extending the archimedean copula methodology to model multivariate survival data grouped in clusters of variable size summary for the analysis of clustered survival data two different types of model that take the association into account are commonly used frailty models and copula models frailty models assume that conditionally on a frailty term for each cluster the hazard functions of individuals within that cluster are independent these unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster copula models in contrast assume that the joint survival function of the individuals within a cluster is given by a copula function evaluated in the marginal survival function of each individual it is the copula function which describes the association between the lifetimes within a cluster a major disadvantage of the present copula models over the frailty models is that the size of the different clusters must be small and equal to set up manageable estimation procedures for the different model parameters we describe a copula model for clustered survival data where the clusters are allowed to be moderate to large and varying in size by considering the class of archimedean copulas with completely monotone generator we develop both one and two stage estimators for the copula parameters furthermore we show the consistency and asymptotic normality of these estimators finally we perform a simulation study to investigate the finite sample properties of the estimators we illustrate the method on a data set containing the time to first insemination in cows with cows clustered in herds

nonparametric inference of quantile curves for nonstationary time series the paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes using bahadur representation and gaussian approximation results for nonstationary time series simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type i error rates a wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the asymptotic results in particular our results can be used to test the trends of extremes of climate variables an important problem in understanding climate change our methodology is applied to the analysis of the maximum speed of tropical cyclone winds it was found that an inhomogeneous upward trend for cyclone wind speeds is pronounced at high quantile values however there is no trend in the mean lifetime maximum wind speed this example shows the effectiveness of the quantile regression technique

estimation of extreme conditional quantiles through power transformation the estimation of extreme conditional quantiles is an important issue in numerous disciplines quantile regression qr provides a natural way to capture the covariate effects at different tails of the response distribution however without any distributional assumptions estimation from conventional qr is often unstable at the tails especially for heavy tailed distributions due to data sparsity in this article we develop a new three stage estimation procedure that integrates qr and extreme value theory by estimating intermediate conditional quantiles using qr and extrapolating these estimates to tails based on extreme value theory using the power transformed qr the proposed method allows more flexibility than existing methods that rely on the linearity of quantiles on the original scale while extending the applicability of parametric models to borrow information across covariates without resorting to nonparametric smoothing in addition we propose a test procedure to assess the commonality of ext

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

instrumental variable quantile regression a robust inference approach abstract in this paper we develop robust inference procedures for an instrumental variables model defined by y d u where d u is strictly increasing in u and u is a uniform variable that may depend on d but is independent of a set of instrumental variables z the proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely the use of the proposed procedures is illustrated through two empirical examples

local dependence functions for some families of bivariate distributions and total positivity the purpose of this paper is to investigate a very useful application of a certain local dependence function c f x y which was considered recently by holland and wang 20 an interesting property of c f x y is that the underlying joint density f x y is tp 2 that is totally positive of order 2 if and only if c f x y 0 this gives an elegant way to investigate the tp 2 property of any bivariate distribution for the saramanov family the ali mikhail haq family of bivariate distributions and the family of bivariate elliptical distributions we derive the local dependence function and obtain conditions for f x y to be tp 2 these families are quite rich and include many other large classes of bivariate distributions as their special cases similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with pareto conditionals

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

bootstrap approximations in model checks for regression abstract let m m be a parametric model for an unknown regression function m for example m may consist of all polynomials or trigonometric polynomials with a given bound on the degree to check the full model m i e to test for h 0 m e m it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals in this article we show that the distribution of this process may be approximated by the wild bootstrap the method is applied to simulated datasets as well as to real data

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

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

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

pairwise dependence diagnostics for clustered failure time data frailty and copula models specify a parametric dependence structure for multivariate failure time data estimation of some joint quantities can be highly sensitive to the assumed parametric form and hence model fit is an important issue this paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models the approach is based on the cumulative sum of residuals that are calculated in bivariate time the residuals reflect the difference between the observed and expected bivariate association structures the proposed model checking process is interpretable with a limiting distribution which can be approximated using the bootstrap simulations and a data example illustrate the practical application of the method

copulas based time series combined forecasters time series combined forecasters have been superior to the respective single models in statistical terms in this way the linear combination functions e g the simple average sa and the minimal variance mv approaches have been the main alternatives for aggregation in the literature in this work it is presented a copulas based method for combining biased single models copulas are multivariate functions that operate on marginal probability distributions and have the specific advantage of generalizing mv by flexibly modelling the forecasters residuals and then the dependence among them a typical divide and conquer framework that can result in superior combined forecasters the usefulness of the copulas based combination method is highlighted by means of a comparison with sa and mv models based on a number of simulated cases and a real world time series

