projections onto translation invariant subspaces of l1 g abstract let g be a locally compact abelian group a translation invariant subspace in l 1 g may or may not be complemented depending on the structure of its hull in techniques for deciding this complementation problem in a variety of situations are developed and illustrated with examples a complete characterization is obtained for those ideals with a discrete hull

weak fixed point property and asymptotic centre for the fourier stieltjes algebra of a locally compact group in this paper we show that the fourier stieltjes algebra b g of a non compact locally compact group g cannot have the weak fixed point property for nonexpansive mappings this answers two open problems posed at a conference in marseille luminy in 1989 we also show that a locally compact group is compact exactly if the asymptotic centre of any non empty weak closed bounded convex subset c in b g with respect to a decreasing net of bounded subsets is a non empty norm compact subset in particular when g is compact b g has the weak fixed point property for left reversible semigroups this generalizes a classical result of t c lim for the circle group as a consequence of our main results we obtain that a number of properties some of which were known to hold for compact groups in fact characterize compact groups

complemented ideals in the fourier algebra and the radon nikodym property necessary and sufficient conditions are given for an ideal i h of the fourier algebra to be complemented when h is a closed subgroup of g using the radon nikodym property an example of a group g with a normal abelian subgroup h for which i h is not complemented is presented

the importance of assessing measurement reliability in multivariate regression abstract in many contexts involving multivariate linear regression models some or all of the independent predictor variables are measured with error it is argued that if the goal is to assess the relationship of the dependent variables to the true predictor variables then it is important to determine the reliability matrix of the measurement x of the vector of true predictors if is singular then the slope matrix b is not identifiable if is nearly singular then b cannot be accurately estimated a two step estimation procedure is proposed in which is estimated from data on the measured predictors x and on prior information from reliability studies on these predictors and the parameters of the latent linear relationship are estimated by classical linear regression methods this approach not only allows the use of available software but also lends itself to traditional diagnostic methods large sample properties of the estimators resulting from this approach are derived it is shown how a c

new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

testing and estimation in marker set association study using semiparametric quantile regression kernel machine we consider quantile regression for partially linear models where an outcome of interest is related to covariates and a marker set e g gene or pathway the covariate effects are modeled parametrically and the marker set effect of multiple loci is modeled using kernel machine we propose an efficient algorithm to solve the corresponding optimization problem for estimating the effects of covariates and also introduce a powerful test for detecting the overall effect of the marker set our test is motivated by traditional score test and borrows the idea of permutation test our estimation and testing procedures are evaluated numerically and applied to assess genetic association of change in fasting homocysteine level using the vitamin intervention for stroke prevention trial data

iterated stack automata and complexity classes abstract an iterated pushdown is a pushdown of pushdowns of of pushdowns an iterated exponential function is 2 to the 2 to the to the 2 to some polynomial the main result presented here is that the nondeterministic 2 way and multi head iterated pushdown automata characterize the deterministic iterated exponential time complexity classes this is proved by investigating both nondeterministic and alternating auxiliary iterated pushdown automata for which similar characterization results are given in particular it is shown that alternation corresponds to one more iteration of pushdowns these results are applied to the 1 way iterated pushdown automata 1 they form a proper hierarchy with respect to the number of iterations and 2 their emptiness problem is complete in deterministic iterated exponential time similar results are given for iterated stack checking stack nonerasing stack nested stack checking stack pushdown automata

hardy s inequality and the l1 norm of exponential sums in this paper we generalize hardy s inequality 3 for measures of analytic type and obtain a proof of the littlewood conjecture 4 for the l norm of exponential sums as a simple consequence let t be the circle group z the additive group of integers and m t the customary convolution algebra of borel measures on t for pe e m t and n g z put m e ino dp o denote by h t the classical space of all measures e e m t such that j n 0 for all n 0 and let c denote the complex numbers we now state hardy s inequality for measures of analytic type theorem 1 if m c h t then

