raney distributions and random matrix theory recent works have shown that the family of probability distributions with moments given by the fuss catalan numbers permit a simple parameterized form for their density we extend this result to the raney distribution which by definition has its moments given by a generalization of the fuss catalan numbers such computations begin with an algebraic equation satisfied by the stieltjes transform which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the raney distribution for the fuss catalan distribution an equilibrium problem characterizing the density is identified the stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from q inverse standard gaussian matrices and s standard gaussian matrices is shown to satisfy a variant of the algebraic equation relating to the raney distribution supported on 0 infty we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization as an application the leading asymptotic form of the density as the endpoints of the support are approached is computed and is shown to have some universal features

semiparametric transformation models for semicompeting survival data semicompeting risk outcome data e g time to disease progression and time to death are commonly collected in clinical trials however analysis of these data is often hampered by a scarcity of available statistical tools as such we propose a novel semiparametric transformation model that improves the existing models in the following two ways first it estimates regression coefficients and association parameters simultaneously second the measure of surrogacy for example the proportion of the treatment effect that is mediated by the surrogate and the ratio of the overall treatment effect on the true endpoint over that on the surrogate endpoint can be directly obtained we propose an estimation procedure for inference and show that the proposed estimator is consistent and asymptotically normal extensive simulations demonstrate the valid usage of our method we apply the method to a multiple myeloma trial to study the impact of several biomarkers on patients semicompeting outcomes namely time to progression and time to death

asymptotic form of the density profile for gaussian and laguerre random matrix ensembles with orthogonal and symplectic symmetry in a recent study we have obtained correction terms to the large n asymptotic expansions of the eigenvalue density for the gaussian unitary and laguerre unitary ensembles of random n n matrices both in the bulk and at the soft edge of the spectrum in the present study these results are used to similarly analyze the eigenvalue density for gaussian and laguerre random matrix ensembles with orthogonal and symplectic symmetry as in the case of unitary symmetry a matching is exhibited between the asymptotic expansion of the bulk density expanded about the edge and the asymptotic expansion of the edge density expanded into the bulk in addition aspects of the asymptotic expansion of the smoothed density which involves delta functions at the endpoints of the support are interpreted microscopically

applications and generalizations of fisher hartwig asymptotics fisher hartwig asymptotics refers to the large n form of a class of toeplitz determinants with singular generating functions this class of toeplitz determinants occurs in the study of the spin spin correlations for the two dimensional ising model and the ground state density matrix of the impenetrable bose gas amongst other problems in mathematical physics we give a new application of the original fisher hartwig formula to the asymptotic decay of the ising correlations above tc while the study of the bose gas density matrix leads us to generalize the fisher hartwig formula to the asymptotic form of random matrix averages over the classical groups and the gaussian and laguerre unitary matrix ensembles another viewpoint of our generalizations is that they extend to hankel determinants the fisher hartwig asymptotic form known for toeplitz determinants

regression analysis of doubly truncated data abstractdoubly truncated data are found in astronomy econometrics and survival analysis literature they arise when each observation is confined to an interval that is only those which fall wit

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

local rank inference for varying coefficient models by allowing the regression coefficients to change with certain covariates the class of varying coefficient models offers a flexible approach to modeling nonlinearity and interactions between covariates this article proposes a novel estimation procedure for the varying coefficient models based on local ranks the new procedure provides a highly efficient and robust alternative to the local linear least squares method and can be conveniently implemented using existing r software package theoretical analysis and numerical simulations both reveal that the gain of the local rank estimator over the local linear least squares estimator measured by the asymptotic mean squared error or the asymptotic mean integrated squared error can be substantial in the normal error case the asymptotic relative efficiency for estimating both the coefficient functions and the derivative of the coefficient functions is above 96 even in the worst case scenarios the asymptotic relative efficiency has a lower bound 88 96

a simple resampling method by perturbing the minimand suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a u process structure the covariance matrix of the estimator is generally a function of the underlying density function which may be difficult to estimate well by conventional methods in this paper we present a simple resampling method by perturbing the objective function repeatedly inferences of the parameters can then be made based on a large collection of the resulting optimisers we illustrate our proposal by three examples with a heteroscedastic regression model

censored quantile regression with partially functional effects quantile regression offers a flexible approach to analyzing survival data allowing each covariate effect to vary with quantiles in practice constancy is often found to be adequate for some covariates in this paper we study censored quantile regression tailored to the partially functional effect setting with a mixture of varying and constant effects such a model can offer a simpler view regarding covariate survival association and moreover can enable improvement in estimation efficiency we propose profile estimating equations and present an iterative algorithm that can be readily and stably implemented asymptotic properties of the resultant estimators are established a simple resampling based inference procedure is developed and justified extensive simulation studies demonstrate efficiency gains of the proposed method over a naive two stage procedure the proposed method is illustrated via an application to a recent renal dialysis study

