is applicable and computationally feasible for large dimensional predictors the method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response the approach is illustrated using an application to an hiv drug resistance dataset

on the global attractivity for a logistic equation with piecewise constant arguments in this paper we consider the following logistic equation with piecewise constant arguments dn t dt rn t 1 j 0majn t j t 0 m 1 n 0 n0 0 n j n j 0 j 1 2 m where r 0 a0 a1 am 0 j 0maj 0 and x means the maximal integer not greater than x the sequence nn n 0 where nn n n n 0 1 2 satisfies the difference equation nn 1 nnexpr1 j 0majnn j n 0 1 2 under the condition that the first term a0 dominates the other m coefficients ai 1 i m we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium n 1 j 0maj

minimizing the effect of period determination on the computation of amplitude perturbation in voice current methods of computing amplitude perturbation present in human voices depend upon being able to accurately determine fundamental period in this paper two methods of estimating the amplitude perturbation present in human voices which do not depend on accurate determination of the boundaries between fundamental periods are described in both of these methods amplitude perturbation is computed as the variance of an ensemble of periods calculated after these periods have been aligned in time in one method time alignment is accomplished using zero phase transformation in the second method an unconstrained dynamic programming procedure is used the accuracy of estimating amplitude perturbation by these two methods is evaluated using synthetic and natural voice signals and is also compared with an estimation using zero padding based time alignment the unconstrained dynamic programming method is shown to provide accurate estimation of voice amplitude perturbation over a variety of signal conditions

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

composite coefficient of determination and its application in ultrahigh dimensional variable screening in this article we propose to measure the dependence between two random variables through a composite coefficient of determination ccd of a set of nonparametric regressions these regressions ta

censored regression quantiles using quantile regression to analyze survival times offers an valuable complement to traditional cox proportional hazards modelling unfortunately this approach has been hampered by the lack of a conditional quantile estimator for censored data that is directly analogous to the kaplan meier estimator and applies under standard assumptions for censored regression models here a recursively reweighted estimator of the regression quantile process is developed as a direct generalization of the kaplan meier estimator specifically the asymptotic behavior is directly analogous to that of the kaplan meier estimator and computation is essentially equivalent to current simplex methods for the quantile process in the uncensored case some preliminary examples suggest the strong potential of these methods as a complement to the use of cox models

feature selection for varying coefficient models with ultrahigh dimensional covariates this article is concerned with feature screening and variable selection for varying coefficient models with ultrahigh dimensional covariates we propose a new feature screening procedure for these models based on conditional correlation coefficient we systematically study the theoretical properties of the proposed procedure and establish their sure screening property and the ranking consistency to enhance the finite sample performance of the proposed procedure we further develop an iterative feature screening procedure monte carlo simulation studies were conducted to examine the performance of the proposed procedures in practice we advocate a two stage approach for varying coefficient models the two stage approach consists of a reducing the ultrahigh dimensionality by using the proposed procedure and b applying regularization methods for dimension reduced varying coefficient models to make statistical inferences on the coefficient functions we illustrate the proposed two stage approach by a real data example supplementary materials for this article are available online

time normalization of voice signals using functional data analysis the harmonics to noise ratio hnr has been used to quantify the waveform irregularity of voice signals yumoto et al j acoust soc am 71 1544 1550 1982 this measure assumes that the signal consists of two components a harmonic component which is the common pattern that repeats from cycle to cycle and an additive noise component which produces the cycle to cycle irregularity it has been shown j qi j acoust soc am 92 2569 2576 1992 that a valid computation of the hnr requires a nonlinear time normalization of the cycle wavelets to remove phase differences between them this paper shows the application of functional data analysis to perform an optimal nonlinear normalization and compute the hnr of voice signals results obtained for the same signals using zero padding linear normalization and dynamic programming algorithms are presented for comparison functional data analysis offers certain advantages over other approaches it preserves meaningful features of signal shape produces differentiable results and allows flexibility in selecting the optimization criteria for the wavelet alignment an extension of the technique for the time normalization of simultaneous voice signals such as acoustic egg and airflow signals is also shown the general purpose of this article is to illustrate the potential of functional data analysis as a powerful analytical tool for studying aspects of the voice production process