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

the use of gaussian quadrature for estimation in frailty proportional hazards models in this paper we propose a novel gaussian quadrature estimation method in various frailty proportional hazards models we approximate the unspecified baseline hazard by a piecewise constant one resulting in a parametric model that can be fitted conveniently by gaussian quadrature tools in standard software such as sas proc nlmixed we first apply our method to simple frailty models for correlated survival data e g recurrent or clustered failure times then to joint frailty models for correlated failure times with informative dropout or a dependent terminal event such as death simulation studies show that our method compares favorably with the well received penalized partial likelihood method and the monte carlo em mcem method for both normal and gamma frailty models we apply our method to three real data examples 1 the time to blindness of both eyes in a diabetic retinopathy study 2 the joint analysis of recurrent opportunistic diseases in the presence of death for hiv infected patients and 3 the joint modeling of local distant tumor recurrences and patients survival in a soft tissue sarcoma study the proposed method greatly simplifies the implementation of the joint frailty models and makes them much more accessible to general statistical practitioners

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

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

two interpretations of the discrimination parameter in this paper we propose two interpretations for the discrimination parameter in the two parameter logistic model 2plm the interpretations are based on the relation between the 2plm and two stochastic models in the first interpretation the 2plm is linked to a diffusion model so that the probability of absorption equals the 2plm the discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given for the second interpretation the 2plm is connected to a specific type of race model in the race model the discrimination parameter is inversely related to the dependency of the information used in the decision process extended versions of both models with person to person variability in the difficulty parameter are considered when fitted to a data set it is shown that a generalization of the race model that allows for dependency between choices and response times rts is the best fitting model

the shift invariant discrete wavelet transform and application to speech waveform analysis the discrete wavelet transform may be used as a signal processing tool for visualization and analysis of nonstationary time sampled waveforms the highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity and accepting a least squares inverse pseudoinverse in place of a true inverse a new algorithm for the pseudoinverse of the shift invariant transform that is easier to implement in array oriented scripting languages than existing algorithms is presented together with self contained proofs representing only one of the many and varied potential applications a recorded speech waveform illustrates the benefits of shift invariance with pseudoinvertibility visualization shows the glottal modulation of vowel formants and frication noise revealing secondary glottal pulses and other waveform irregularities additionally performing sound waveform editing operations i e cutting and pasting sections on the shift invariant wavelet representation automatically produces quiet click free section boundaries in the resulting sound the capabilities of this wavelet domain editing technique are demonstrated by changing the rate of a recorded spoken word individual pitch periods are repeated to obtain a half speed result and alternate individual pitch periods are removed to obtain a double speed result the original pitch and formant frequencies are preserved in informal listening tests the results are clear and understandable

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

failure time models with matched data summary holt prentice 1974 adapted the proportional hazards model to give failure time models for matched pairs in which a member of the ith pair with covariate z has hazard function aoi t exp bz with full data more efficient estimators of b can be obtained if a weibull specialization ai qt11 of the baseline hazard can be assumed but these estimators are unavailable for censored data estimates of formed by assuming the ai s are independent gamma variates are investigated the resulting estimators are found to be more efficient than those obtained by holt prentice when the ai s are in fact gamma to be available for censored data and to perform well under a number of very different unimodal alternatives to a gamma distribution for the ai s

quantile association regression models it is often important to study the association between two continuous variables in this work we propose a novel regression framework for assessing conditional associations on quantiles we develop general methodology which permits covariate effects on both the marginal quantile models for the two variables and their quantile associations the proposed quantile copula models have straightforward interpretation facilitating a comprehensive view of association structure which is much richer than that based on standard product moment and rank correlations we show that the resulting estimators are uniformly consistent and weakly convergent as a process of the quantile index simple variance estimators are presented which perform well in numerical studies extensive simulations and a real data example demonstrate the practical utility of the methodology supplementary materials for this article are available online