a bootstrapped spectral test for adequacy in weak arma models this paper proposes a cramer von mises cm test statistic to check the adequacy of weak arma models without posing a martingale difference assumption on the error terms the asymptotic null distribution of the cm test is obtained moreover this cm test is consistent and has nontrivial power against the local alternative of order n 1 2 due to the unknown dependence of error terms and the estimation effects a new block wise random weighting method is constructed to bootstrap the critical values of the test statistic the new method is easy to implement and its validity is justified the theory is illustrated by a small simulation study and an application to s p 500 stock index

information ratio test for model misspecification in quasi likelihood inference in this article we focus on the circumstances in quasi likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment but the estimation efficiency could be diminished due to misspecification of the second moment we propose an information ratio ir statistic to test for model misspecification of the variance covariance structure through a comparison between two forms of information matrix the negative sensitivity matrix and the variability matrix we establish asymptotic distributions of the proposed ir test statistics we also suggest an approximation to the asymptotic distribution of the ir statistic via a perturbation resampling method moreover we propose a selection criterion based on the ir test to select the best fitting variance covariance structure from a class of candidates through simulation studies it is shown that the ir statistic provides a powerful statistical tool to detect different scenarios of misspecific

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

empirical likelihood analysis of the rank estimator for the censored accelerated failure time model summary we use the empirical likelihood method to derive a test and thus a confidence interval based on the rank estimators of the regression coefficient in the accelerated failure time model standard chi squared distributions are used to calculate the p value and to construct the confidence interval simulations and examples show that the chi squared approximation to the distribution of the log empirical likelihood ratio performs well and has some advantages over the existing methods

transformed dynamic quantile regression on censored data we propose a class of power transformed linear quantile regression models for time to event observations subject to censoring by introducing a process of power transformation with different transf

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

partial rank estimation of duration models with general forms of censoring abstract in this paper we propose estimators for the regression coefficients in censored duration models which are distribution free impose no parametric specification on the baseline hazard function and can accommodate general forms of censoring the estimators are shown to have desirable asymptotic properties and monte carlo simulations demonstrate good finite sample performance among the data features the new estimators can accommodate are covariate dependent censoring double censoring and fixed individual or group specific effects we also examine the behavior of the estimator in an empirical illustration

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

on approximately symmetric informationally complete positive operator valued measures and related systems of quantum states we address the problem of constructing positive operator valued measures povms in finite dimension n consisting of n2 operators of rank one which have an inner product close to uniform this is motivated by the related question of constructing symmetric informationally complete povms sic povms for which the inner products are perfectly uniform however sic povms are notoriously hard to construct and despite some success of constructing them numerically there is no analytic construction known we present two constructions of approximate versions of sic povms where a small deviation from uniformity of the inner products is allowed the first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power the second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases moreover we construct vector systems in cn which are almost orthogonal and which might turn out

exact density of states for finite gaussian random matrix ensembles via supersymmetry we calculate the exact density of states dos for the three classical and two non classical random matrix ensembles for finite matrix size n using supersymmetric integrals the 1 n expansion yields already in lowest order good approximations to the exact result even for small values of n 5 we conjecture a connection between the n dependence of the oscillating part of the dos and the short distance behaviour of the two level correlation function

induced smoothing for rank regression with censored survival times adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies however for only one simple weighting scheme gehan or wilcoxon weights are estimating equations guaranteed to be monotone in parameter components and even in this case are step functions requiring the equivalent of linear programming for computation the lack of smoothness makes standard error or covariance matrix estimation even more difficult an induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations including conventional rank regression the present paper applies induced smoothing to the gehan wilcoxon weighted rank regression for the accelerated failure time model for the more difficult case of survival time data subject to censoring where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions smooth monotone parameter estimation and rapid reliable standard error or covariance matrix estimation is obtained

density of states for gaussian unitary ensemble gaussian orthogonal ensemble and interpolating ensembles through supersymmetric approach we use the supersymmetric formalism to derive an integral formula for the density of states of the gaussian orthogonal ensemble and then apply saddle point analysis to give a new derivation of the 1 n correction to wigner s law this extends the work of disertori on the gaussian unitary ensemble we also apply our method to the interpolating ensembles of mehta pandey

standard errors and covariance matrices for smoothed rank estimators a pseudo bayesian interpretation of standard errors yields a natural induced smoothing of statistical estimating functions when applied to rank estimation the lack of smoothness which prevents standard error estimation is remedied efficiency and robustness are preserved while the smoothed estimation has excellent computational properties in particular convergence of the iterative equation for standard error is fast and standard error calculation becomes asymptotically a one step procedure this property also extends to covariance matrix calculation for rank estimates in multi parameter problems examples and some simple explanations are given

