a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

stable cohomology of spaces of non singular hypersurfaces abstract we prove that the rational cohomology of the space x d n of non singular complex homogeneous polynomials of degree d in n variables stabilizes to the cohomology of gl n c for d sufficiently large

design of signature sequences for overloaded cdma and bounds on the sum capacity with arbitrary symbol alphabets in this paper we explore some of the fundamentals of synchronous code division multiple access cdma as applied to wireless and optical communication systems under very general settings of any size for the user symbols and the signature matrix entries the channel is modeled by real complex additive noise of arbitrary distribution two problems are addressed the first problem concerns whether uniquely detectable overloaded matrices exist in the absence of additive noise under these general settings and if so whether there are any practical optimum detection algorithms the second one is about the bounds for the sum channel capacity when user data and signature matrices employ any real or complex alphabets finite or infinite in response to the first problem we have developed practical maximum likelihood detection algorithms for overloaded cdma systems for a large class of alphabets in response to the second problem a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users spreading gain and signal to noise ratio can be derived to show the power and utility of the main theorem a number of sum capacity bounds for special cases are evaluated an important conclusion of this paper is that the lower and upper bounds of the sum capacity for small medium size cdma systems depend on both the input and the signature symbols this is contrary to the asymptotic results for large scale systems reported in the literature also confirmed in this paper where the signature symbols and statistics disappear for signature matrices and input vectors with i i d entries furthermore upper and asymptotic bounds are derived and compared to other derivations

on estimation and prediction for spatial generalized linear mixed models we use spatial generalized linear mixed models glmm to model non gaussian spatial variables that are observed at sampling locations in a continuous area in many applications prediction of random effects in a spatial glmm is of great practical interest we show that the minimum mean squared error mmse prediction can be done in a linear fashion in spatial glmms analogous to linear kriging we develop a monte carlo version of the em gradient algorithm for maximum likelihood estimation of model parameters a by product of this approach is that it also produces the mmse estimates for the realized random effects at the sampled sites this method is illustrated through a simulation study and is also applied to a real data set on plant root diseases to obtain a map of disease severity that can facilitate the practice of precision agriculture

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

homological stability for topological chiral homology of completions abstract by proving that several new complexes of embedded disks are highly connected we obtain several new homological stability results our main result is homological stability for topological chiral homology on an open manifold with coefficients in certain partial framed e n algebras using this we prove a special case of a conjecture of vakil and wood on homological stability for complements of closures of particular strata in the symmetric powers of an open manifold and we prove that the bounded symmetric powers of closed manifolds satisfy homological stability rationally

pairwise likelihood methods for inference in image models summary we consider parameter estimation for certain random set models for image data for the spatial models considered here a full likelihood based approach to this problem is often difficult since the likelihood generally cannot be computed for images of typical size this has motivated the consideration of various less computationally demanding parameter estimation techniques we discuss one method based on likelihoods for small subsets of the data consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach results of a simulation study are reported for some variants of the boolean model and excursion sets of random fields the methods are illustrated for some data on the spatial incidence of heather

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

conics in the grothendieck ring abstract the subring of the grothendieck ring of k varieties generated by smooth conics is described giving many zero divisors the proof uses only elementary projective geometry

spectral methods for nonstationary spatial processes summary we propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process we also study the asymptotic properties of the proposed estimators via shrinking asymptotics assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound with this type of asymptotic model we can uniquely determine the spectral density avoiding the aliasing problem we also present a new class of nonstationary processes based on a convolution of local stationary processes this model has the advantage that the model is simultaneously defined everywhere unlike moving window approaches but it retains the attractive property that locally in small regions it behaves like a stationary spatial process applications include the spatial analysis and modelling of air pollution data provided by the us environmental protection agency

estimation for a partial linear single index model in this paper we study the estimation for a partial linear single index model a two stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index as well as the parameters in the linear component of the model asymptotic normality is established for both parametric components for the index a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance the estimator of the nonparametric link function achieves optimal convergence rates and the structural error variance is obtained in addition the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters a simulation study is performed and an application to a real dataset is illustrated the extension to multiple indices is briefly sketched

the grothendieck ring of varieties and piecewise isomorphisms let k0 var k be the grothendieck ring of algebraic varieties over a field k l et x y be two algebraic varieties over k which are piecewise isomorphic i e x and y admit finite partitions x1 xn y1 yn into locally closed subvarieties such that xi is iso morphic to yi for all i n then x y in k0 var k larsen and lunts ask whether the converse is true for characteristic zero and algebraically closedfield k we answer positively this question when dim x 1o rx is a smooth connected projective surface or if x contains only finitely many rational curves

coincidences between homological densities predicted by arithmetic abstract motivated by analogies with basic density theorems in analytic number theory we introduce a notion and variations of the homological density of one space in another we use weil s number field function field analogy to predict coincidences for limiting homological densities of various sequences z n d 1 d m x of spaces of 0 cycles on manifolds x the main theorem in this paper is that these topological predictions which seem strange from a purely topological viewpoint are indeed true one obstacle to proving such a theorem is the combinatorial complexity of all possible collisions of points this problem does not arise in the simplest and classical case m n 1 2 of configuration spaces to overcome this obstacle we apply the bjorner wachs theory of lexicographic shellability from algebraic combinatorics