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

estimation of the retransformed conditional mean in health care cost studies summary we propose a new approach for analyzing skewed and heteroscedastic health care cost data through regression of the conditional quantiles of the transformed cost using the appealing equivariance property of quantiles to monotone transformations we propose a distribution free estimator of the conditional mean cost on the original scale the proposed method is extended to a two part heteroscedastic model to account for zero costs commonly seen in health care cost studies simulation studies indicate that the proposed estimator has competitive and more robust performance than existing estimators in various heteroscedastic models

a specification test for univariate and multivariate proportional hazards models this paper applies white s 1982 econometrica 50 1 25 information matrix im test for correct model specification to proportional hazards models of univariate and multivariate censored survival data several alternative estimators of the test statistic are presented and their size performance examined white also suggested an estimator of the parameter covariance matrix that was robust to certain forms of model misspecification this has been subsequently proposed by others e g royall 1986 international statistical review 54 221 226 and applied by huster brookmeyer and self 1989 biometrics 45 145 156 as part of an independence working model iwm approach to multivariate censored survival data we illustrate how the im test can be used for both univariate data and as part of the iwm approach to multivariate data

diagnostics for assessing regression models abstract we concern ourselves with diagnostics for checking the overall and local goodness of fit of a model s x used in the regression of y on x u 0 1 d the model for s x is a functional form that depends on a finite number of unknown parameters two statistics and w are proposed that measure the level of agreement between the model fit to the data and the nonparametric kernel estimator on m preselected points in u conditions are given under which and w are asymptotically equivalent both of these statistics measure overall lack of fit and are related to the deviance their asymptotic distribution under the null model and under local alternatives is derived this work is motivated by the local mean deviance plot of landwehr pregibon and shoemaker for assessing overall lack of fit in logistic regression their plot is summarized by our test statistics and is extended to other likelihood based regressions of y on x

adaptive hypothesis testing using wavelets let a function f be observed with a noise we wish to test the null hypothesis that the function is identically zero against a composite nonparametric alternative functions from the alternative set are separated away from zero in an integral e g l 2 norm and also possess some smoothness properties the minimax rate of testing for this problem was evaluated in earlier papers by ingster and by lepski and spokoiny under different kinds of smoothness assumptions it was shown that both the optimal rate of testing and the structure of optimal in rate tests depend on smoothness parameters which are usually unknown in practical applications in this paper the problem of adaptive assumption free testing is considered it is shown that adaptive testing without loss of efficiency is impossible an extra log log factor is inessential but unavoidable payment for the adaptation a simple adaptive test based on wavelet technique is constructed which is nearly minimax for a wide range of besov classes

weighted quantile regression for analyzing health care cost data with missing covariates analysis of health care cost data is often complicated by a high level of skewness heteroscedastic variances and the presence of missing data most of the existing literature on cost data analysis have been focused on modeling the conditional mean in this paper we study a weighted quantile regression approach for estimating the conditional quantiles health care cost data with missing covariates the weighted quantile regression estimator is consistent unlike the naive estimator and asymptotically normal furthermore we propose a modified bic for variable selection in quantile regression when the covariates are missing at random the quantile regression framework allows us to obtain a more complete picture of the effects of the covariates on the health care cost and is naturally adapted to the skewness and heterogeneity of the cost data the method is semiparametric in the sense that it does not require to specify the likelihood function for the random error or the covariates we investigate the weighted quantile regression procedure and the modified bic via extensive simulations we illustrate the application by analyzing a real data set from a health care cost study copyright 2013 john wiley sons ltd

a simple estimator for a shared frailty regression model summary we propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution inferences for the frailty parameter can be obtained by using output from cox regression analyses the computational burden is substantially less than that of the other approaches to estimation the large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes the methods are motivated by studies of familial associations in the natural history of diseases their practical utility is illustrated with sib pair data from beaver dam wisconsin

an adaptive rate optimal test of linearity for median regression models this article is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness we develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate the test does not require knowledge of the distribution of the model s random noise component and it permits conditional heteroscedasticity of unknown form the numerical performance and usefulness of the test are illustrated by the results of monte carlo experiments and an empirical example