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

on the asymptotics of some large hankel determinants generated by fisher hartwig symbols defined on the real line we investigate the asymptotics of hankel determinants of the form detj k 0n 1 dx n x i 1m i x 2qixj k as n with q and fixed where is an infinite subinterval of r and n x is a positive weight on such objects are natural analogs of toeplitz determinants generated by fisher hartwig symbols and arise in random matrix theory in the investigation of certain expectations involving random characteristic polynomials the reduced density matrices of certain one dimensional systems of trapped impenetrable bosons can also be expressed in terms of hankel determinants of this form we focus on the specific cases of scaled hermite and laguerre weights we compute the asymptotics by using a duality formula expressing the n n hankel determinant as a 2 q1 qm fold integral which is valid when each qi is natural we thus verify for such q a recent conjecture of forrester and frankel derived using a log gas argument

painleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons the recent experimental realisation of a one dimensional bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable bose gas of primary concern is the ground state occupation of effective single particle states in the finite system and thus the tendency for bose einstein condensation this requires the computation of the density matrix for the impenetrable bose gas on a circle we evaluate the density matrix in terms of a particular painleve vi transcendent in form and furthermore show that the density matrix satisfies a recurrence relation in the number of particles for the impenetrable bose gas in a harmonic trap and with dirichlet or neumann boundary conditions we give a determinant form for the density matrix a form as an average over the eigenvalues of an ensemble of random matrices and in special cases an evaluation in terms of a transcendent related to painleve v and vi we discuss how our results can be used to compute the ground state occupations

limit theorems for u processes a u process is a collection of u statistics concretely a u process over a family h of kernels h of m variables based on a probability measure p on s s is the collection u n m h p h in mathcal h of u statistics this chapter is devoted to the asymptotic theory of u processes we are interested in finding conditions on h and p ensuring that the law of large numbers or the central limit theorem or the law of the iterated logarithm hold for u n m h p uniformly in h h the theory of empirical processes deals with the same questions for the case m 1 and u process theory is patterned after it this is a relatively new subject at least in the generality presented here h being an arbitrary collection of kernels which are defined on a general measurable space there is therefore a need to indicate its usefulness to this effect a section on applications is added at the end of the chapter section 5 5 there we illustrate the use of each of the main theorems in this chapter by deriving properties of certain multidimensional generalizations of the median and in general of m estimators and by studying estimators of the cumulative hazard and distribution functions of a random variable based on truncated data

quantile calculus and censored regression quantile regression has been advocated in survival analysis to assess evolving covariate effects however challenges arise when the censoring time is not always observed and may be covariate dependent particularly in the presence of continuously distributed covariates in spite of several recent advances existing methods either involve algorithmic complications or impose a probability grid the former leads to difficulties in the implementation and asymptotics whereas the latter introduces undesirable grid dependence to resolve these issues we develop fundamental and general quantile calculus on cumulative probability scale in this article upon recognizing that probability and time scales do not always have a one to one mapping given a survival distribution these results give rise to a novel estimation procedure for censored quantile regression based on estimating integral equations a numerically reliable and efficient progressive localized minimization plmin algorithm is proposed for the computation this procedure reduces exactly to the kaplan meier method in the k sample problem and to standard uncensored quantile regression in the absence of censoring under regularity conditions the proposed quantile coefficient estimator is uniformly consistent and converges weakly to a gaussian process simulations show good statistical and algorithmic performance the proposal is illustrated in the application to a clinical study

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

analysis of least absolute deviation summary we develop a unified l 1 based analysis of variance type method for testing linear hypotheses like the classical l2 based analysis of variance the method is coordinate free in the sense that it is invariant under any linear transformation of the covariates or regression parameters moreover it allows singular design matrices and heterogeneous error terms a simple approximation using stochastic perturbation is proposed to obtain cut offvalues for the resulting test statistics both test statistics and distributional approximations can be computed using standard linear programming an asymptotic theory is derived for the method special cases of one and multi way analysis of variance and analysis of covariance models are worked out in detail the main results of this paper can be extended to general quantile regression extensive simulations show that the method works well in practical settings the method is also applied to a dataset from general social surveys

