the neron component series of an abelian variety we introduce the neron component series of an abelian variety a over a complete discretely valued field this is a power series in mathbb z left left t right right which measures the behaviour of the number of components of the neron model of a under tame ramification of the base field if a is tamely ramified then we prove that the neron component series is rational it has a pole at t 1 whose order equals one plus the potential toric rank of a this result is a crucial ingredient of our proof of the motivic monodromy conjecture for abelian varieties we expect that it extends to the wildly ramified case we prove this if a is an elliptic curve and if a has potential purely multiplicative reduction

dimension reduction for nonelliptically distributed predictors sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor or when such conditions are not satisfied rely on marginal transformation or reweighting to fulfill them approximately for example a typical dimension reduction method would require the predictor to have elliptical or even multivariate normal distribution in this paper we reformulate the commonly used dimension reduction methods via the notion of central solution space so as to circumvent the requirements of such strong assumptions while at the same time preserve the desirable properties of the classical methods such as n consistency and asymptotic normality imposing elliptical distributions or even stronger assumptions on predictors is often considered as the necessary tradeoff for overcoming the curse of dimensionality but the development of this paper shows that this need not be the case the new methods will be compared with existing methods by simulation and applied to a data set

using the bootstrap to select one of a new class of dimension reduction methods dimension reduction in a regression analysis of response y given a p dimensional vector of predictors x reduces the dimension of x by replacing it with a lower dimensional linear combination x of the x s without specifying a parametric model and without loss of information about the conditional distribution of y given x we unify three existing methods sliced inverse regression sir sliced average variance estimate save and principal hessian directions phd into a larger class of methods each method estimates a particular candidate matrix essentially a matrix of parameters we introduce broad classes of dimension reduction candidate matrices and we distinguish estimators of the matrices from the matrices themselves given these classes of methods and several ways to estimate any matrix we now have the problem of selecting a particular matrix and estimation method we propose bootstrap methodology to select among candidate matrices estimators and dimension and in particular we investigate l

local multiple imputation dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships if such parametric assumptions do not hold the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results in this paper a fully nonparametric and a semiparametric imputation method are studied both based on local resampling principles it is shown that the final estimator based on these local imputations is consistent under fewer or no parametric assumptions asymptotic expressions for bias variance and mean squared error are derived showing the theoretical impact of the different smoothing parameters simulations illustrate the usefulness and applicability of the method

efficient estimation and inferences for varying coefficient models abstract this article deals with statistical inferences based on the varying coefficient models proposed by hastie and tibshirani local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established the standard error formulas for estimated coefficients are derived and are empirically tested a goodness of fit test technique based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying coefficient model are constant or whether any covariates are statistically significant in the model the null distribution of the test is estimated by a conditional bootstrap method our estimation techniques involve solving hundreds of local likelihood equations to reduce the computational burden a one step newton raphson estimator is proposed and implemented the resulting one step procedure is shown to save computational cost on an order of tens with no

sparse sufficient dimension reduction existing sufficient dimension reduction methods suffer from the fact that each dimension reduction component is a linear combination of all the original predictors so that it is difficult to interpret the resulting estimates we propose a unified estimation strategy which combines a regression type formulation of sufficient dimension reduction methods and shrinkage estimation to produce sparse and accurate solutions the method can be applied to most existing sufficient dimension reduction methods such as sliced inverse regression sliced average variance estimation and principal hessian directions we demonstrate the effectiveness of the proposed method by both simulations and real data analysis

an effective semiparametric estimation approach for the sufficient dimension reduction model abstractin the exploratory data analysis the sufficient dimension reduction model has been widely used to characterize the conditional distribution of interest different from the existing approaches our main achievement is to simultaneously estimate two essential elements basis and structural dimension of the central subspace and the bandwidth of a kernel distribution estimator through a single estimation criterion with an appropriate order of kernel function the proposed estimation procedure can be effectively carried out by starting with a dimension of zero until the first local minimum is reached meanwhile the optimal bandwidth selector is ensured to be a valid tuning parameter for the central subspace estimator an important advantage of this estimation technique is its flexibility to allow a response to be discrete and some of covariates to be discrete or categorical providing that a certain continuity condition holds under very mild assumptions we further derive the uniform consistency of