weak closedness of subspaces of fourier stieltjes algebras and weak continuity of the restriction map let g be a locally compact group and b g the fourier stieltjes algebra of g we study the problem of how weak8 closedness of some translation invariant subspaces of b g is related to the structure of g moreover we prove that for a closed subgroup h of g the restriction map from b g to b h is weak8 continuous only when h is open in g introduction let g be a locally compact group and let b g be the fourier stieltjes algebra of g as defined by eymard 8 recall that b g is the linear span of all continuous positive definite functions on g and can be identified with the banach space dual of c g the group c algebra of g the space b g with the xlorm as dual of c g is a commutative banach algebra with pointwise multiplication and complex conjugation the fourier algebra a g of g is the closed subalgebra of b g generated by the functions in b g with compact support in particular a g is contained in co g the algebra of complex valued continuous functions on g vanishing at infinity as is well known a g is weak dense in b g if and only if g is amenable in 3 translation invariant subalgebras a of b g were studied and it was shown that if such a is weak closed and point separating then it must contain a g however apart from this very little seems to be known about weak closed subspaces of b g the first purpose of this paper is to investigate the relation between weak closedness of certain interesting norm closed translation invariant subspaces of b g and the structure of g secondly we solve the problem of whexl for a closed subgroup h of g the restriction map from b g to b h is weak continuous a brief outline of the paper is as follows in section 2 we estsablish for almost connected locally compact groups g the relation between weclk closed ness of bo g b g n co g in e3 g and the structure of g theorem 2 10 the key result is that for a connected lie group g bo g is weak closed in b g if and only if g is a reductive lie group with compact centre and kazhdan s property t received by the editors december 1s 1995 199l mathematics subject classification primary 22d10 43a30 work supported by nato collaborative research grant crg 940184 g 1997 american mathematical society

partially linear additive quantile regression in ultra high dimension we consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data this model has several appealing features 1 by considering different conditional quantiles we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates 2 the sparsity level is allowed to be different at different quantile levels 3 the partially linear additive structure accommodates nonlinearity and circumvents the curse of dimensionality 4 it is naturally robust to heavy tailed distributions in this paper we approximate the nonlinear components using b spline basis functions we first study estimation under this model when the nonzero components are known in advance and the number of covariates in the linear part diverges we then investigate a nonconvex penalized estimator for simultaneous variable selection and estimation we derive its oracle property for a general class of nonconvex penalty functions in the presence of ultra high dimensional covariates under relaxed conditions to tackle the challenges of nonsmooth loss function nonconvex penalty function and the presence of nonlinear components we combine a recently developed convex differencing method with modern empirical process techniques monte carlo simulations and an application to a microarray study demonstrate the effectiveness of the proposed method we also discuss how the method for a single quantile of interest can be extended to simultaneous variable selection and estimation at multiple quantiles

partially linear models with missing response variables and error prone covariates we consider partially linear models of the form y x t beta nu z epsilon when the response variable y is sometimes missing with missingness probability pi depending on x z and the covariate x is measured with error where nu z is an unspecified smooth function the missingness structure is therefore missing not at random rather than the usual missing at random we propose a class of semiparametric estimators for the parameter of interest beta as well as for the population mean e y the resulting estimators are shown to be consistent and asymptotically normal under general assumptions to construct a confidence region for beta we also propose an empirical likelihood based statistic which is shown to have a chi squared distribution asymptotically the proposed methods are applied to an aids clinical trial dataset a simulation study is also reported

characterization of closed ideals with bounded approximate identities in commutative banach algebras complemented subspaces of the group von neumann algebras and applications

decomposition of b g for any locally compact group g let a g and b g be the fourier and the fourier stieltjes algebras of g respectively b g is decomposed as a direct sum of a g and bs g where bs g is a subspace of b g consisting of all elements b e b g that satisfy the property for any e 0 and any compact subset k c g there is an f c l1 g with if llc g libil e a g is characterizecl by the following an element b e b g is in a g if and only if for any e 0 there is a compact subset k c g such that i f b i e for all f e l1 g with llfllc g 1 and supp f c k note that we do not assume the amenability of g consequently we have ili all 1 lall for all a e a g if g is noncompact we will apply this characterization of bs g to investigate the general properties of bs g and we will see that bs g is not a subalgebra of b g even for abelian locally compact groups if g is an amenable locally compact group then bs g is the subspace of b g consisting of all elements b e b g with the property that for any compact subset k c g ll bi sup llabl a e a g supp a c kc and lhall 1