robust rank estimation for transformation models with random effects summarysemiparametric transformation models with random effects are useful in analysing recurrent and clustered data with specified error and random effect distributions zeng lin 2007a proved that nonparametric maximum likelihood estimators are semiparametric efficient in this paper we consider a more general class of transformation models with random effects under which an unknown monotonic transformation of the response is linearly related to the covariates and the random effects with unspecified error and random effect distributions this includes many popular models we propose an estimator based on the maximum rank correlation which relies on symmetry of the random effect distribution and establish its consistency and asymptotic normality a random weighting resampling scheme is employed for inference the proposed method can be extended to censored and clustered data numerical studies demonstrate that the proposed method performs well in practical situations application of the method is illustrated with the framingham cholesterol data

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

strict stationarity testing and glad estimation of double autoregressive models abstract in this article we develop a tractable procedure for testing strict stationarity in a double autoregressive model and formulate the problem as testing if the top lyapunov exponent is negative without strict stationarity assumption we construct a consistent estimator of the associated top lyapunov exponent and employ a random weighting approach for its variance estimation which in turn are used in a t type test we also propose a glad estimation for parameters of interest relaxing key assumptions on the commonly used qmle all estimators except for the intercept are shown to be consistent and asymptotically normal in both stationary and explosive situations the finite sample performance of the proposed procedures is evaluated via monte carlo simulation studies and a real dataset of interest rates is analyzed

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

semiparametric estimation of a censored regression model with endogeneity abstract censoring and endogeneity are common in empirical applications however the existing semiparametric estimation methods for the censored regression model with endogeneity under an independence restriction are associated with some drawbacks in this paper we propose a new semiparametric estimator that overcomes these drawbacks we derive conditional quantile moment conditions for all the conditional quantiles and propose a moment based estimator in particular we construct two types of moment conditions and develop a computationally attractive estimator we show that our estimator is consistent and asymptotic normal a monte carlo study indicates that our estimator performs well in finite samples and compares favorably with existing methods

universality limits in the bulk for varying measures abstract universality limits are a central topic in the theory of random matrices we establish universality limits in the bulk of the spectrum for varying measures using the theory of entire functions of exponential type in particular we consider measures that are of the form w n 2 n x d x in the region where universality is desired w n does not need to be analytic nor possess more than one derivative and then only in the region where universality is desired we deduce universality in the bulk for a large class of weights of the form w 2 n x d x for example when w e q where q is convex and q satisfies a lipschitz condition of some positive order we also deduce universality for a class of fixed exponential weights on a real interval

asymptotic corrections to the eigenvalue density of the gue and lue we obtain correction terms to the large n asymptotic expansions of the eigenvalue density for the gaussian unitary and laguerre unitary ensembles of random n n matrices both in the bulk of the spectrum and near the spectral edge this is achieved by using the well known orthogonal polynomial expression for the kernel to construct a double contour integral representation for the density to which we apply the saddle point method the main correction to the bulk density is oscillatory in n and depends on the distribution function of the limiting density while the corrections to the airy kernel at the soft edge are again expressed in terms of the airy function and its first derivative we demonstrate numerically that these expansions are very accurate a matching is exhibited between the asymptotic expansion of the bulk density expanded about the edge and the asymptotic expansion of the edge density expanded into the bulk

eigenvalue statistics for product complex wishart matrices the eigenvalue statistics for complex wishart matrices where is equal to the product of r complex gaussian matrices and the inverse of s complex gaussian matrices are considered in the case r s the exact form of the global density is computed the averaged characteristic polynomial for the corresponding generalized eigenvalue problem is calculated in terms of a particular generalized hypergeometric function for finite n the eigenvalue probability density function is computed and is shown to be an example of a biorthogonal ensemble a double contour integral form of the corresponding correlation kernel is derived which allows the hard edge scaled limit to be computed the limiting kernel is given in terms of certain meijer g functions and is identical to that found in the recent work of kuijlaars and zhang in the case s 0 properties of the kernel and corresponding correlation functions are discussed