reweighting to achieve elliptically contoured covariates in regression abstract we investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates in particular new estimation methods like sir sirii save and phd have been built around the assumption of elliptically contoured covariates finite samples of regression covariates may deviate from this ideal in practice and the method developed here termed voronoi weighting can be used to induce elliptical symmetry in such samples in a number of examples we show that reweighting cases by the voronoi method can substantially enhance various procedures for covariates that deviate from elliptical symmetry we show that voronoi weighting in conjunction with some trimming via the minimum volume ellipsoid method can be effective

likelihood based sufficient dimension reduction we obtain the maximum likelihood estimator of the central subspace under conditional normality of the predictors given the response analytically and in simulations we found that our new estimator can preform much better than sliced inverse regression sliced average variance estimation and directional regression and that it seems quite robust to deviations from normality

asymptotics for kernel estimate of sliced inverse regression to explore nonlinear structures hidden in high dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression li and duan proposed the sliced inverse regression sir method which is simple to use in this paper the asymptotic properties of the kernel estimate of sliced inverse regression are investigated it turns out that regardless of the kernel function the asymptotic distribution remains the same for a wide range of smoothing parameters

stable reduction of curves and tame ramification we study stable reduction of curves in the case where a tamely ramified base extension is sufficient if x is a smooth curve defined over the fraction field of a strictly henselian discrete valuation ring there is a criterion due to saito that describes precisely in terms of the geometry of the minimal model with strict normal crossings of x when a tamely ramified extension suffices in order for x to obtain stable reduction for such curves we construct an explicit extension that realizes the stable reduction and we furthermore show that this extension is minimal we also obtain a new proof of saito s criterion avoiding the use of l adic cohomology and vanishing cycles

median regression models for longitudinal data with dropouts summary recently median regression models have received increasing attention when continuous responses follow a distribution that is quite different from a normal distribution usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily in this article we discuss using median regression models to deal with longitudinal data with dropouts weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data where the weights are determined by modeling the dropout process consistency and the asymptotic distribution of the resultant estimators are established the proposed method is used to analyze a longitudinal data set arising from a controlled trial of hiv disease volberding et al 1990 the new england journal of medicine 322 941 949 simulation studies are conducted to assess the performance of the proposed method under various situations an extension to estimation of the association parameters is outlined

groupwise dimension reduction via envelope method the family of sufficient dimension reduction sdr methods that produce informative combinations of predictors or indices are particularly useful for high dimensional regression analysis in many such analyses it becomes increasingly common that there is available a priori subject knowledge of the predictors for example they belong to different groups while many recent sdr proposals have greatly expanded the scope of the methods applicability how to effectively incorporate the prior predictor structure information remains a challenge in this article we aim at dimension reduction that recovers full regression information while preserving the predictor group structure built upon a new concept of the direct sum envelope we introduce a systematic way to incorporate the group information in most existing sdr estimators as a result the reduction outcomes are much easier to interpret moreover the envelope method provides a principled way to build a variety of prior structures into dimension reduc

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

an adaptive estimation of dimension reduction space summary searching for an effective dimension reduction space is an important problem in regression especially for high dimensional data we propose an adaptive approach based on semiparametric models which we call the conditional minimum average variance estimation mave method within quite a general setting the mave method has the following advantages most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters than for that of the nonparametric function in contrast a faster consistency rate can be achieved by the mave method even without undersmoothing the nonparametric link function estimator the mave method is applicable to a wide range of models with fewer restrictions on the distribution of the covariates to the extent that even time series can be included because of the faster rate of consistency for the parameter estimators it is possible for us to estimate the dimension of the space consistently the relationship of the mave method with other methods is also investigated in particular a simple outer product gradient estimator is proposed as an initial estimator in addition to theoretical results we demonstrate the efficacy of the mave method for high dimensional data sets through simulation two real data sets are analysed by using the mave approach

a constructive approach to the estimation of dimension reduction directions in this paper we propose two new methods to estimate the dimension reduction directions of the central subspace cs by constructing a regression model such that the directions are all captured in the regression mean compared with the inverse regression estimation methods e g j amer statist assoc 86 1991 328 332 j amer statist assoc 86 1991 316 342 j amer statist assoc 87 1992 1025 1039 the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable and have better performance than the inverse regression estimation methods for finite samples compared with the direct regression estimation methods e g j amer statist assoc 84 1989 986 995 ann statist 29 2001 1537 1566 j r stat soc ser b stat methodol 64 2002 363 410 which can only estimate the directions of cs in the regression mean the new methods can detect the directions of cs exhaustively consistency of the estimators and the convergence of corresponding algorithms are proved