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

a semiparametric threshold model for censored longitudinal data analysis motivated by an investigation of the relationship between blood pressure change and progression of microalbuminuria ma among individuals with type i diabetes we propose a new semiparametric threshold model for censored longitudinal data analysis we also study a new semiparametric bayes information criterion type criterion for identifying the parametric component of the proposed model cluster effects in the model are implemented as unknown fixed effects asymptotic properties are established for the proposed estimators a quadratic approximation used to implement the estimation procedure makes the method very easy to implement by avoiding the computation of multiple integrals and the need for iterative algorithms simulation studies show that the proposed methods work well in practice an illustration using the wisconsin diabetes registry dataset suggests some interesting findings

a relation between levenshtein type distances and insertion and deletion correcting capabilities of codes a code is a collection of words or strings not necessarily all of the same length over come fixed alphabet a relation is established between the insertion and deletion correcting capability of a code and its minimum distance for suitable levenshtein type distance measures

bias analysis and simex approach in generalized linear mixed measurement error models abstract we consider generalized linear mixed models glmms for clustered data when one of the predictors is measured with error when the measurement error is additive and normally distributed and the error prone predictor is itself normally distributed we show that the observed data also follow a glmm but with a different fixed effects structure from the original model a different and more complex random effects structure and restrictions on the parameters this characterization enables us to compute the biases that result in common glmms when one ignores measurement error for instance in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases both for regression coefficients and for variance components parameter estimation is described using the simex method a relatively new functional method that makes no assumptions about the structure of the unobservable predictors simulations and an example illustrate the results

pushdown machines for the macro tree transducer the macro tree transducer can be considered as a system of recursive function procedures with parameters where the recursion is on a tree e g the syntax tree of a program we investigate characterizations of the class of tree tree to string translations which is induced by macro tree transducers macro tree to string transducers respectively for this purpose we define several pushdown machines of which the control is recursive without parameters or even iterative and which work on a generalized pushdown as storage because of the relevance for semantics of programming languages we stress besides the nondeterministic case the study of machines for the total deterministic macro tree to string transducer which translates every input tree into exactly one output tree string respectively finally we characterize the n fold composition of total deterministic macro tree transducers by recursive pushdown machines with an iterated pushdown as storage which is a pushdown of pushdowns of of pushdowns

a general bahadur representation of m estimators and its application to linear regression with nonstochastic designs we obtain strong bahadur representations for a general class of m estimators that satisfies sigma i psi x i theta o delta n where the x i s are independent but not necessarily identically distributed random variables the results apply readily to m estimators of regression with nonstochastic designs more specifically we consider the minimum l p distance estimators bounded influence gm estimators and regression quantiles under appropriate design conditions the error ratesobtained for the first order approximations are sharp in these cases we also provide weaker and more easily verifiable conditions that suffice for an error rate that is suboptimal but strong enough for deriving the asymptotic distribution of m estimators in a wide variety of problems

an algebra of discrete channels that involve combinations of three basic error types recently the author introduced a nonprobabilistic mathematical model of discrete channels the bee channels that involve the error types substitution insertion and deletion this paper defines an important class of bee channels the sid channels which include channels that permit a bounded number of scattered errors and possibly at the same time a bounded burst of errors in any segment of predefined length of a message a formal syntax is defined for generating channel expressions and appropriate semantics is provided for interpreting a given channel expression as a communication channel sid channel that permits combinations of substitutions insertions and deletions of symbols our framework permits one to generalize notions such as error correction and unique decodability and express statements of the form the code k can correct all errors of type and it is decidable whether the code k is uniquely decodable for the channel described by where is any sid channel expression

transducers and the decidability of independence in free monoids abstract a transducer based general method is derived by which proofs of the decidability of independence of regular languages with respect to a given relation can be obtained this permits a uniform proof of the decidability of certain code properties which so far has only been obtained using separate quite different and ad hoc proofs

fixed point property for banach algebras associated to locally compact groups abstract in this paper we investigate when various banach algebras associated to a locally compact group g have the weak or weak fixed point property for left reversible semigroups we proved for example that if g is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms then the fourier stieltjes algebra of g has the weak fixed point property for left reversible semigroups if and only if g is compact this generalizes a classical result of t c lim for the case when g is the circle group t

independent sets codes and their properties the concept that strict binary relation on free monoids is introduced some characterizations for strict binary relations is given the ordering properties of the set of all strict binary relations as well as some subsets of it are exhibited moreover it is proved that the independent languages of co compatible quasi strict relations are codes