code construction for the t user noiseless adder channel a general method for constructing codes for the t user noiseless adder channel is proposed which achieves the largest sum rate known the authors consider a multiple access communication system in this system t statistically independent sources which use binary block codes c sub 1 c sub t of equal length n simultaneously transmit information via one common channel maintaining synchronization with respect to words and bits the output of the adder channel is the t l ary vector which is the component wise arithmetic sum of the transmitted binary vectors the task of the decoder is to uniquely determine the messages of all users

identifiability of single index models and additive index models summary we provide a proof for the identifiability for both single index models and partially linear single index models assuming only the continuity of the regression function a condition much weaker than the differentiability conditions assumed in the existing literature our discussion is then extended to the identifiability of the additive index models

elliptic genera of singular varieties the notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced and the relation between them is studied the elliptic genus of singular varieties is given in terms of a resolution of singularities and extends the elliptic genus of calabi yau hypersurfaces in fano gorenstein toric varieties introduced earlier the orbifold elliptic genus is given in terms of the fixed point sets of the action we show that the generating function for the orbifold elliptic genus ellorb x 6n p for symmetric groups 6n acting on n fold products coincides with the one proposed by r dijkgraaf g moore e verlinde and h verlinde the two notions of elliptic genera are conjectured to coincide

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

on optimum asymptotic multiuser efficiency of randomly spread cdma we extend the result by tse and verdu on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access cdma with binary phase shift keying input random gaussian and random binary antipodal spreading are considered we obtain the optimum asymptotic multiuser efficiency of a k user system with spreading gain n when k and n rightarrow infty and the loading factor k n grows logarithmically with k under some conditions it is shown that the optimum detector in a gaussian randomly spread cdma system has a performance close to the single user system at high signal to noise ratio when k and n rightarrow infty and the loading factor k n is kept less than log 3 k 2 random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained furthermore we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency we obtain a condition such that for any binary input an n times k random matrix whose entries are chosen randomly from a finite set is a detecting matrix as k and n rightarrow infty

direct estimation of the index coefficient in a single index model single index modeling is widely applied in for example econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models by such modeling the statistical analysis usually focuses on estimating the index coefficients the average derivative estimator ade of the index vector is based on the fact that the average gradient of a single index function f x t is proportional to the index vector unfortunately a straightforward application of this idea meets the so called curse of dimensionality problem if the dimensionality d of the model is larger than 2 however prior information about the vector can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative the method proposed in this paper consists of such iterative improvements of the original ade the whole procedure requires at most 2 log n iterations and the resulting estimator is n consistent under relatively mild assumptions on the model independently of the dimensionality d

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

a valid matern class of cross covariance functions for multivariate random fields with any number of components we introduce a valid parametric family of cross covariance functions for multivariate spatial random fields where each component has a covariance function from a well celebrated matern class unlike previous attempts our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components we present the conditions on the parameter space that result in valid models with varying degrees of complexity we discuss practical implementations including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency we perform various monte carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging the application of the proposed multivariate matern model is illustrated on two meteorological datasets temperature pressure over the pacific northwest bivariate and wind temperature pressure in oklahoma trivariate in the latter case our flexi

aberrant crypt foci and semiparametric modeling of correlated binary data motivated by the spatial modeling of aberrant crypt foci acf in colon carcinogenesis we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent gaussian spatial process that accounts for short range dependencies the mean is modeled in a general way using regression splines the mean function can be viewed as a fixed effect and is estimated with a penalty for regularization with the latent process viewed as another random effect the model becomes a generalized linear mixed model in our motivating data set and other applications the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation reml so pairwise likelihood a special case of composite likelihood is used instead we develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications including but not limited to the problem that motivated this work the splines have penalty parameters that must converge to zero asymptotically we derive theory for this along with a data driven method for selecting the penalty parameter a method that is shown in simulations to improve greatly upon standard devices such as likelihood crossvalidation finally we apply the methods to the data from our experiment acf we discover an unexpected location for peak formation of acf

germs of arcs on singular algebraic varieties and motivic integration we study the scheme of formal arcs on a singular algebraic variety and its images under truncations we prove a rationality result for the poincare series of these images which is an analogue of the rationality of the poincare series associated to p adic points on a p adic variety the main tools which are used are semi algebraic geometry in spaces of power series and motivic integration a notion introduced by m kontsevich in particular we develop the theory of motivic integration for semi algebraic sets of formal arcs on singular algebraic varieties we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of oesterle

