nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

estimating medical costs with censored data incompleteness of follow up data is a common problem in estimating medical costs naive analysis using summary statistics on the collected data can result in severely misleading statistical inference this paper focuses on the problem of estimating the mean medical cost from a sample of individuals whose medical costs may be right censored a class of weighted estimators which account appropriately for censoring are introduced our estimators are shown to be consistent and asymptotically normal with easily estimated variances the efficiency of these estimators is studied with the goal of finding as efficient an estimator for the mean medical cost as is feasible extensive simulation studies are used to show that our estimators perform well in finite samples even with heavily censored data for a variety of circumstances the methods are applied to a set of cost data from a cardiology trial conducted by the duke university medical center extensions to other censored data problems are also discussed

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

mitigation of loopback self interference in full duplex mimo relays full duplex relaying is more spectrally efficient than half duplex relaying as only one channel use is needed per two hops however it is crucial to minimize relay self interference to render full duplex feasible for this purpose we analyze a broad range of multiple input multiple output mimo mitigation schemes natural isolation time domain cancellation and spatial suppression cancellation subtracts replicated interference signal from the relay input while suppression reserves spatial dimensions for receive and transmit filtering spatial suppression can be achieved by antenna subset selection null space projection i e receiving and transmitting in orthogonal subspaces or joint transmit and receive beam selection to support more spatial streams by choosing the minimum eigenmodes for overlapping subspaces in addition minimum mean square error mmse filtering can be employed to maintain the desired signal quality which is inherent for cancellation and the combination of time and spatial domain processing may be better than either alone targeting at minimal interference power we solve optimal filters for each scheme in the cases of joint separate and independent design the performance of mitigation schemes is evaluated and compared by simulations the results confirm that self interference can be mitigated effectively also in the presence of imperfect side information

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

simultaneous inferences on the contrast of two hazard functions with censored observations in survival analysis often times the pattern of instantaneous risk over time is more interesting than that of the cumulative risk for this case a nonparametric hazard function estimate is more appropriate for summarizing the risk experience of a group of patients than the corresponding kaplan meier estimate in comparing a new treatment with a standard therapy it is important to know if the treatment loses it potency during the follow up period and if it does one would like to know when it becomes ineffective unfortunately with a plot of the differences of two kaplan meier curves it is rather difficult to capture such temporal trends in this article we propose simple procedures for constructing confidence bands for the contrast of two hazard functions with censored data the simultaneous interval estimates are quite useful for identifying possible values of the contrast over time with a certain degree of confidence the new proposals are illustrated with an example and a small simulation study

quantile regression adjusting for dependent censoring from semicompeting risks in this work we study quantile regression when the response is an event time subject to potentially dependent censoring we consider the semi competing risks setting where time to censoring remains observable after the occurrence of the event of interest while such a scenario frequently arises in biomedical studies most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time be independent by imposing rather mild assumptions on the association structure between the time to event response and the censoring time variable we propose quantile regression procedures which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring an efficient and stable algorithm is provided for implementing the new method we establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence the theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals extensive simulation studies suggest that the proposed method performs well with moderate sample sizes we illustrate the practical utility of our proposals through an application to a bone marrow transplant trial

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

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

maximum likelihood estimation of a multi dimensional log concave density fn is shown to have smaller mean integrated squared error compared with kernel based methods even when we allow the use of a theoret ical optimal fixed bandwidth for the kernel estimator that would not be available in practice we also present a real data clustering example which shows that our methodology can be used in conjunction with the expectation maximization algorithm to fit finite mixtures of log concave densities

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

nonparametric estimation of the concordance correlation coefficient under univariate censoring assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects lin s 1989 biometrics 45 255 268 concordance correlation coefficient ccc has become a popular measure of agreement for correlated continuous outcomes however commonly used estimation methods for the ccc do not accommodate censored observations and are therefore not applicable for survival outcomes in this article we estimate the ccc nonparametrically through the bivariate survival function the proposed estimator of the ccc is proven to be strongly consistent and asymptotically normal with a consistent bootstrap variance estimator furthermore we propose a time dependent agreement coefficient as an extension of lin s 1989 ccc for measuring the agreement between survival times among subjects who survive beyond a specified time point a nonparametric estimator is developed for the time dependent agreement coefficient as well it has the same asymptotic properties as the estimator of the ccc simulation studies are conducted to evaluate the performance of the proposed estimators a real data example from a prostate cancer study is used to illustrate the method