weak fixed point property of reduced fourier stieltjes algebra and generalization of baggett s theorem abstract in this paper we show that if the reduced fourier stieltjes algebra b g of a second countable locally compact group g has either weak fixed point property or asymptotic center property then g is compact as a result we give affirmative answers to open problems raised by fendler and et al in 2013 we then conclude that a second countable group with a discrete reduced dual must be compact this generalizes a theorem of baggett we also construct a compact scattered hausdorff space for which the dual of the scattered c algebra c lacks weak fixed point property the c algebra c provides a negative answer to a question of randrianantoanina in 2010 in addition we prove a variant of bruck s generalized fixed point theorem for the preduals of von neumann algebras furthermore we give some examples emphasizing that the conditions in bruck s generalized conjecture bgc can not be weakened any more

lebesgue type decomposition of subspaces of fourier stieltjes algebras let g be a locally compact group and let a g and b g be the fourier algebra and the fourier stieltjes algebra of g respectively for any unitary representation of g let b g denote the w closed linear subspace of b g generated by all coefficient functions of and b 0 g the closure of b g a c g where a c g consists of all functions in a g with compact support in this paper we present descriptions of b 0 g and its orthogonal complement b s g in b g generalizing a recent result of t miao we show that for some classes of locally compact groups g there is a dichotomy in the sense that for arbitrary either b 0 g 0 or b 0 g a g we also characterize functions in b 0 g a c g b 0 g and study the question of whether b 0 g a g implies that weakly contains the regular representation

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

lee metric bch codes and their application to constrained and partial response channels shows that each code in a certain class of bch codes over gf p specified by a code length n spl les p sup m 1 and a runlength r spl les p 1 2 of consecutive roots in gf p sup m has minimum lee distance spl ges 2r for the very high rate range these codes approach the sphere packing bound on the minimum lee distance furthermore for a given r the length range of these codes is twice as large as that attainable by berlekamp s 1984 extended negacyclic codes the authors present an efficient decoding procedure based on euclid s algorithm for correcting up to r 1 errors and detecting r errors that is up to the number of lee errors guaranteed by the designed minimum lee distance 2r bounds on the minimum lee distance for r spl ges p 1 2 are provided for the reed solomon case i e when the bch code roots are in gf p the authors present two applications first lee metric bch codes can be used for protecting against bitshift errors and synchronization errors caused by insertion and or deletion of zeros in d k constrained channels second the code construction with its decoding algorithm can be formulated over the integer ring providing an algebraic approach to correcting errors in partial response channels where matched spectral null codes are used

error detecting properties of languages the language property of error detection ensures that the communications medium cannot transform a word of the language to another word of the language in this paper we provide some insights on the notion of error detection from a language theoretic point of view we define certain error detecting properties of languages and codes including the notion of error detection with finite delay which is a natural extension of unique decodability with finite delay we obtain results about the error detecting capabilities of regular and other languages and of known classes of codes moreover we consider the problem of estimating the optimal redundancy of infinite languages with the property of detecting errors of the deletion type

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

codes orderings and partial words codes play an important role in the study of the combinatorics of words in this paper we introduce pcodes that play a role in the study of combinatorics of partial words partial words are strings over a finite alphabet that may contain a number of do not know symbols pcodes are defined in terms of the compatibility relation that considers two strings over the same alphabet that are equal except for a number of insertions and or deletions of symbols we describe various ways of defining and analyzing pcodes in particular many pcodes can be obtained as antichains with respect to certain partial orderings using a technique related to dominoes we show that the pcode property is decidable

analysis of longitudinal data with semiparametric estimation of covariance function improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data both involve estimation of the covariance function yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed a kernel estimator for estimating the nonparametric variance function is developed two methods for estimating parameters in the correlation structure a quasi likelihood approach and a minimum generalized variance method are proposed a semiparametric varying coefficient partially linear model for longitudinal data is introduced and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed sampling properties of the proposed estimation procedures are studied and asy

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

groups whose fourier algebra and rajchman algebra coincide abstract we study locally compact groups for which the fourier algebra coincides with the rajchman algebra in particular we show that there exist uncountably many non compact groups with this property generalizing a result of hewitt and zuckerman we show that no non compact nilpotent group has this property whereas non compact solvable groups with this property are known to exist we provide several structural results on groups whose fourier and rajchman algebras coincide as well as new criteria for establishing this property finally we study the relation between groups with completely reducible regular representation and groups whose fourier and rajchman algebras coincide for unimodular groups with completely reducible regular representation we show that the fourier algebra may in general be strictly smaller than the rajchman algebra

variable selection using mm algorithms variable selection is fundamental to high dimensional statistical modeling many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and or nonconcave this article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions these algorithms operate by perturbing the penalty function slightly to render it differentiable then optimizing this differentiable function using a minorize maximize mm algorithm mm algorithms are useful extensions of the well known class of em algorithms a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for em algorithms in particular we prove that when our mm algorithms converge they must converge to a desirable point we also discuss conditions under which this convergence may be guaranteed we exploit the newton raphson like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators our method performs well in numerical tests