fourier methods for estimating the central subspace and the central mean subspace in regression in regression with a high dimensional predictor vector it is important to estimate the central and central mean subspaces that preserve sufficient information about the response and the mean response using the fourier transform we have derived the candidate matrices whose column spaces recover the central and central mean subspaces exhaustively under the normality assumption of the predictors explicit estimates of the central and central mean subspaces are derived bootstrap procedures are used for determining dimensionality and choosing tuning parameters simulation results and an application to a real data are reported our methods demonstrate competitive performance compared with sir save and other existing methods the approach proposed in the article provides a novel view on sufficient dimension reduction and may lead to more powerful tools in the future

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

vanishing cycles and geometry of curves over a discrete valuation ring 0 introduction geometry of curves over a discrete valuation ring is reflected in the action of the monodromy on the f adic cohomology groups the stable reduction theorem d m gives an equivalent geometrical condition for the action of the inertia group to be unipotent in the global situation where global means that the curve in consideration is proper in this paper we will generalize it in two directions one is to the local situation with the isolated singularity the other is to consider the geometrical condition for the action of the wild ramification group to be trivial we will also give a purely cohomological proof without using picard schemes of the stable reduction theorem and a new proof of the formula of deligne la theorem 5 1 1 based only on the stable reduction theorem here we only treat a strictly local discrete valuation ring with algebraically closed residue field however the results apply to any discrete valuation ring with perfect residue field since they are etale local we introduce some notations and terminologies

a semiparametric estimation of mean functionals with nonignorable missing data parameter estimation with nonignorable missing data is a challenging problem in statistics the fully parametric approach for joint modeling of the response model and the population model can produce results that are quite sensitive to the failure of the assumed model we propose a more robust modeling approach by considering the model for the nonresponding part as an exponential tilting of the model for the responding part the exponential tilting model can be justified under the assumption that the response probability can be expressed as a semiparametric logistic regression model in this paper based on the exponential tilting model we propose a semiparametric estimation method of mean functionals with nonignorable missing data a semiparametric logistic regression model is assumed for the response probability and a nonparametric regression approach for missing data discussed in cheng 1994 is used in the estimator by adopting nonparametric components for the model the estimation method can be mad

vibrational feedback control of time delay systems this paper applies vibrational feedback control to time lag systems averaging theory for differential delay systems is presented and then applied to aid in the design of periodic controllers both stabilization and transient issues are discussed an illustrative example is given which demonstrates that the proposed controller 1 provides superior robustness properties in comparison to time invariant controllers when applied correctly 2 is not robust with respect to unmodeled delays and 3 does not have zero placement capabilities in the sense defined in the paper

a trace formula for varieties over a discretely valued field we study the motivic serre invariant of a smoothly bounded alge braic or rigid variety x over a complete discretely valued field k with perfect residue field k if k has characteristic zero we extend the definition to arbi trary k varieties using bittner s presentation of the grothendieck ring and a process of neron smoothening of pairs of varieties the motivic serre invariant can be considered as a measure for the set of unramified points on x under certain tameness conditions it admits a cohomological interpretation by means of a trace formula in the curve case we use t saito s geometric criterion for cohomological tameness to obtain more detailed results we discuss some applications to weil chatelet groups chow motives and the structure of the grothendieck ring of varieties msc 2000 11s15 14g05 14g22

a general framework for quantile estimation with incomplete data quantile estimation has attracted significant research interests in recent years however there has been only a limited literature on quantile estimation in the presence of incomplete data in this paper we propose a general framework to address this problem our framework combines the two widely adopted approaches for missing data analysis the imputation approach and the inverse probability weighting approach via the empirical likelihood method the proposed method is capable of dealing with many different missingness settings we mainly study three of them i estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates ii estimating the conditional quantile of a fully observed response while the covariates are partially available and iii estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables the proposed method allows multiple models for both the missingness probability and the data distribution the resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified the asymptotic distributions are established using the empirical process theory

efficient quantile regression analysis with missing observations this article examines the problem of estimation in a quantile regression model when observations are missing at random under independent and nonidentically distributed errors we consider three approaches of handling this problem based on nonparametric inverse probability weighting estimating equations projection and a combination of both an important distinguishing feature of our methods is their ability to handle missing response and or partially missing covariates whereas existing techniques can handle only one or the other but not both we prove that our methods yield asymptotically equivalent estimators that achieve the desirable asymptotic properties of unbiasedness normality and n consistency because we do not assume that the errors are identically distributed our theoretical results are valid under heteroscedasticity a particularly strong feature of our methods under the special case of identical error distributions all of our proposed estimators achieve the semiparametric efficiency b