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

analysis of time to event data with incomplete event adjudication in many multicenter randomized clinical trials the primary outcome is the time to the first of a number of possible clinical events an event classification committee may be convened to determine whether events that have been reported by investigators meet the predetermined criteria for primary endpoint events when interim analyses are performed in such trials the final classification for many reported events will not be known failure to account for the uncertain status of these events may result in incorrect interim analysis the probability that an unadjudicated event will be confirmed as a primary event can typically be estimated from those events for which adjudication is complete we show that if each unadjudicated event is weighted according to the probability that it will be the first primary event then consistent estimates of survival probabilities and regression parameters can be obtained and unbiased log rank tests of treatment differences performed moderate sample consistency of point es

nonparametric independence screening in sparse ultra high dimensional varying coefficient models the varying coefficient model is an important class of nonparametric statistical model which allows us to examine how the effects of covariates vary with exposure variables when the number of covariates is large the issue of variable selection arises in this article we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra high dimensional varying coefficient models the proposed nonparametric independence screening nis selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable the sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order and the dimensionality reduction of nis is quantified to enhance the practical utility and finite sample performance two data driven iterative nis inis methods are proposed for selecting thresholding parameters and variables conditional permutation and greedy metho

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

large sample theory for semiparametric regression models with two phase outcome dependent sampling outcome dependent two phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by lawless kalbfleisch and wild 1999 under two phase sampling designs we show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient the efficient influence function for the parametric part agrees with the more general information bound calculations of robins hsieh and newey 1995 by verifying the conditions of murphy and van der vaart 2000 for a least favorable parametric submodel we provide asymptotic justification for statistical inference based on profile likelihood

capacity of the gaussian two hop full duplex relay channel with residual self interference in this paper we investigate the capacity of the gaussian two hop full duplex fd relay channel with residual self interference this channel is comprised of a source an fd relay and a destination where a direct source destination link does not exist and the fd relay is impaired by residual self interference we adopt the worst case linear self interference model with respect to the channel capacity and model the residual self interference as a gaussian random variable whose variance depends on the amplitude of the transmit symbol of the relay for this channel we derive the capacity and propose an explicit capacity achieving coding scheme thereby we show that the optimal input distribution at the source is gaussian and its variance depends on the amplitude of the transmit symbol of the relay on the other hand the optimal input distribution at the relay is discrete or gaussian where the latter case occurs only when the relay destination link is the bottleneck link the derived capacity converges to the capacity of the two hop ideal fd relay channel without self interference and to the capacity of the two hop half duplex hd relay channel in the limiting cases when the residual self interference is zero and infinite respectively our numerical results show that significant performance gains are achieved with the proposed capacity achieving coding scheme compared with the achievable rates of conventional hd relaying and or conventional fd relaying

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

a nonparametric test for panel count data summary panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points in this situation observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points we propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available the asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance the method is illustrated using data from a medical follow up study

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

semi localizations of semi abelian categories abstract a semi localization of a category is a full reflective subcategory with the property that the reflector is semi left exact there are many interesting examples of semi localizations as for instance any torsion free subcategory of a semi abelian category by specializing a result due to s mantovani we first characterize the categories which are semi localizations of exact mal tsev categories we then prove a new characterization of protomodular categories in terms of binary relations allowing us to obtain an abstract characterization of the semi localizations of exact protomodular categories this result is very useful to study the hereditarily torsion free subcategories of semi abelian categories some examples are considered in detail in the categories of groups crossed modules commutative rings and topological groups we finally explain how these results extend the corresponding ones obtained in the abelian context by w rump