the consistency of nonlinear regression minimizing the l_1 norm we consider conditions in a nonlinear regression model for the consistency of the estimator obtained by minimizing the l 1 norm i e the sum of absolute deviations

on robustness of marginal regression coefficient estimates and hazard functions in multivariate survival analysis of family data when the frailty distribution is mis specified the shared frailty model is an extension of the cox model to correlated failure times and essentially a random effects model for failure time outcomes in this model the latent frailty shared by individual members in a cluster acts multiplicatively as a factor on the hazard function and is typically modelled parametrically one commonly used distribution is gamma where both shape and scale parameters are set to be the same to allow for unique identification of baseline hazard function it is popular because it is a conjugate prior and the posterior distribution possesses the same form as gamma in addition the parameter can be interpreted as a time independent cross ratio function a natural extension of odds ratio to failure time outcomes in this paper we study the effect of frailty distribution mis specification on the marginal regression estimates and hazard functions under assumed gamma distribution with an application to family studies the simulation results show that the biases are generally 10 and lower even when the true frailty distribution deviates substantially from the assumed gamma distribution this suggests that the gamma frailty model can be a practical choice in real data analyses if the regression parameters and marginal hazard function are of primary interest and individual cluster members are exchangeable with respect to their dependencies

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

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

on the use of nonparametric regression for model checking summary the use of nonparametric regression is explored to check the fit of a parametric regression model the principal aim is to check the validity of the regression curve rather than necessarily to detect outliers a pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model the types of data considered include discrete response variables where standard diagnostic techniques are often not appropriate and first order autoregressive series several numerical examples are given nonparametric regression can be used in an informal graphical way to assess the relationship between a response and an explanatory variable in this paper we aim to develop more formal methods of assessing the assumptions of a parametric model in particular when regression diagnostics of the type developed for normal linear models are not readily available the principal aim is to check the validity of the systematic part of the model by comparing a nonparametric estimate of the regression curve with a parametric one such a comparison may also identify outliers although the distinction between outliers and model inadequacy is not always easy two techniques are used to assess the fit of a parametric model in 2 confidence bands are constructed around the fitted regression curve by simulation a comparison of these with the nonparametric curve gives an indication of the nature of any departures from the model in 3 a pseudo likelihood ratio test is developed this provides a quantitative global assessment of fit in applying these ideas special emphasis is given to discrete data and notably logistic regression because of the difficulty in applying standard residual based model checking techniques to this type of response variable a poisson regression example is discussed in 4 however the underlying ideas have wider applications autoregressive time series of order 1 are discussed in 6 sections 5 and 7 discuss general issues we first discuss the context of binary regression with a single covariate and the difficulties caused by the discreteness of the response variable the observed data are assumed to be of the form xi yi ni where xi is a covariate value and yi has a binomial

automatic and reliable estimation of glottal closure instant and period the authors present an automatic and reliable algorithm for determining glottal closure instant gci as a byproduct nonstationary fundamental period estimation is achieved the computation includes twelve pole speech linear prediction analysis cross correlation and both direct and inverse fast fourier transforms or a convolution maximum likelihood epoch determination is used as the basis for locating gcis and the hilbert transformation is applied to improve performance and reliability a description of the system and the voiced unvoiced mixed v uv m decision procedure is given the results show that the algorithm works in noise free noisy and very noisy signals for vowels as well as for voiced constants the proposed pitch estimation only needs a very short frame length and gives accurate results at voice onset

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

the identifiability of the competing risks model summary this paper considers the consequences for identifiability of introducing regressors into the competing risks model of multistate duration analysis we establish conditions under which access to regressors overturns the nonidentification theorem of cox and tsiatis for both proportional and accelerated failure time models

local asymptotics for quantile smoothing splines quantile smoothing splines were introduced by koenker ng and portnoy as natural and appealing estimates of conditional quantiles of response variables the natural setting for the problem considers minimization of a weighted combination of a fit penalty and a roughness penalty over the space of functions whose derivatives have bounded variation although this space is not traditional shen has shown recently that the quantile smoothing splines do indeed converge at the usual optimal rate n 2 5 in various norms here local asymptotic results are obtained by establishing bahadur representations for local parameters of the splines these are used to obtain local rates of convergence to establish uniform convergence rates to provide local distribution theory for quantile b splines and to expand the fit measure in order to analyze an information criterion for determining the smoothing parameter examples of using derivatives of the smoothing splines for estimating jump functions are also presented