efficiency loss caused by linearity condition in dimension reduction linearity sometimes jointly with constant variance is routinely assumed in the context of sufficient dimension reduction it is well understood that when these conditions do not hold blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace surprisingly we discover that even if these conditions do hold using them will bring efficiency loss this paradoxical phenomenon is illustrated through sliced inverse regression and principal hessian directions the efficiency loss also applies to other dimension reduction procedures we explain this empirical discovery by theoretical investigation

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

a semiparametric method of multiple imputation in this paper we describe how to use multiple imputation semiparametrically to obtain estimates of parameters and their standard errors when some individuals have missing data the methods given require the investigator to know or be able to estimate the process generating the missing data but requires no full distributional form for the data the method is especially useful for non standard problems such as estimating the median when data are missing

elliptic curves and hilbert s tenth problem for algebraic function fields over real and p adic fields let k be a field of characteristic zero v a smooth positive dimensional quasiprojective variety over k and d a nonempty effective divisor on v let k be the function field of v and a the semilocal ring of d in k in this paper we prove the diophantine undecidability of 1 a in all cases 2 k when k is formally real and v has a real point 3 k when k is a subfield of a p adic field for some odd prime p to achieve this we use denef s method from an elliptic curve e over q without complex multiplication one constructs a quadratic twist e of e over q t which has mordell weil rank one most of the paper is devoted to proving using a theorem of r noot that one can choose f in k vanishing at d such that the group e k deduced from the field extension k q f q t is equal to e q t then we mimic the arguments of denef for the real case and of kim and roush for the p adic case

weighted semiparametric estimation in regression analysis with missing covariate data abstract this article investigates estimation of the regression coefficients in an assumed mean function when covariates on some subjects are missing we examine the performance of a horvitz and thompson 1952 type weighted estimator by using different estimates of the selection probabilities which may be treated as nuisance parameters or a nuisance function in particular we investigate the properties of the estimate of the regression parameters when the selection probabilities are estimated by kernel smoothers we present large sample theory for the new estimator and conduct simulation studies comparing the proposed estimator to the maximum likelihood estimator and multiple imputation under various model assumptions and different missingness mechanisms in addition we provide two real examples that motivate this investigation

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

on almost linearity of low dimensional projections from high dimensional data this paper studies the shapes of low dimensional projections from high dimensional data after standardization let mathbf x be a p dimensional random variable with mean zero and identity covariance for a projection beta mathbf x beta 1 find another direction b so that the regression curve of b mathbf x against beta mathbf x is as nonlinear as possible we show that when the dimension of mathbf x is large for most directions beta even the most nonlinear regression is still nearly linear our method depends on the construction of a pair of p dimensional random variables mathbf w 1 mathbf w 2 called the rotational twin and its density function with respect to the standard normal density with this we are able to obtain closed form expressions for measuring deviation from normality and deviation from linearity in a suitable sense of average as an interesting by product from a given set of data we can find simple unbiased estimates of e f beta mathbf x t phi 1 t 1 2 and e lbrack e mathbf x mid beta beta mathbf x t 2 t 2 f 2 beta mathbf x t phi 2 1 t rbrack where phi 1 is the standard normal density f beta mathbf x is the density for beta mathbf x and the e is taken with respect to the uniformly distributed beta this is achieved without any smoothing and without resorting to any laborious projection procedures such as grand tours our result is related to the work of diaconis and freedman the impact of our result on several fronts of data analysis is discussed for example it helps establish the validity of regression analysis when the link function of the regression model may be grossly wrong a further generalization which replaces beta mathbf x by b mathbf x with b beta 1 ldots beta k for k randomly selected orthonormal vectors beta i i 1 ldots k helps broaden the scope of application of sliced inverse regression sir

dimension reduction for conditional mean in regression in many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors and less concerned with the other aspects of the conditional distribution in this paper we develop dimension reduction methods that incorporate this consideration we introduce the notion of the central mean subspace cms a natural inferential object for dimension reduction when the mean function is of interest we study properties of the cms and develop methods to estimate it these methods include a new class of estimators which requires fewer conditions than phd and which displays a clear advantage when one of the conditions for phd is violated cms also reveals a transparent distinction among the existing methods for dimension reduction ols phd sir and save we apply the new methods to a data set involving recumbent cows

