a class of semiparametric regressions for the accelerated failure time model in this paper a general class of nonparametric test statistics which includes both linear and nonlinear rank tests for the accelerated failure time model is inverted into estimating equations for multiple regression for right censored data this general class of semiparametric regression procedures includes the linear rank estimators of tsiatis 1990 extends the theil sen estimator based on kendall s to multiple regression and introduces several new families of regression methods based on inverting nonlinear rank tests these new families include the weighted generalised logrank estimators and the weighted logit rank estimators several estimators of the standard errors of the regression coefficients are given the regression coefficient estimators are consistent and asymptotically normal with variances that can be consistently estimated several linear and nonlinear rank based estimators of the regression parameters and several methods of estimating their standard errors and the corresponding confidence intervals are compared in a small sample simulation in settings with and without outliers among the covariates in these simulations the generalised logrank estimators performed well as compared to the logrank estimators when there was no outlier among the covariates and had less bias than the logrank estimators when covariate outliers existed

asymptotic theory for the semiparametric accelerated failure time model with missing data we consider a class of doubly weighted rank based estimating methods for the transformation or accelerated failure time model with missing data as arise for example in case cohort studies the weights considered may not be predictable as required in a martingale stochastic process formulation we treat the general problem as a semiparametric estimating equation problem and provide proofs of asymptotic properties for the weighted estimators with either true weights or estimated weights by using empirical process theory where martingale theory may fail simulations show that the outcome dependent weighted method works well for finite samples in case cohort studies and improves efficiency compared to methods based on predictable weights further it is seen that the method is even more efficient when estimated weights are used as is commonly the case in the missing data literature the gehan censored data wilcoxon weights are found to be surprisingly efficient in a wide class of problems

adaptive nonparametric bayesian inference using location scale mixture priors we study location scale mixture priors for nonparametric statistical problems including multivariate regression density estimation and classification we show that a rate adaptive procedure can be obtained if the prior is properly constructed in particular we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a gaussian kernel an inverse gamma bandwidth and gaussian mixing weights

posterior consistency of gaussian process prior for nonparametric binary regression consider binary observations whose response probability is an unknown smooth function of a set of covariates suppose that a prior on the response probability function is induced by a gaussian process mapped to the unit interval through a link function in this paper we study consistency of the resulting posterior distribution if the covariance kernel has derivatives up to a desired order and the bandwidth parameter of the kernel is allowed to take arbitrarily small values we show that the posterior distribution is consistent in the l 1 distance as an auxiliary result to our proofs we show that under certain conditions a gaussian process assigns positive probabilities to the uniform neighborhoods of a continuous function this result may be of independent interest in the literature for small ball probabilities of gaussian processes

testing single index restrictions with a focus on average derivatives abstract this paper considers a situation where the violation of a single index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives we propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives the test has a 1 2 limiting distribution under the null hypothesis and even accommodates the case where the parameter estimates have a convergence rate slower than n as in the case of maximum score estimation the testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates multivariate average derivatives or linear restrictions other than those of average derivatives results from monte carlo experiments show that the asymptotic theory is a reasonable approximation of the finite sample distributions and an application of our methods to female labor market participation illustrates the importance of this non omnibus approach

cox regression in cohort studies with validation sampling summary an estimation procedure is proposed for the cox model in cohort studies with validation sampling where crude covariate information is observed for the full cohort and true covariate information is collected on a validation set sampkled randomly from the full cohort the method proposed makes use of the partial information from data that are available on the entire cohort by fitting a working cox model relating crude covariates to the failure time the resulting estimator is consistent regardless of the specification of the working model and is asymptotically more efficient than the validation set only estimator approximate asymptotic relative efficiencies with respect ot some alternative methods are derived under a simple scenaria and further studied numerically the finite sample performance is investigated and compared with alternative methods via simulation studies a similar procedure also works for the case where the validation set is a stratified random sample from the cohort