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

quantile correlations and quantile autoregressive modeling in this article we propose two important measures quantile correlation qcor and quantile partial correlation qpcor we then apply them to quantile autoregressive qar models and introduce two valuable quantities the quantile autocorrelation function qacf and the quantile partial autocorrelation function qpacf this allows us to extend the box jenkins three stage procedure model identification model parameter estimation and model diagnostic checking from classical autoregressive models to quantile autoregressive models specifically the qpacf of an observed time series can be employed to identify the autoregressive order while the qacf of residuals obtained from the fitted model can be used to assess the model adequacy we not only demonstrate the asymptotic properties of qcor and qpcor but also show the large sample results of qacf qpacf and the quantile version of the box pierce test moreover we obtain the bootstrap approximations to the distributions of parameter estimators and p

model diagnosis for parametric regression in high dimensional spaces summary we study tools for checking the validity of a parametric regression model when the dimension of the regressors is large many of the existing tests face the curse of dimensionality or require some ordering of the data our tests are based on the residual empirical process marked by proper functions of the regressors they are able to detect local alternatives converging to the null at parametric rates parametric and nonparametric alternatives are considered in the latter case through a proper principal component decomposition we are able to derive smooth directional tests which are asymptotically distribution free under the null model the new tests take into account precisely the geometry of the model a simulation study is carried through and an application to a real dataset is illustrated

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

goodness of fit tests for parametric regression models several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives these tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive neyman test and other methods the testing procedures formalize the traditional model diagnostic tools based on residual plots we examine the rates of contiguous alternatives that can be detected consistently by the adaptive neyman test applications of the procedures to the partially linear models are thoroughly discussed our simulation studies show that the new testing procedures are indeed powerful and omnibus the power of the proposed tests is comparable to the f test statistic even in the situations where the f test is known to be suitable and can be far more powerful than the f test statistic in other situations an application to testing linear models versus additive models is also discussed

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

semiparametrically efficient inference based on signs and ranks for median restricted models since the pioneering work of koenker and bassett 1978 econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest contrary to the traditional models where the noise is assumed to have mean zero median restricted models enjoy a rich group invariance structure in this paper we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models these procedures are based on residual signs and ranks and therefore insensitive to possible misspecification of the underlying innovation density yet semiparametrically efficient at correctly specified densities this latter combination is a definite advantage of these procedures over classical quasi likelihood methods the techniques we propose can be applied without additional technical difficulties to both cross sectional and time series models they do not require any explicit tangent space calculation nor any projections on these

test of significance based on wavelet thresholding and neyman s truncation abstract traditional nonparametric tests such as the kolmogorov smirnov test and the cramer von mises test are based on the empirical distribution functions although these tests possess root n consistency they effectively use only information contained in the low frequencies this leads to low power in detecting fine features such as sharp and short aberrants as well as global features such as high frequency alternations the drawback can be repaired via smoothing based test statistics in this article we propose two such kind of test statistics based on the wavelet thresholding and the neyman truncation we provide extensive evidence to demonstrate that the proposed tests have higher power in detecting sharp peaks and high frequency alternations while maintaining the same capability in detecting smooth alternative densities as the traditional tests similar conclusions can be made for two sample nonparametric tests of distribution functions in that case the traditional linear rank tests such as th

quantile regression for analyzing heterogeneity in ultra high dimension ultra high dimensional data often display heterogeneity due to either heteroscedastic variance or other forms of non location scale covariate effects to accommodate heterogeneity we advocate a more general interpretation of sparsity which assumes that only a small number of covariates influence the conditional distribution of the response variable given all candidate covariates however the sets of relevant covariates may differ when we consider different segments of the conditional distribution in this framework we investigate the methodology and theory of nonconvex penalized quantile regression in ultra high dimension the proposed approach has two distinctive features 1 it enables us to explore the entire conditional distribution of the response variable given the ultra high dimensional covariates and provides a more realistic picture of the sparsity pattern 2 it requires substantially weaker conditions compared with alternative methods in the literature thus it greatly alleviates the