multiple imputation in quantile regression summary we propose a multiple imputation estimator for parameter estimation in a quantile regression model when some covariates are missing at random the estimation procedure fully utilizes the entire dataset to achieve increased efficiency and the resulting coefficient estimators are root n consistent and asymptotically normal to protect against possible model misspecification we further propose a shrinkage estimator which automatically adjusts for possible bias the finite sample performance of our estimator is investigated in a simulation study finally we apply our methodology to part of the eating at american s table study data investigating the association between two measures of dietary intake

vibrational control of chemical reactions in a cstr with delayed recycle stream vibrational control is a method of modification of dynamic properties obtained by introducing zero mean oscillations into system parameters this paper shows that by introducing oscillations into the flow rates of a continuous stirred tank reactor with delayed recycle stream it is possible to operate reactions in the vicinity of previously unstable steady states

a paradox concerning nuisance parameters and projected estimating functions summary this paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters in a statistical model with unknown nuisance parameters the efficiency of an estimator of a parameter usually increases when the nuisance para meters are known however the opposite phenomenon can sometimes occur in this paper we elucidate the occurrence of this paradox by examining estimating functions in particular we focus on the projected estimating function which is defined by the projection of the score function on to a given estimating function a sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters in addition a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators

sliced regression for dimension reduction a new dimension reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed compared with the traditional inverse regression methods e g sliced inverse regression sir the new method is free of the linearity condition and has much better estimation accuracy compared with the direct estimation methods e g mave the new method is much more robust against extreme values and can capture the entire central subspace cs exhaustively to determine the cs dimension a consistent cross validation criterion is developed extensive numerical studies including a real example confirm our theoretical findings

fundamental theorems of averaging for functional differential equations abstract in this paper we improve on classical averaging theorems for functional differential equations by proposing new averaged models specifically we present averaged models which retain functional dependence on state variables delays and additional parametric dependence as shown in three examples the new models often yield improvements in approximation accuracy

semiparametric inverse propensity weighting for nonignorable missing data to estimate unknown population parameters based on data having nonignorable missing values with a semiparametric exponential tilting propensity kim yu 2011 assumed that the tilting parameter is known or can be estimated from external data in order to avoid the identifiability issue to remove this serious limitation on the methodology we use an instrument i e a covariate related to the study variable but unrelated to the missing data propensity to construct some estimating equations because these estimating equations are semiparametric we profile the nonparametric component using a kernel type estimator and then estimate the tilting parameter based on the profiled estimating equations and the generalized method of moments once the tilting parameter is estimated so is the propensity and then other population parameters can be estimated using the inverse propensity weighting approach consistency and asymptotic normality of the proposed estimators are established the finite sample performance of the estimators is studied through simulation and a real data example is also presented

direction estimation in single index regressions we propose a general dimension reduction method that combines the ideas of likelihood correlation inverse regression and information theory we do not require that the dependence be confined to particular conditional moments nor do we place restrictions on the predictors or on the regression that are necessary for methods like ordinary least squares and sliced inverse regression although we focus on single index regressions the underlying idea is applicable more generally illustrative examples are presented

estimating equations inference with missing data there is a large and growing body of literature on estimating equation ee as an estimation approach one basic property of ee that has been universally adopted in practice is that of unbiasedness and there are deep conceptual reasons why unbiasedness is a desirable ee characteristic this article deals with inference from ees when data are missing at random the investigation is motivated by the observation that direct imputation of missing data in ees generally leads to ees that are biased and thus violates a basic assumption of the ee approach the main contribution of this article is that it goes beyond existing imputation methods and proposes a procedure whereby one mitigates the effects of missing data through a reformulation of ees imputed through a kernel regression method these modified ees then constitute a basis for inference by the generalized method of moments gmm and empirical likelihood el asymptotic properties of the gmm and el estimators of the unknown parameters are derived a

efficient integration of sufficient dimension reduction and prediction in discriminant analysis abstractsufficient dimension reduction sdr methods are popular model free tools for preprocessing and data visualization in regression problems where the number of variables is large unfortunate