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

a note on the validity of statistical bootstrapping for estimating the uncertainty of tensor parameters in diffusion tensor images diffusion tensors are estimated from magnetic resonance images mris that are diffusion weighted and those images inherently contain noise therefore noise in the diffusion weighted images produces uncertainty in estimation of the tensors and their derived parameters which include eigenvalues eigenvectors and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise the aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters such as fractional anisotropy fa depends critically on the morphology of the diffusion tensor that is being estimated the wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction pd of isotropic or oblate tensor we also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations simulation studies are also used to understand more thoroughly our theoretical results our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors oblate tensors or multiple tensors

a pairwise likelihood augmented cox estimator for left truncated data survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging conditional approaches for left truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times length biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform otherwise they may generate biased estimates we propose a semiparametric method for left truncated data under the cox model with no parametric distributional assumption about the truncation times our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood which eliminates the truncation distribution yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood an iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously by empirical process and u process theories it has been shown that the proposed estimator is consistent and asymptotically normal with a closed form consistent variance estimator simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator when the uniform truncation assumption holds our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator an application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method

characterization of the asymptotic distribution of semiparametric m estimators this paper develops a concrete formula for the asymptotic distribution of two step possibly non smooth semiparametric m estimators under general misspecification our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature the first stage nonparametric estimation may depend on finite dimensional parameters we characterize 1 conditions under which the first stage estimation of nonparametric components do not affect the asymptotic distribution 2 conditions under which the asymptotic distribution is affected by the derivatives of the first stage nonparametric estimator with respect to the finite dimensional parameters and 3 conditions under which one can allow non smooth objective functions our framework is illustrated by applying it to three examples 1 profiled estimation of a single index quantile regression model 2 semiparametric least squares estimation under model misspecification and 3 a smoothed matching estimator 2010 elsevier b v all rights reserved

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

coarsening at random in general sample spaces and random censoring in continuous time heitjan and rubin proposed a concept coarsening at random generalizing rubin s theory of missing at random their analysis was done in discrete sample spaces we propose a generalization to general sample spaces among heitjan and rubin s applications was right censoring in survival analysis we discuss the application of the generalized theory to various censoring patterns in continuous time and connect to the modern theory of random censoring

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

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

estimating the survival distribution when ascertainment of vital status is subject to delay summary during the interim stages of most large scale clinical trials knowledge that a patient is alive or dead is usually not up to date this is due to the pattern of patient visits to hospitals as well as the administrative set up used by the study to obtain the information on vital status if the process of ascertaining vital status is not completely random then the usual method of estimating the survival curve based on the kaplan meier estimator may be biased for this situation we propose another estimator and show that it is consistent and asymptotically normal comparison with the kaplan meier estimator is made for several patterns of ascertainment of vital status using numerical simulations

using hermite bases in studying capacity achieving distributions over awgn channels this paper studies classes of generic deterministic discrete time memoryless and nonlinear additive white gaussian noise awgn channels subject to multiple types of constraints such as the even moment and compact support constraints or a mixture the optimal input is proved to be discrete with finite number of mass points in the vast majority of the cases only under the even moment constraint and for special cases that emulate the average power constrained linear channel capacity is found to be achieved by an absolutely continuous input the results are extended to channels where the distortion is generally piecewise nonlinear where the discrete nature of the optimal input is conserved these results are reached through the development of methodology and tools that are based on standard decompositions in a hilbert space with the hermite polynomials as a basis and it is showcased how these bases are natural candidates for general information theoretic studies of the capacity of channels affected by awgn intermediately novel results regarding the output rate of decay of gaussian channels are derived namely the output probability distribution of any channel subjected to additive gaussian noise decays necessarily slower than the gaussian itself finally numerical computations are provided for some sample cases optimal inputs are determined and capacity curves are drawn these results put into question the accuracy of adopting the widely used expression 1 1 snr for computing capacities of gaussian deterministic channels

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

length biased sampling with right censoring when survival data arise from prevalent cases ascertained through a cross sectional study it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases length biased data have been treated both unconditionally and conditionally in the literature in the latter case where length bias is viewed as being induced by random left truncation of the survival times the truncating distribution is assumed to be unknown conditioning on the observed truncation times hence causes very little loss of information in many instances however it can be supposed that the truncating distribution is uniform and it has been pointed out that under these circumstances an unconditional analysis will be more informative there are no results in the current literature that give the asymptotic properties of the unconditional nonparametric maximum likelihood estimator npmle of the unbiased survivor function in the presence of cen

torsion theories in homological categories we introduce and study the notion of torsion theory in the non abelian context of homological categories and we investigate the properties of the corresponding closure operator we then consider several new examples of torsion theories in the category of topological groups and more generally in any category of topological semi abelian algebras we finally characterize the hereditary torsion theories and we analyse a new example in the homological category of crossed modules c 2006 elsevier inc all rights reserved