effect of a cutoff on pushed and bistable fronts of the reaction diffusion equation we give an explicit formula for the change of speed of pushed and bistable fronts of the reaction diffusion equation when a small cutoff is applied to the reaction term at the unstable or metastable equilibrium point the results are valid for arbitrary reaction terms and include the case of density dependent diffusion

additive hazard regression with auxiliary covariates we consider the additive hazard model when some of the true covariates are measured only on a randomly selected validation set whereas auxiliary covariates are observed for all study subjects an updated pseudoscore estimation approach is proposed for the parameters of the additive hazard model it allows one to fit the model with auxiliary covariates while leaving the baseline hazard unspecified asymptotic properties of the proposed estimators are established and consistent standard error estimators are developed simulations demonstrate that the asymptotic approximations of the proposed estimates are adequate for practical use a real example is used to illustrate the performance of the proposed method

improving efficiency of parameter estimation in case cohort studies with multivariate failure time data the case cohort study design is an effective way to reduce cost of assembling and measuring expensive covariates in large cohort studies recently several weighted estimators were proposed for the case cohort design when multiple diseases are of interest however these existing weighted estimators do not make effective use of the covariate information available in the whole cohort furthermore the auxiliary information for the expensive covariates which may be available in the studies cannot be incorporated directly in this article we propose a class of updated estimators we show that by making effective use of the whole cohort information the proposed updated estimators are guaranteed to be more efficient than the existing weighted estimators asymptotically furthermore they are flexible to incorporate the auxiliary information whenever available the advantages of the proposed updated estimators are demonstrated in simulation studies and a real data analysis

rigorous results for the minimal speed of kolmogorov petrovskii piscounov monotonic fronts with a cutoffa we study the effect of a cutoff on the speed of pulled fronts of the one dimensional reaction diffusion equation to accomplish this we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles this existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut off parameter from these bounds we estimate the range of validity of the brunet derrida formula for a general class of reaction terms

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

shift in the speed of reaction diffusion equation with a cut off pushed and bistable fronts abstract we study the change in the speed of pushed and bistable fronts of the reaction diffusion equation in the presence of a small cut off we give explicit formulas for the shift in the speed for arbitrary reaction terms f u the dependence of the speed shift on the cut off parameter is a function of the front speed and profile in the absence of the cut off in order to determine the speed shift we solve the leading order approximation to the front profile u z in the neighborhood of the leading edge and use a variational principle for the speed we apply the general formula to the nagumo equation and recover the results which have been obtained recently by geometric analysis the formulas given are of general validity and we also apply them to a class of reaction terms which have not been considered elsewhere

censored linear regression for case cohort studies summary right censored data from a classical case cohort design and a stratified case cohort design are considered in the classical case cohort design the subcohort is obtained as a simple random sample of the entire cohort whereas in the stratified design this subcohort is elected by independent bernoulli sampling with arbitrary selection probabilities for each design and under a linear regression model methods for estimating the regression parameters are proposed and analysed these methods are derived by modifying the linear ranks tests and estimating equations that arise from full cohort data using methods that are similar to the pseudolikelihood estimating equation that has been used in relative risk regression for these models the estimators so obtained are shown to be consistent and asymptotically normal variance estimation and numerical illustrations are also provided

a test of non identifying restrictions and confidence regions for partially identified parameters abstract we propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables which do not necessarily identify the data generating process the restrictions can be derived from any model of interactions allowing censoring and multiple equilibria when the restrictions are parameterized the test can be inverted to yield confidence regions for partially identified parameters thereby complementing other proposals primarily chernozhukov et al chernozhukov v hong h tamer e 2007 estimation and confidence regions for parameter sets in econometric models econometrica 75 1243 1285