counting process based dimension reduction methods for censored outcomes we propose counting process based dimension reduction methods for right censored survival data semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model our methods address two limitations of existing approaches first using the counting process formulation they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace second the nonparametric estimation involved adapts to the structural dimension so our methods circumvent the curse of dimensionality asymptotic normality is established for the estimators we propose a computationally efficient approach that requires only a singular value decomposition to estimate the dimension reduction subspace numerical studies suggest that our new approaches exhibit significantly improved performance the methods are implemented in the formula see text package formula see text

dimension reduction for non elliptically distributed predictors second order methods summary many classical dimension reduction methods especially those based on inverse conditional moments require the predictors to have elliptical distributions or at least to satisfy a linearity condition such conditions however are too strong for some applications li and dong 2009 introduced the notion of the central solution space and used it to modify first order methods such as sliced inverse regression so that they no longer rely on these conditions in this paper we generalize this idea to second order methods such as sliced average variance estimation and directional regression in doing so we demonstrate that the central solution space is a versatile framework we can use it to modify essentially all inverse conditional moment based methods to relax the distributional assumption on the predictors simulation studies and an application show a substantial improvement of the modified methods over their classical counterparts

on directional regression for dimension reduction we introduce directional regression dr as a method for dimension reduction like contour regression dr is derived from empirical directions but achieves higher accuracy and requires substantially less computation dr naturally synthesizes the dimension reduction estimators based on conditional moments such as sliced inverse regression and sliced average variance estimation and in doing so combines the advantages of these methods under mild conditions it provides exhaustive and consistent estimate of the dimension reduction space we develop the asymptotic distribution of the dr estimator and from that a sequential test procedure to determine the dimension of the central space we compare the performance of dr with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models finally we apply dr to analyze a data set concerning the identification of hand written digits

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

diagnostic studies in sufficient dimension reduction sufficient dimension reduction in regression aims to reduce the predictor dimension by replacing the original predictors with some set of linear combinations of them without loss of information numerous dimension reduction methods have been developed based on this paradigm however little effort has been devoted to diagnostic studies within the context of dimension reduction in this paper we introduce methods to check goodness of fit for a given dimension reduction subspace the key idea is to extend the so called distance correlation to measure the conditional dependence relationship between the covariates and the response given a reduction subspace our methods require minimal assumptions which are usually much less restrictive than the conditions needed to justify the original methods asymptotic properties of the test statistic are studied numerical examples demonstrate the effectiveness of the proposed approach

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

a semiparametric approach to dimension reduction we provide a novel and completely different approach to dimension reduction problems from the existing literature we cast the dimension reduction problem in a semiparametric estimation framework and derive estimating equations viewing this problem from the new angle allows us to derive a rich class of estimators and obtain the classical dimension reduction techniques as special cases in this class the semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact the common assumption of linearity and or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression the semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example this article has online supplementary material

a missing information principle and m estimators in regression analysis with censored and truncated data a general missing information principle is proposed for constructing mestimators of regression parameters in the presence of left truncation and right censoring on the observed responses by making use of martingale central limit theorems and empirical process theory the asymptotic normality of m estimators is established under certain assumptions asymptotically efficient m estimators are also developed by using data dependent score functions in addition robustness properties of the estimators are discussed and formulas for their influence functions are derived for the robustness analysis

a semiparametric correction for attenuation abstract a correction method is proposed for models including the generalized linear model when the covariate is measured with error the method requires a separate validation data set that consists of the surrogate w and the true covariate x or an unbiased estimate x of x we do not require the classical additive measurement error model in which the surrogate is unbiased for the true covariates we first obtain an estimate of e x w by using nonparametric kernel regression of x or x on w based on the validation data then we perform a standard analysis with the unknown x replaced by the estimate of e x w the asymptotic distribution of the resulting regression parameter estimator is obtained generalizations to include components of x measured without error are also discussed

geometric criteria for tame ramification we prove an a campo type formula for the tame monodromy zeta function of a smooth and proper variety over a discretely valued field k as a first application we relate the orders of the tame monodromy eigenvalues on the l adic cohomology of a k curve to the geometry of a relatively minimal sncd model and we show that the semi stable reduction theorem and saito s criterion for cohomological tameness are immediate consequences of this result as a second application we compute the error term in the trace formula for smooth and proper k varieties we see that the validity of the trace formula would imply a partial generalization of saito s criterion to arbitrary dimension