torsion theories and radicals in normal categories we introduce a relativized notion of semi normalcy for categories that come equipped with a proper stable factorization system and we use radicals in the sense of module theory and normal closure operators in order to study torsion theories in such categories our results generalize and complement recent studies in the realm of semi abelian and in part homological categories in particular we characterize both torsion free and torsion classes in terms of their closure under extensions we pay particular attention to the homological and for our purposes more importantly normal categories of topological algebra such as the category of topological groups but our applications go far beyond the realm of these types of categories as they include for example the normal but non homological category of pointed topological spaces which is in fact a rich supplier for radicals of topological groups

fast estimation of regression parameters in a broken stick model for longitudinal data abstractestimation of change point locations in the broken stick model has significant applications in modeling important biological phenomena in this article we present a computationally economical likelihood based approach for estimating change point s efficiently in both cross sectional and longitudinal settings our method based on local smoothing in a shrinking neighborhood of each change point is shown via simulations to be computationally more viable than existing methods that rely on search procedures with dramatic gains in the multiple change point case the proposed estimates are shown to have n consistency and asymptotic normality in particular they are asymptotically efficient in the cross sectional setting allowing us to provide meaningful statistical inference as our primary and motivating longitudinal application we study the michigan bone health and metabolism study cohort data to describe patterns of change in log estradiol levels before and after the final menstrual period

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

refined generalization bounds of gradient learning over reproducing kernel hilbert spaces gradient learning gl initially proposed by mukherjee and zhou 2006 has been proved to be a powerful tool for conducting variable selection and dimensional reduction simultaneously this approach presents a nonparametric version of a gradient estimator with positive definite kernels without estimating the true function itself so that the proposed version has wide applicability and allows for complex effects between predictors in terms of theory however existing generalization bounds for gl depend on capacity independent techniques and the capacity of kernel classes cannot be characterized completely thus this letter considers gl estimators that minimize the empirical convex risk we prove generalization bounds for such estimators with rates that are faster than previous results moreover we provide a novel upper bound for rademacher chaos complexity of order two which also plays an important role in general pairwise type estimations including ranking and score problems

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

adaptive confidence sets in l 2 the problem of constructing confidence sets that are adaptive in l 2 loss over a continuous scale of sobolev classes of probability densities is considered adaptation holds where possible with respect to both the radius of the sobolev ball and its smoothness degree and over maximal parameter spaces for which adaptation is possible two key regimes of parameter constellations are identified one where full adaptation is possible and one where adaptation requires critical regions be removed techniques used to derive these results include a general nonparametric minimax test for infinite dimensional null and alternative hypotheses and new lower bounds for l 2 adaptive confidence sets

quantitative estimates of the convergence of the empirical covariance matrix in log concave ensembles let k be an isotropic convex body in rn given e 0 how many independent points xi uniformly distributed on k are neededfor the empirical covariance matrix to approximate the identity up to e with overwhelming probability our paper answers this question from 12 more precisely let x rn be a centered random vector with a log concave distribution and with the identity as covariance matrix an example of such a vector x is a random point in an isotropic convex body we show that for any e 0 there existsc e 0 su ch that if n c e n and xi i n are i i d copies of 1 n x then n i 1 xi xi id e with probability larger than 1 exp c n

topological semi abelian algebras given an algebraic theory t whose category of models is semi abelian we study the category top t of topological models of t and generalize to it most classical results on topological groups in particular top t is homological which includes barr regularity and forces the mal cev property every open subalgebra is closed and every quotient map is open we devote special attention to the hausdorff compact locally compact connected totally disconnected and profinite t algebras c 2004 elsevier inc all rights reserved

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

nonparametric association analysis of exchangeable clustered competing risks data summary the work is motivated by the cache county study of aging a population based study in utah in which sibship associations in dementia onset are of interest complications arise because only a fraction of the population ever develops dementia with the majority dying without dementia the application of standard dependence analyses for independently right censored data may not be appropriate with such multivariate competing risks data where death may violate the independent censoring assumption nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data as needed with the large sibships in the cache county study time dependent association measures are evaluated using these estimators large sample inferences are studied rigorously using empirical process techniques the practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the cache county study where dementia onset clustering among siblings varies strongly by age