functional form for the leading correction to the distribution of the largest eigenvalue in the gue and lue the neighbourhood of the largest eigenvalue max in the gaussian unitary ensemble gue and laguerre unitary ensemble lue is referred to as the soft edge it is known that there exists a particular centring and scaling such that the distribution of max tends to a universal form with an error term bounded by 1 n2 3 we take up the problem of computing the exact functional form of the leading error term in a large n asymptotic expansion for both the gue and lue two versions of the lue are considered one with the parameter a fixed and the other with a proportional to n both settings in the lue case allow for an interpretation in terms of the distribution of a particular weighted path length in a model involving exponential variables on a rectangular grid as the grid size gets large we give operator theoretic forms of the corrections which are corollaries of knowledge of the first two terms in the large n expansion of the scaled kernel and are readily computed using a method due to bornemann we also give expressions in terms of the solutions of particular systems of coupled differential equations which provide an alternative method of computation both characterisations are well suited to a thinned generalisation of the original ensemble whereby each eigenvalue is deleted independently with probability 1 in sec v we investigate using simulation the question of whether upon an appropriate centring and scaling a wider class of complex hermitian random matrix ensembles have their leading correction to the distribution of max proportional to 1 n2 3 the neighbourhood of the largest eigenvalue max in the gaussian unitary ensemble gue and laguerre unitary ensemble lue is referred to as the soft edge it is known that there exists a particular centring and scaling such that the distribution of max tends to a universal form with an error term bounded by 1 n2 3 we take up the problem of computing the exact functional form of the leading error term in a large n asymptotic expansion for both the gue and lue two versions of the lue are considered one with the parameter a fixed and the other with a proportional to n both settings in the lue case allow for an interpretation in terms of the distribution of a particular weighted path length in a model involving exponential variables on a rectangular grid as the grid size gets large we give operator theoretic forms of the corrections which are corollaries of knowledge of the first two terms in the large n expansion of the scaled kernel and are readily computed using a method due to bornemann we also

combining multiple markers for classification using roc summary in biomedical studies it is of great interest to develop methodologies for combining multiple markers for the purpose of disease classification the receiving operating characteristic roc technique has been widely used where classification performance can be measured with the area under the roc curve auc in this article we study a roc based method for effectively combining multiple markers for disease classification we propose a sigmoid auc sauc estimator that maximizes the sigmoid approximation of the empirical auc the sauc estimator is computationally affordable n1 2 consistent and achieves the same asymptotic efficiency as the auc estimator inference based on the weighted bootstrap is investigated we also propose monte carlo methods to assess the overall prediction performance and the relative importance of individual markers finite sample performance is evaluated using simulation studies and two public data sets

some recent methods for establishing universality limits abstract we survey some recent methods for establishing universality limits for random matrices in the unitary case these include levin s method using a markov bernstein inequality a comparison inequality of the author and a method based on complex analysis and reproducing kernels we focus on the bulk of the spectrum for measures with compact support but the methods may also be used at the soft or hard edge and for measures with unbounded support

large n expansions for the laguerre and jacobi β ensembles from the loop equations the ensembles of random matrix theory with classical weights have many special properties one is that the loop equations specifying the resolvent and corresponding multipoint correlators permit a derivation at the general order of the correlator via aomoto s method from the theory of the selberg integral we use aomoto s method to derive the full hierarchy of loop equations for laguerre and jacobi ensembles and use these to systematically construct the explicit form of the 1 n expansion at low orders this allows us to give the explicit form of corrections to the global density and allows various moments to be computed complementing results available in the literature motivated by problems in quantum transport

quantile regression for left truncated semicompeting risks data summary semicompeting risks is often encountered in biomedical studies where a terminating event censors a nonterminating event but not vice versa in practice left truncation on the terminating event may arise and can greatly complicate the regression analysis on the nonterminating event in this work we propose a quantile regression method for left truncated semicompeting risks data which provides meaningful interpretations as well as the flexibility to accommodate varying covariate effects we develop estimation and inference procedures that can be easily implemented by existing statistical software asymptotic properties of the resulting estimators are established including uniform consistency and weak convergence the finite sample performance of the proposed method is evaluated via simulation studies an application to a registry dataset provides an illustration of our proposals

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

scaled limit and rate of convergence for the largest eigenvalue from the generalized cauchy random matrix ensemble in this paper we are interested in the asymptotic properties for the largest eigenvalue of the hermitian random matrix ensemble called the generalized cauchy ensemble gcye whose eigenvalues pdf is given by textrm const cdot prod 1 leq j k leq n x j x k 2 prod j 1 n 1 ix j s n 1 ix j overline s n dx j where s is a complex number such that s 1 2 and where n is the size of the matrix ensemble using results by borodin and olshanski commun math phys 223 1 87 123 2001 we first prove that for this ensemble the law of the largest eigenvalue divided by n converges to some probability distribution for all s such that s 1 2 using results by forrester and witte nagoya math j 174 29 114 2002 on the distribution of the largest eigenvalue for fixed n we also express the limiting probability distribution in terms of some non linear second order differential equation eventually we show that the convergence of the probability distribution function of the re scaled largest eigenvalue to the limiting one is at least of order 1 n