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

locally efficient estimators for semiparametric models with measurement error we derive constructive locally efficient estimators in semiparametric measurement error models the setting is one in which the likelihood function depends on variables measured with and without error where the variables measured without error can be modeled nonparametrically the algorithm is based on backfitting we show that if one adopts a parametric model for the latent variable measured with error and if this model is correct then the estimator is semiparametric efficient if the latent variable model is misspecified then our methods lead to a consistent and asymptotically normal estimator our method further produces an estimator of the nonparametric function that achieves the standard bias and variance property we extend the methodology to allow estimation of parameters in the measurement error model by additional data in the form of replicates or instrumental variables the methods are illustrated through a simulation study and a data example where the putative latent variable distribution i

separating sets by fourier stieltjes transforms abstract it is shown that if a and b are uniformly separated closed subsets of a locally compact abelian group and a and b are in the coset ring of with the discrete topology then there is a compactly supported measure on the dual of with fourier transform equal to one on a and zero on b

the io and oi hierarchies abstract an analysis of recursive procedures in algol 68 with finite modes shows that a denotational semantics of this language can be described on the level of program schemes using a typed calculus with fixed point operators in the first part of this paper we derive classical schematological theorems for the resulting class of level n schemes in part two we investigate the language families obtained by call by value and call by name interpretation of level n schemes over the algebra of formal languages it is proved that differentiating according to the functional level of recursion leads to two infinite hierarchies of recursive languages the io and oi hierarchies which can be characterized as canonical extensions of the regular context free and io and oi macro languages respectively sufficient conditions are derived to establish strictness of io like hierarchies finally we derive that recursion on higher types induces an infinite hierarchy of control structures by proving that level n schemes are strictly less powerful than level n 1 schemes

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

bayesian variable selection for high dimensional generalized linear models convergence rates of the fitted densities bayesian variable selection has gained much empirical success recently in a variety of applications when the number k of explanatory variables x 1 ldots x k is possibly much larger than the sample size n for generalized linear models if most of the x j s have very small effects on the response y we show that it is possible to use bayesian variable selection to reduce overfitting caused by the curse of dimensionality k gg n in this approach a suitable prior can be used to choose a few out of the many x j s to model y so that the posterior will propose probability densities p that are often close to the true density p in some sense the closeness can be described by a hellinger distance between p and p that scales at a power very close to n 1 2 which is the finite dimensional rate corresponding to a low dimensional situation these findings extend some recent work of jiang technical report 05 02 2005 dept statistics northwestern univ on consistency of bayesian variable selection for binary classification

minimax estimation of a functional on a structured high dimensional model we introduce a new method of estimation of parameters in semi parametric and nonparametric models the method is based on estimating equations that are u statistics in the observations the u statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest and represent higher derivatives of this parameter for parameters for which the representation cannot be perfect the method leads to a bias variance trade off and results in estimators that converge at a slower than n rate in a number of examples the resulting rate can be shown to be optimal we are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity where the parameter of interest cannot be estimated at n rate but we also consider efficient n estimation using novel nonlinear estimators the general approach is applied in detail to the example of estimating a mean response when the response is not always observed

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

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

independent sums of hn1 t and hn1 δ abstract we construct a new idempotent fourier multiplier on the hardy space on the bidisc which could not be obtained by applying known one dimensional results the main tool is a new l 1 equivalent of the stein martingale inequality which holds for a special filtration of periodic subsets of t with some restrictions on the functions involved we also identify the isomorphic type of the range of the associated operator as the independent sum of dyadic h n 1 which is known to be a complemented and invariant subspace of dyadic h 1