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

optimal aggregation of classifiers in statistical learning classification can be considered as nonparametric estimation of sets where the risk is defined by means of a specific distance between sets associated with misclassification error it is shown that the rates of convergence of classifiers depend on two parameters the complexity of the class of candidate sets and the margin parameter the dependence is explicitly given indicating that optimal fast rates approaching o n 1 can be attained where n is the sample size and that the proposed classifiers have the property of robustness to the margin the main result of the paper concerns optimal aggregation of classifiers we suggest a classifier that automatically adapts both to the complexity and to the margin and attains the optimal fast rates up to a logarithmic factor

boundedly pivotal structural change tests in continuous updating gmm with strong weak identification and completely unidentified cases abstract this paper develops structural change tests in the continuous updating gmm framework that are robust to weak identification we propose likelihood ratio like anderson rubin 1949 estimation of the parameters of a single equation in a complete system of stochastic equations annals of mathematical statistics 20 46 63 and kleinbergen 2005 testing parameters in gmm without assuming that they are identified manuscript brown university types of tests since the limits of the test statistics are not nuisance parameter free bounds for the limit of the test statistics are derived the bounds are nuisance parameter free and robust to identification problems simulations show that the anderson rubin 1949 and kleinbergen 2005 testing parameters in gmm without assuming that they are identified manuscript brown university type of tests have very good small sample properties in the case of weak instruments the sup lm test of andrews 1993a tests for parameter instability and structural change with unknown change point econometrica 61 821 856 rejects the true null of parameter stability more than the nominal level and also has low power in the weak instrument setup

finite sample properties of linear model identification in this paper we consider the finite sample properties of prediction error methods using a quadratic criterion function for system identification the problem we pose is how many data points are required to guarantee with high probability that the expected value of the quadratic identification criterion is close to its empirical mean value the sample sizes are obtained using risk minimization theory which provides uniform probabilistic bounds on the difference between the expected value of the squared prediction error and its empirical mean evaluated on a finite number of data points the bounds are very general no assumption is made about the true system belonging to the model class and the noise sequence is not assumed to be uniformly bounded further analysis shows that in order to maintain a given bound on the deviation the number of data points needed grows no faster than quadratically with the number of parameters for fir and arx models

two stage plans for estimating the inverse of a monotone function this study investigates two stage plans based on nonparametric procedures for estimating an inverse regression function at a given point specifically isotonic regression is used at stage one to obtain an initial estimate followed by another round of isotonic regression in the vicinity of this estimate at stage two it is shown that such two stage plans accelerate the convergence rate of one stage procedures and are superior to existing two stage procedures that use local parametric approximations at stage two when the available budget is moderate and or the regression function is ill behaved both wald and likelihood ratio type confidence intervals for the threshold value of interest are investigated and the latter are recommended in applications due to their simplicity and robustness the developed plans are illustrated through a comprehensive simulation study and an application to car fuel efficiency data

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

on the bootstrap of the maximum score estimator this paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator the theory developed also applies to other estimators within a cube root convergence class for some single parameter estimators in this class the results suggest a simple method for inference based upon the bootstrap

convex clustering via l1 fusion penalization summary we study the large sample behaviour of a convex clustering framework which minimizes the sample within cluster sum of squares under an l1 fusion constraint on the cluster centroids this recently proposed approach has been gaining in popularity however its asymptotic properties have remained mostly unknown our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems we use this representation to provide a simple and intuitive formulation for the population clustering procedure we then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence the proof conducts a careful simultaneous analysis of a collection of m estimation problems whose cardinality grows together with the sample size on the basis of the new perspectives gained from the asymptotic investigation we propose a key post processing modification of the original clustering framework we show both theoretically and empirically that the resulting approach can be successfully used to estimate the number of clusters in the population using simulated data we compare the proposed method with existing number of clusters and modality assessment approaches and obtain encouraging results we also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single cell virology study

u processes and preference learning preference learning has caused great attention in machining learning in this letter we propose a learning framework for pairwise loss based on empirical risk minimization of u processes via rademacher complexity we first establish a uniform version of bernstein inequality of u processes of degree 2 via the entropy methods then we estimate the bound of the excess risk by using the bernstein inequality and peeling skills finally we apply the excess risk bound to the pairwise preference and derive the convergence rates of pairwise preference learning algorithms with squared loss and indicator loss by using the empirical risk minimization with respect to u processes

stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by analytic extension the d dimensional fractional brownian motion fbm for short b t b 1 t b d t t r with hurst exponent 0 1 is a d dimensional centered self similar gaussian process with covariance e b i s b i t 1 2 i j lsl 2 ltl 2 t s 2 the long standing problem of defining a stochastic integration with respect to fbm and the related problem of solving stochastic differential equations driven by fbm has been addressed successfully by several different methods although in each case with a restriction on the range of either d or the case corresponds to the usual stochastic integration with respect to brownian motion while most computations become singular when gets under various threshhold values due to the growing irregularity of the trajectories as 0 we provide here a new method valid for any d and for 1 4 by constructing an approximation e t e 0 of fbm which allows to define iterated integrals and then applying the geometric rough path theory the approximation relies on the definition of an analytic process z on the cut plane z c r of which fbm appears to be a boundary value and allows to understand very precisely the well known see 5 but as yet a little mysterious divergence of levy s area for 1 4

tailor made tests for goodness of fit to semiparametric hypotheses 1 introduction the practice of statistical testing plays several roles inempirical research these roles range from the careful assessment of theevidence against speci c scienti c hypotheses to the judgment of whetheran estimated model displays decent goodness of t to the empirical data the paradigmatic situation we consider is one where the investigator viewssome departures from the hypothesized model as being of primary impor tance with others of interest if su ciently gross but otherwise secondary for instance low frequency departures from a signal hypothesized to beconstant might be considered of interest even if of low amplitude whilehigh frequency departures are less so unless they are of high amplitude the optimal testing of a simple hypothesis against a simple alternativeis the cornerstone of modern statistical theory however there is no clearnotion of optimality for more complicated situations the h ajek le camasymptotic theory proved that there exist strong concepts of asymptotic ef ciency in parametric estimation these ideas have been extended to semi parametric models see 3 14 22 however there is no compelling sense ofan asymptotically optimum test in either the parametric or the semipara metric asymptotic theories save for some simple one parameter hypotheses

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

a geometric approach to bistable front propagation in scalar reaction diffusion equations with cut off abstract cut offs were introduced to model front propagation in reaction diffusion systems in which the reaction is effectively deactivated at points where the concentration lies below some threshold in this article we investigate the effects of a cut off on fronts propagating into metastable states in a class of bistable scalar equations we apply the method of geometric desingularization from dynamical systems theory to calculate explicitly the change in front propagation speed that is induced by the cut off we prove that the asymptotics of this correction scales with fractional powers of the cut off parameter and we identify the source of these exponents thus explaining the structure of the resulting expansion in particular we show geometrically that the speed of bistable fronts increases in the presence of a cut off in agreement with results obtained previously via a variational principle we first discuss the classical nagumo equation as a prototypical example of bistable front propagation then we present corresponding results for the equivalent cut off schlogl equation finally we extend our analysis to a general family of reaction diffusion equations that support bistable fronts and we show that knowledge of an explicit front solution to the associated problem without cut off is necessary for the correction induced by the cut off to be computable in closed form

parametric rate inference for one sided differentiable parameters suppose one has a collection of parameters indexed by a possibly infinite dimensional set given data generated from some distribution the objective is to estimate the maximal parameter in this

information theoretic upper and lower bounds for statistical estimation in this paper we establish upper and lower bounds for some statistical estimation problems through concise information theoretic arguments our upper bound analysis is based on a simple yet general inequality which we call the information exponential inequality we show that this inequality naturally leads to a general randomized estimation method for which performance upper bounds can be obtained the lower bounds applicable for all statistical estimators are obtained by original applications of some well known information theoretic inequalities and approximately match the obtained upper bounds for various important problems moreover our framework can be regarded as a natural generalization of the standard minimax framework in that we allow the performance of the estimator to vary for different possible underlying distributions according to a predefined prior