specification tests of parametric dynamic conditional quantiles this article proposes omnibus specification tests of parametric dynamic quantile models in contrast to the existing procedures we allow for a flexible specification where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data generating process since the null limit distribution of tests is not pivotal we propose a subsampling approximation of the asymptotic critical values a monte carlo study shows that the asymptotic results provide good approximations for small sample sizes finally an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk

translation invariant data visualization with orthogonal discrete wavelets orthogonal discrete wavelet transforms can be made translation invariant by adding redundant wavelet coefficients through repeated shifting operations orthogonality is lost but isometry and compact time support can be preserved the practical application to data visualization of scalograms based on such transforms is discussed and illustrated with measured transient signals

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

cumulative incidence association models for bivariate competing risks data association models like frailty and copula models are frequently used to analyze clustered survival data and evaluate within cluster associations the assumption of noninformative censoring is commonly applied to these models though it may not be true in many situations in this paper we consider bivariate competing risk data and focus on association models specified for the bivariate cumulative incidence function cif a nonparametrically identifiable quantity copula models are proposed which relate the bivariate cif to its corresponding univariate cifs similarly to independently right censored data and accommodate frailty models for the bivariate cif two estimating equations are developed to estimate the association parameter permitting the univariate cifs to be estimated either parametrically or nonparametrically goodness of fit tests are presented for formally evaluating the parametric models both estimators perform well with moderate sample sizes in simulation studies the practical use of the methodology is illustrated in an analysis of dementia associations

commonality of cusum von neumann and smoothing based goodness of fit tests summary recent papers by munson jernigan 1989 and buckley 1991 propose nonparametric tests for the hypothesis of no predictor effect in regression the munson jernigan test is similar to the von neumann 1941 test while that of buckley is based on a functional of cusums these tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas fourier analysis is used to qualitatively compare the munson jernigan and buckley tests with two new tests constructed from nonparametric smoothers their relative powers are then studied by means of large sample analysis and simulation the cusum test is the most powerful for very smooth departures from the no effect hypothesis while the new tests based on smoothing ideas are clearly superior when the alternative is high frequency

competing risks quantile regression quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized in this paper we study quantile regression with competing risks data formulating the model based on conditional quantiles defined using the cumulative incidence function which includes as a special case an analog to the usual accelerated failure time model the proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and moreover relaxes the constancy constraint on regression coefficients thereby providing a useful perhaps more flexible alternative to the popular subdistribution proportional hazards model we derive an unbiased monotone estimating equation for regression parameters in the quantile model the uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum we develop inferences including covariance estimation second

detecting a smooth signal optimality of cusum based procedures summary cox et al 1988 show that under a random smooth function model with signal covariance matrix v a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic ytvy we show that if a well known difference based roughness measure is used to derive a natural choice for v then this statistic is the sum of squares of a residual cusum sequence thus we confirm theoretically the long held impression that the residual cusum sequence is powerful as a tool for the detection of smooth signal

on consistency of kendall s tau under censoring necessary and sufficient conditions for consistency of a simple estimator of kendall s tau under bivariate censoring are presented the results are extended to data subject to bivariate left truncation as well as right censoring

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

a translation invariant wavelet representation algorithm with applications we address the time varying problem of wavelet transforms and a new translation invariant wavelet representation algorithm is proposed using the algorithm introduced by beylkin see siam j numer anal vol 29 p 1716 1740 1992 we compute the wavelet transform for all the circular time shifts of a length n signal in o n log n operations the wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function we apply the translation invariant representation algorithm to a geoacoustic data compression application the results show that the new algorithm can reduce the distortion the squared error in our case substantially if the input signals are transients that are sensitive to time shifts

power transformed linear quantile regression with censored data we propose a class of power transformed linear quantile regression models for survival data subject to random censoring the estimation procedure follows two sequential steps first for a given transformation parameter we can easily obtain the estimates for the regression coefficients by minimizing a well defined convex objective function second we can estimate the transformation parameter based on a model discrepancy measure by constructing cumulative sum processes we show that both the regression and transformation parameter estimates are strongly consistent and asymptotically normal the variance covariance matrix depends on the unknown density function of the error term so we estimate the variance by the usual bootstrap approach we examine the performance of the proposed method for finite sample sizes through simulation studies and illustrate it with a real data example