projectivity of modules over fourier algebras in this paper we will study the homological properties of various natural modules associated to the fourier algebra of a locally compact group in particular we will focus on the question of identifying when such modules will be projective in the category of operator spaces we will show that pro jectivity often implies that the underlying group is discrete and give evidence to show that amenability also plays an important role over the past thirty years there has been a rich body of work dedicated to understanding the cohomological properties of the various banach algebras arising in the study of locally compact groups the seminal paper in this respect is certainly barry johnson s memoir 22 in which he introduces the concept of amenability for a banach algebra and shows that for a locally compact group g the group algebra l 1 g is amenable if and only if g is amenable in the classical sense while applications of cohomology to harmonic anlysis may be more celebrated there have also been a number of significant studies related to the homological properties of the algebras arising from groups recently h g dales and m e polyakov 12 gave a detailed study of the homological properties of modules over the group algebra of a locally compact group in their work they focused primarily on the question of whether or not certain natural left l 1 g modules are respectively projective injective or flat they were able to show for example that when viewed as the dual left module of l 1 g l g is projective precisely when the group g is finite in stark contrast they prove that l g is always injective they also showed that the measure algebra m g is projective precisely when g is discrete while in this case injectivity is equivalent to the group g being amenable when g is abelian the classical fourier transform identifies l 1 g with a com

malmem model averaging in linear measurement error models we develop model averaging estimation in the linear regression model where some covariates are subject to measurement error the absence of the true covariates in this framework makes the calculation of the standard residual based loss function impossible we take advantage of the explicit form of the parameter estimators and construct a weight choice criterion it is asymptotically equivalent to the unknown model average estimator minimizing the loss function when the true model is not included in the set of candidate models the method achieves optimality in terms of minimizing the relative loss whereas when the true model is included the method estimates the model parameter with root n rate simulation results in comparison with existing bayesian information criterion and akaike information criterion model selection and model averaging methods strongly favour our model averaging method the method is applied to a study on health

duality cohomology and geometry of locally compact quantum groups abstract in this paper we study various convolution type algebras associated with a locally compact quantum group from cohomological and geometrical points of view the quantum group duality endows the space of trace class operators over a locally compact quantum group with two products which are operator versions of convolution and pointwise multiplication respectively we investigate the relation between these two products and derive a formula linking them furthermore we define some canonical module structures on these convolution algebras and prove that certain topological properties of a quantum group can be completely characterized in terms of cohomological properties of these modules we also prove a quantum group version of a theorem of hulanicki characterizing group amenability finally we study the radon nikodym property of the l 1 algebra of locally compact quantum groups in particular we obtain a criterion that distinguishes discreteness from the radon nikodym property in this setting

fixed point properties of semigroups of nonexpansive mappings abstract we prove that if h is a hilbert space then the schatten trace class operators on h has the weak fixed point property for left reversible semigroups this answered positively a problem raised by a t m lau we also prove that if m is a finite von neumann algebra then any nonempty bounded convex subset of the non commutative l 1 space associated to m that is compact for the measure topology has the fixed point property for left reversible semigroups

projections onto translation invariant subspaces of recently i klemes has characterized the complemented translation invariant subspaces of hl t in this paper we investigate the case of r the main results are that the hull of a complemented translation invariant sub space is e separated for some e 0 and that an e separated subset of r which is in the ring generated by cosets of closed subgroups of r intersected with r and lacunary sequences is the hull of a complemented ideal

construction of fixed length insertion deletion correcting runlength limited codes an algorithm is presented for the construction of fixed length insertion deletion correcting runlength limited rll codes in this construction binary d k constrained codewords are generated by codewords of a q ary lee metric based code it is shown that this new construction always yields better codes than known constructions the use of a q ary lee 1987 metric code q odd is based on the assumption that an error insertion deletion or peak shift has maximal size q 1 2 it is shown that a decoding algorithm for the lee metric code can be extended so that it can also be applied to insertion deletion correcting rll codes furthermore such an extended algorithm can also correct some error patterns containing errors of size more than q 1 2 as a consequence if s denotes the maximal size of an error then in some cases the alphabet size of the generating code can be s 1 instead of 2 spl middot s 1

consistent covariate selection and post model selection inference in semiparametric regression this paper presents a model selection technique of estimation in semiparametric regression models of the type y i x i f t i w i i 1 n the parametric and nonparametric components are estimated simultaneously by this procedure estimation is based on a collection of finite dimensional models using a penalized least squares criterion for selection we show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models we can consistently estimate the subset of nonzero coefficients of the linear part moreover the selected estimator of the linear component is asymptotically normal