new dependence coefficients examples and applications to statistics to measure the dependence between a real valued random variable x and a algebra we consider four distances between the conditional distribution function of x given and the distribution function of x the coefficients obtained are weaker than the corresponding mixing coefficients and may be computed in many situations in particular we show that they are well adapted to functions of mixing sequences iterated random functions and dynamical systems starting from a new covariance inequality we study the mean integrated square error for estimating the unknown marginal density of a stationary sequence we obtain optimal rates for kernel estimators as well as projection estimators on a well localized basis under a minimal condition on the coefficients using recent results we show that our coefficients may be also used to obtain various exponential inequalities a concentration inequality for lipschitz functions and a berry esseen type inequality

a geometric analysis of front propagation in an integrable nagumo equation with a linear cut off abstract we investigate the effects of a linear cut off on front propagation in the nagumo equation at a so called maxwell point where the corresponding front solution in the absence of a cut off is stationary we show that the correction to the propagation speed induced by the cut off is positive in this case moreover we determine the leading order asymptotics of that correction in terms of the cut off parameter and we calculate explicitly the corresponding coefficient our analysis is based on geometric techniques from dynamical systems theory and in particular on the method of geometric desingularization blow up

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

adjusted regression estimation for time to event data with differential measurement error differential measurement error data plausibly arise in epidemiology and biomedical studies but have been rarely dealt with explicitly especially for time to event data we propose an estimation equation correction method in semiparametric censored linear regression to deal with differential measurement error for time to event data with validation samples the method does not require explicit modelling of the error prone covariates and leads to unbiased estimation copyright 2013 oxford university press

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

a note on appointment scheduling with piecewise linear cost functions we consider the problem of determining the optimal schedules for a given sequence of jobs on a single processor the objective is to minimize the expected total cost incurred by job waiting and processor idling where the job processing times are random variables it is known in the prior literature that if the processing times are integers and the costs are linear functions satisfying a mild condition then the problem can be solved in a polynomial number of expected cost evaluations in this work we extend the result to piecewise linear cost functions which include many useful objective functions in practice our analysis explores the hidden dual network flow structure of the appointment scheduling problem and thus greatly simplifies that of prior work we also find the number of samples needed to compute a near optimal solution when only some independent samples of processing times are known

regression analysis with covariates that have heteroscedastic measurement error we consider the estimation of the regression of an outcome y on a covariate x where x is unobserved but a variable w that measures x with error is observed a calibration sample that measures pairs of values of x and w is also available we consider calibration samples where y is measured internal calibration and not measured external calibration one common approach for measurement error correction is regression calibration rc which substitutes the unknown values of x by predictions from the regression of x on w estimated from the calibration sample an alternative approach is to multiply impute the missing values of x given y and w based on an imputation model and then use multiple imputation mi combining rules for inferences most of current work assumes that the measurement error of w has a constant variance whereas in many situations the variance varies as a function of x we consider extensions of the rc and mi methods that allow for heteroscedastic measurement error and compare them by simulation the mi method is shown to provide better inferences in this setting we also illustrate the proposed methods using a data set from the biocycle study

efficient shrinkage in parametric models this paper introduces shrinkage for general parametric models we show how to shrink maximum likelihood estimators towards parameter subspaces de ned by general nonlinear restrictions we derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework we show that if the shrinkage dimension exceeds two the asymptotic risk of the shrinkage estimator is strictly less than that of the mle this reduction holds globally in the parameter space we show that the reduction in asymptotic risk is substantial even for moderately large values of the parameters the formula simplify in a very convenient way in the context of high dimensional models we derive a simple bound for the asymptotic risk we also provide a new large sample minimax e ciency bound we use the concept of local asymptotic minimax bounds a generalization of the conventional asymptotic minimax bounds the

calibration regression of censored lifetime medical cost analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow up particularly the latter with limited study duration as is typical in medical research this article proposes the so called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time in a semiparametric fashion it is postulated that both outcomes on possibly transformed scales linearly relate to the covariates however the bivariate model error distribution is completely unspecified whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model this article proposes an inference procedure by extending the weighted log rank estimating function to the marked point process framework the resulting estimators are consistent and asymptotically normal in addition robustness and efficiency issues are discussed furthermore a novel sample based variance estimation procedure is proposed for es