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

fundamental group functors in descent exact homological categories abstract we study the notion of a fundamental group in the framework of descent exact homological categories this setting is sufficiently large to include several categories of algebraic nature such as almost abelian categories semi abelian categories and categories of topological semi abelian algebras for many adjunctions in this context we describe the fundamental groups by generalised brown ellis hopf formulae for the integral homology of groups

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

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

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

locally efficient estimation of the survival distribution with right censored data and covariates when collection of data is delayed summary for many sources of survival data there is a delay between the recording of vital status and its availability to the analyst and the kaplan meier estimator is typically inconsistent in these situations in this paper we identify the optimal estimation problem as a result of the curse of dimensionality no globally efficient nonparametric estimator exists with a good practical performance at moderate sample sizes following the approach of robins rotnitzky 1992 given a correctly specified model for the hazard of censoring conditional on the delay process and t we propose a closed form one step estimator of the distribution of t whose asymptotic variance attains the efficiency bound if we can correctly specify a lower dimensional working model for the conditional distribution of t given the ascertainment process the estimator remains consistent and asymptotically normal even if this latter submodel is misspecified in particular if we choose as working model independence between t and the ascertainment process then the estimator is efficient when this holds and remains consistent and asymptotically linear otherwise moreover we incorporate in our data structure a covariate process that is observed during the follow up time and is reported with the same delays we propose closed form locally efficient estimators of the type described above which use all the data and allow for dependent censoring

bayesian regression with nonparametric heteroskedasticity abstract this paper studies large sample properties of a semiparametric bayesian approach to inference in a linear regression model the approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates the main result of the paper is a semiparametric bernstein von mises theorem under misspecification even when the distribution of the regression error term is not normal the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound

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

boosting method for local learning in statistical pattern recognition we propose a local boosting method in classification problems borrowing from an idea of the local likelihood method our proposal local boosting includes a simple device for localization for computational feasibility we proved the bayes risk consistency of the local boosting in the framework of probably approximately correct learning inspection of the proof provides a useful viewpoint for comparing ordinary boosting and local boosting with respect to the estimation error and the approximation error both boosting methods have the bayes risk consistency if their approximation errors decrease to zero compared to ordinary boosting local boosting may perform better by controlling the trade off between the estimation error and the approximation error ordinary boosting with complicated base classifiers or other strong classification methods including kernel machines may have classification performance comparable to local boosting with simple base classifiers for example decision stumps local boosting however has an advantage with respect to interpretability local boosting with simple base classifiers offers a simple way to specify which features are informative and how their values contribute to a classification rule even though locally several numerical studies on real data sets confirm these advantages of local boosting

overidentification in regular models in the unconditional moment restriction model of hansen specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest we show that a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings specifically a condition we name local overidentification is shown to be equivalent to both the existence of specification tests with nontrivial local power and the existence of more efficient estimators of some smooth parameters in general semi nonparametric models under our notion of local overidentification various locally nontrivial specification tests such as hausman tests incremental sargan tests or optimally weighted quasi likelihood ratio tests naturally extend to general semi nonparametric settings we further obtain simple characterizations of local overidentification for general models of nonparametric conditional moment restrictions with possibly different conditioning sets the results are applied to determining when semi nonparametric models with endogeneity are locally testable and when nonparametric plug in and semiparametric two step gmm estimators are semiparametrically efficient examples of empirically relevant semi nonparametric structural models are presented

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

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

estimation of treatment effects in randomized trials with non compliance and a dichotomous outcome summary we propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non compliance recent papers by vansteelandt and goetghebeur and robins and rotnitzky have presented consistent and asymptotically linear estimators of a causal odds ratio which rely beyond correct specification of a model for the causal odds ratio on a correctly specified model for a potentially high dimensional nuisance parameter in this paper we propose consistent asymptotically linear and locally efficient estimators of a causal relative risk and a new parameter called a switch causal relative risk which relies only on the correct specification of a model for the parameter of interest our estimators are always consistent and asymptotically linear at the null hypothesis of no treatment effect thereby providing valid testing procedures we examine the finite sample properties of these instrumental variable based estimators and the associated testing procedures in simulations and a data analysis of decaffeinated coffee consumption and miscarriage

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