some geometric properties on the fourier and fourier stieltjes algebras of locally compact groups arens regularity and related problems let g be a locally compact topological group and a g b g be respectively the fourier and fourier stieltjes algebras of g it is one of the purposes of this paper to investigate the rnp radon nikodym property and some other geometric properties such as weak rnp the dunford pettis property and the schur property on the algebras a g and b g and to relate these properties to the properties of the multiplication operator on the group c algebra c g we also investigate the problem of arens regularity of the projective tensor products c g a when b g c g has the rnp and a is any c algebra some related problems on the measure algebra the group algebra and the algebras a p g pf p g pm p g 1 p are also discussed

fixed point property and the fourier algebra of a locally compact group we establish some characterizations of the weak fixed point property weak fpp for noncommutative and commutative l 1 spaces and use this for the fourier algebra a g of a locally compact group g in particular we show that if g is an in group then a g has the weak fpp if and only if g is compact we also show that if g is any locally compact group then a g has the fixed point property fpp if and only if g is finite furthermore if a nonzero closed ideal of a g has the fpp then g must be discrete

linear model selection when covariates contain errors prediction precision is arguably the most relevant criterion of a model in practice and is often a sought after property a common difficulty with covariates measured with errors is the impossibility of performing prediction evaluation on the data even if a model is completely given without any unknown parameters we bypass this inherent difficulty by using special properties on moment relations in linear regression models with measurement errors the end product is a model selection procedure that achieves the same optimality properties that are achieved in classical linear regression models without covariate measurement error asymptotically the procedure selects the model with the minimum prediction error in general and selects the smallest correct model if the regression relation is indeed linear our model selection procedure is useful in prediction when future covariates without measurement error become available e g due to improved technology or better management and design of data collection procedures

tuning parameter selectors for the smoothly clipped absolute deviation method summary the penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method it not only automatically and consistently selects the important variables but also produces estimators which are as efficient as the oracle estimator however these attractive features depend on appropriate choice of the tuning parameter we show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily with a nonignorable overfitting effect in the resulting model in addition we propose a bic tuning parameter selector which is shown to be able to identify the true model consistently simulation studies are presented to support theoretical findings and an empirical example is given to illustrate its use in the female labor supply data

an automata theoretical characterization of the oi hierarchy this paper gives an automata theoretical characterization of the oi hierarchy damm 1982 engelfriet and schmidt 1977 wand 1975 this hierarchy is generated by so called level n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type i e they are allowed to carry up to n levels of parameters the automata model used for this characterization is the n iterated pushdown automaton its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n the equivalence proof is given constructively its method is illustrated using examples by viewing level n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

estimation in a semiparametric partially linear errors in variables model we consider the partially linear model relating a response y to predictors x t with mean function x t g t when the x s are measured with additive error the semiparametric likelihood estimate of severini and staniswalis leads to biased estimates of both the parameter and the function g when measurement error is ignored we derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation the resulting estimator of is shown to be consistent and its asymptotic distribution theory is derived consistent standard error estimates using sandwich type ideas are also developed

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

dependences related to strict binary relations in this paper we study dependences on a free monoid x and their relations to strict binary relations on x as a consequence we characterize strict binary relations by the notion of dependence moreover some results concerning the relationship between dependences and codes are also obtained a visualization of this work is provided by the theory of graph

variable selection in semiparametric regression modeling in this paper we are concerned with how to select significant variables in semiparametric modeling variable selection for semiparametric regression models consists of two components model selection for nonparametric components and select significant variables for parametric portion thus it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel this leads to very heavy computational burden in this paper we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood the newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously this allows us to establish the sampling properties of the resulting estimate we first establish the rate of convergence of the resulting estimate with proper choices of penalty functions and regularization parameters we then establish the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component we investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi squared distribution which is independent of the nuisance parameters extensive monte carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures

structural analysis of error correcting codes for discrete channels that involve combinations of three basic error types a nonprobabilistic mathematical model is introduced of discrete channels that involve the error types substitution insertion and deletion the model is based on the novelty that errors can be expressed as strings over an alphabet of basic error symbols some general conditions on errors are defined which bound the error effects on messages obtaining thus the class of bounded error effects channels bee channels these channels can be used to model for instance scattered errors and bursts of errors of any combination of the three error types a general notion of error correcting code is defined and a characterization of the error correcting codes for a given bee channel is obtained then an algorithm is presented that tests for a given finite code not necessarily of fixed length and a given description of a bee channel whether the code is error correcting for the channel defined by the given description this result can be considered as an extension of the well known theorem of sardinas and patterson 1953 for testing the unique decodability of a given finite code in this sense it can be said that unique decodability is decidable also in the presence of errors