analysis of dependent survival data applied to lifetimes of amalgam fillings when studying lifetimes of amalgam fillings one is faced with the fact that each patient may contribute multiple survival data this creates a dependence problem and some methods for solving it are presented here analysis for individual patients with simple approaches for combining data is discussed first then a parametric frailty model is applied to analyse variation within and between patients the results are presented in the form of an empirical bayes estimate for each patient

analysis of overdispersed count data by mixtures of poisson variables and poisson processes count data often show overdispersion compared to the poisson distribution overdispersion is typically modeled by a random effect for the mean based on the gamma distribution leading to the negative binomial distribution for the count this paper considers a larger family of mixture distributions including the inverse gaussian mixture distribution it is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures the same approach can be used to generate counting processes from poisson processes where the rate or the time is random a random rate corresponds to variation between patients whereas a random time corresponds to variation within patients

model checks for regression an innovation process approach in the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus smooth and directional goodness of fit tests since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain we propose to replace this process by its innovation martingale it turns out that the resulting tests are asymptotically distribution free under composite null models and may be readily performed a simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes

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

a shift invariant discrete wavelet transform this article presents a unifying approach to the derivation and implementation of a shift invariant wavelet transform of one and two dimensional 1 d and 2 d discrete signals starting with mallat s 1989 multiresolution wavelet representation mrwar it presents an analytical process through which a shift invariant orthogonal discrete wavelet transform called the multiscale wavelet representation mswar is obtained the coefficients in the mswar are shown to be inclusive of those in the mrwar with the implication that the derived representation is invertible the computational complexity of the mswar is quantified in terms of the required convolutions and its implementation is shown to be equivalent to the filter upsampling technique

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

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

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

an interior point algorithm for nonlinear quantile regression abstract a new algorithm for computing quantile regression estimates for problems in which the response function is nonlinear in parameters is described the nonlinear l 1 estimation problem is a special median case the algorithm is closely related to recent developments on interior point methods for solving linear programs performance of the algorithm on a variety of test problems including the censored linear quantile regression problem of powell 1986 is reported

marginal regression models for multivariate failure time data abstract in this article we propose a general cox type regression model to formulate the marginal distributions of multivariate failure time data this model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type we prove that the maximum quasi partial likelihood estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided furthermore we establish the uniform consistency and joint weak convergence of the aalen breslow type estimators for the cumulative baseline hazard functions and develop a resampling technique to approximate the joint distribution of these processes which enables one to make simultaneous inference about the survival functions over the time axis and across failure types finally we assess the small sample pro

smooth goodness of fit tests a quantile function approach abstract a quantile function based analog to neyman s smooth tests for goodness of fit hypotheses is developed these procedures possess asymptotic and small sample power properties similar to those for smooth tests they are however computationally simple applicable to both complete and type ii censored data and easily focused in the direction of any specific set of alternatives these results are used to develop a new test for exponentiality only location scale null hypotheses will be considered the ideas are easily adapted to other types of nulls however neyman first proposed smooth tests for the goodness of fit hypothesis as stated by kopecky and pierce and by rayner and best the basic idea behind these tests is to embed the null density in a larger exponential family the procedure is then based upon the likelihood ratio test statistic for testing that the additional parameters equal zero smooth type tests may be viewed as a compromise between omnibus test procedures with generally low po

bivariate quantile smoothing splines it has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample we introduce bivariate quantile smoothing splines which belong to the space of bilinear tensor product splines as nonparametric estimators for the conditional quantile functions in a two dimensional design space the estimators can be computed by using standard linear programming techniques and can further be used as building blocks for conditional quantile estimations in higher dimensions for moderately large data sets we recommend penalized bivariate b splines as approximate solutions we use real and simulated data to illustrate the methodology proposed

quantile smoothing splines summary although nonparametric regression has traditionally focused on the estimation of conditional mean functions nonparametric estimation of conditional quantile functions is often of substantial practical interest we explore a class of quantile smoothing splines defined as solutions to