an efficient empirical likelihood approach for estimating equations with missing data we explore the use of estimating equations for efficient statistical inference in case of missing data we propose a semiparametric efficient empirical likelihood approach and show that the empirical likelihood ratio statistic and its profile counterpart asymptotically follow central chi square distributions when evaluated at the true parameter the theoretical properties and practical performance of our approach are demonstrated through numerical simulations and data analysis copyright 2012 oxford university press

bootstrap consistency for general semiparametric m estimation consider m estimation in a semiparametric model that is characterized by a euclidean parameter of interest and an infinite dimensional nuisance parameter as a general purpose approach to statistical inferences the bootstrap has found wide applications in semiparametric m estimation and because of its simplicity provides an attractive alternative to the inference approach based on the asymptotic distribution theory the purpose of this paper is to provide theoretical justifications for the use of bootstrap as a semiparametric inferential tool we show that under general conditions the bootstrap is asymptotically consistent in estimating the distribution of the m estimate of euclidean parameter that is the bootstrap distribution asymptotically imitates the distribution of the m estimate we also show that the bootstrap confidence set has the asymptotically correct coverage probability these general conclusions hold in particular when the nuisance parameter is not estimable at root n rate and apply to a broad class of bootstrap methods with exchangeable bootstrap weights this paper provides a first general theoretical study of the bootstrap in semiparametric models

fused estimators of the central subspace in sufficient dimension reduction when studying the regression of a univariate variable y on a vector x of predictors most existing sufficient dimension reduction sdr methods require the construction of slices of y to estimate moments of the conditional distribution of x given y but there is no widely accepted method for choosing the number of slices while a poorly chosen slicing scheme may produce miserable results we propose a novel and easily implemented fusing method that can mitigate the problem of choosing a slicing scheme and improve estimation efficiency at the same time we develop two fused estimators called fire and dire based on an optimal inverse regression estimator the asymptotic variance of fire is no larger than that of the original methods regardless of the choice of slicing scheme while dire is less computational intense and more robust simulation studies show that the fused estimators perform effectively the same as or substantially better than the parent methods fused estimators based on other methods can be

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

an estimating equation approach to dimension reduction for longitudinal data sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data in this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace the proposed method accounts for the covariance structure within each subject and improves estimation efficiency when the covariance structure is correctly specified even if the covariance structure is misspecified our estimator remains consistent in addition our method relaxes distributional assumptions on the covariates and is doubly robust to determine the structural dimension of the central mean subspace we propose a bayesian type information criterion we show that the estimated structural dimension is consistent and that the estimated basis directions are root formula see text consistent asymptotically normal and locally efficient simulations and an analysis of the framingham heart study data confirm the effectiveness of our approach

logarithmic good reduction of abelian varieties let k be a field which is complete for a discrete valuation we prove a logarithmic version of the neron ogg shafarevich criterion if a is an abelian variety over k which is cohomologically tame then a has good reduction in the logarithmic setting i e there exists a projective log smooth model of a over mathcal o k this implies in particular the existence of a projective regular model of a generalizing a result of kunnemann the proof combines a deep theorem of gabber with the theory of degenerations of abelian varieties developed by mumford faltings chai et al

on principal hessian directions for data visualization and dimension reduction another application of stein s lemma abstract modern graphical tools have enhanced our ability to learn many things from data directly with much user friendly graphical software available we are encouraged to plot a lot more often than before the benefits from direct interaction with graphics have been enormous but trailing behind these high tech advances is the issue of appropriate guidance on what to plot there are too many directions to project a high dimensional data set and unguided plotting can be time consuming and fruitless in a recent article li set up a statistical framework for study on this issue based on a notion of effective dimension reduction edr directions they are the directions to project a high dimensional input variable for the purpose of effectively viewing and studying its relationship with an output variable a methodology sliced inverse regression was introduced and shown to be useful in finding edr directions this article introduces another method for finding edr directions it begins with the observat

bayesian quantile regression for longitudinal studies with nonignorable missing data summary we study quantile regression qr for longitudinal measurements with nonignorable intermittent missing data and dropout compared to conventional mean regression quantile regression can characterize the entire conditional distribution of the outcome variable and is more robust to outliers and misspecification of the error distribution we account for the within subject correlation by introducing a l2 penalty in the usual qr check function to shrink the subject specific intercepts and slopes toward the common population values the informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects we assess the performance of the proposed method using simulation studies and illustrate it with data from a pediatric aids clinical trial