fluctuations of shapes of large areas under paths of random walks we discuss statistical properties of random walks conditioned by fixing a large area under their paths we prove the functional central limit theorem invariance principle for these conditional distributions the limiting gaussian measure coincides with the conditional probability distribution of certain timenonhomogeneous gaussian random process obtained by an integral transformation of the white noise from the point of view of statistical mechanics the studied problem is the problem of describing the fluctuations of the phase boundary in the one dimensional sos model

likelihood ratio tests for monotone functions we study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function the likelihood ratio test for this hypothesis is derived in the particular case of interval censoring or current status data and its limiting distribution is obtained the limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving brownian motion t 2 and greatest convex minorants thereof inversion of the family of tests yields pointwise confidence intervals for the unknown distribution function we also study the behavior of the statistic under local and fixed alternatives 1 introduction we shall consider likelihood ratio tests and the corresponding confidence intervals in a class of problems involving nonparametric estimation of a monotone function the problem in each case involves testing the null hypothesis h 0 that the monotone function has a particular value at afixed point t 0 in the domain of the function of course with each testing problem there is a related problem of finding confidence intervals here are some examples of the problems we have in mind

rates of convergence for the gaussian mixture sieve gaussian mixtures provide a convenient method of densityestimation that lies somewhere between parametric models and kernel densityestimators when the number of components of the mixture is allowed to increase as sample size increases the model is called a mixture sieve we establish a bound on the rate of convergence in hellinger distance for densityestimation using the gaussian mixture sieve assuming that the true density is itself a mixture of gaussians the underlying mixing measure of the true densityis not necessarilyassumed to have finite support computing the rate involves some delicate calculations since the size of the sieve as measured bybracketing entropy and the saturation rate cannot be found using standard methods when the mixing measure has compact support using kn n 2 3 log n 1 3 components in the mixture yields a rate of order log n 1 6 n1 6 for every 0 the rates depend heavilyon the tail behavior of the true density the sensitivity to the tail behavior is diminished byusing a robust sieve which includes a long tailed component in the

regression calibration in semiparametric accelerated failure time models summary in large cohort studies it often happens that some covariates are expensive to measure and hence only measured on a validation set on the other hand relatively cheap but error prone measurements of the covariates are available for all subjects regression calibration rc estimation method prentice 1982 biometrika 69 331 342 is a popular method for analyzing such data and has been applied to the cox model by wang et al 1997 biometrics 53 131 145 under normal measurement error and rare disease assumptions in this article we consider the rc estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error asymptotic properties of the proposed method are investigated under a two phase sampling scheme for validation data that are selected via stratified random sampling resulting in neither independent nor identically distributed observations we show that the estimates converge to some well defined parameters in particular unbiased estimation is feasible under additive normal measurement error models for normal covariates and under berkson error models the proposed method performs well in finite sample simulation studies we also apply the proposed method to a depression mortality study

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

limit theorems in financial market models abstract invariance principle states that a scaled simple random walk converges to the standard brownian motion in this article we present a discrete time stochastic process which reflects a microstructure of market dynamics and prove a convergence to a scaling limit process with a drift term and a jump term these terms are derived from a macroscopic condition on volumes traded in some time intervals the mathematical tools for obtaining our results are dobrushin hryniv theory and the method of cluster expansion developed in mathematical studies of statistical mechanics

fluctuations of the phase boundary in the 2d ising ferromagnet we discuss some statistical properties of the phase boundary in the 2d low temperature ising ferromagnet in a box with the two component boundary conditions we prove the weak convergence in c 0 1 of measures describing the fluctuations of phase boundaries in the canonical ensemble of interfaces with fixed endpoints and area enclosed below them the limiting gaussian measure coincides with the conditional distribution of certain gaussian process obtained by the integral transformation of the white noise