meta analysis of studies with bivariate binary outcomes a marginal beta binomial model approach when conducting a meta analysis of studies with bivariate binary outcomes challenges arise when the within study correlation and between study heterogeneity should be taken into account in this paper we propose a marginal beta binomial model for the meta analysis of studies with binary outcomes this model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model chu and cole 2006 and sarmanov beta binomial model chen et al 2012 the advantages of the proposed marginal model include modeling the probabilities in the original scale not requiring any transformation of probabilities or any link function having closed form expression of likelihood function and no constraints on the correlation parameter more importantly because the marginal beta binomial model is only based on the marginal distributions it does not suffer from potential misspecification of the joint distribution of bivariate study specific probabilities such misspecification is difficult to detect and can lead to biased inference using currents methods we compare the performance of the marginal beta binomial model with the bivariate generalized linear mixed model and the sarmanov beta binomial model by simulation studies interestingly the results show that the marginal beta binomial model performs better than the sarmanov beta binomial model whether or not the true model is sarmanov beta binomial and the marginal beta binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications two meta analyses of diagnostic accuracy studies and a meta analysis of case control studies are conducted for illustration

e_n cell attachments and a local to global principle for homological stability we define bounded generation for e n algebras in chain complexes and prove that this property is equivalent to homological stability for n ge 2 using this we prove a local to global principle for homological stability which says that if an e n algebra a has homological stability or equivalently the topological chiral homology int mathbb r n a has homology stability then so has the topological chiral homology int m a of any connected non compact manifold m using scanning we reformulate the local to global homological stability principle so that it applies to compact manifolds we also give several applications of our results

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

penalized spline estimation for partially linear single index models single index models are potentially important tools for multivariate nonparametric regression they generalize linear regression by replacing the linear combination 0tx with a nonparametric component 0 0tx where 0 is an unknown univariate link function by reducing the dimensionality from that of a general covariate vector x to a univariate index 0tx single index models avoid the so called curse of dimensionality we propose penalized spline p spline estimation of 0 in partially linear single index models where the mean function has the form 0 0tx 0tz the p spline approach offers a number of advantages over other fitting methods for single index models all parameters in the p spline single index model can be estimated simultaneously by penalized nonlinear least squares as a direct least squares fitting method our approach is rapid and computationally stable standard nonlinear least squares software can be used moreover joint inference for 0 0 and 0 is possible by

variable selection and function estimation in additive nonparametric regression using a data based prior abstract a hierarchical bayesian approach is proposed for variable selection and function estimation in additive nonparametric gaussian regression models and additive nonparametric binary regression models the prior for each component function is an integrated wiener process resulting in a posterior mean estimate that is a cubic smoothing spline each of the explanatory variables is allowed to be in or out of the model and the regression functions are estimated by model averaging to allow variable selection and model averaging data based priors are used for the smoothing parameter and the slope at 0 of each component function a two step markov chain monte carlo method is used to efficiently obtain the data based prior and to carry out variable selection and function estimation it is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously the methodology is illustrated for a binary regressio

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

smoothing parameter selection in nonparametric regression using an improved akaike information criterion summary many different methods have been proposed to construct nonparametric estimates of a smooth regression function including local polynomial convolution kernel and smoothing spline estimators each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set in this paper an improved version of a criterion based on the akaike information criterion aic termed aicc is derived and examined as a way to choose the smoothing parameter unlike plug in methods aicc can be used to choose smoothing parameters for any linear smoother including local quadratic and smoothing spline estimators the use of aicc avoids the large variability and tendency to undersmooth compared with the actual minimizer of average squared error seen when other classical approaches such as generalized cross validation or the aic are used to choose the smoothing parameter monte carlo simulations demonstrate that the aicc based smoothing parameter is competitive with a plug in method assuming that one exists when the plug in method works well but also performs well when the plug in approach fails or is unavailable

semiparametric regression using variational approximations semiparametric regression offers a flexible framework for modeling nonlinear relationships between a response and covariates a prime example are generalized additive models gams where splines s

further results on coding for t user multiple access channels corresp coding schemes for the noiseless t user binary adder multiple access channel are discussed a class of uniquely decodable codes of arbitrary length satisfying a specific recursive relationship and which are asymptotically good is explicitly constructed

algebraic independence in the grothendieck ring of varieties we give sufficient cohomological criteria for the classes of given varieties over a field k to be algebraically independent in the grothendieck ring of varieties over k and construct some examples

robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data summary in this article we study the robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function under some regularity conditions the asymptotic properties of the proposed robust estimators are shown some simulations are carried out to investigate the performance of the proposed robust estimators just as expected the proposed robust estimators perform better than those resulting from robust estimating equations involving conditional expectation like sinha 2004 journal of the american statistical association99 451 460 and qin and zhu 2007 journal of multivariate analysis98 1658 1683 in the end the proposed robust method is illustrated by the analysis of a real data set

bertini theorems over finite fields let x be a smooth quasiprojective subscheme of pn of dimension m i 0 over fq then there exist homogeneous polynomials f over fq for which the intersection of x and the hypersurface f 0 is smooth in fact the set of such f has a positive density equal to aex m 1 1 where aex s zx q s is the zeta function of x an analogue for regular quasiprojective schemes over z is proved assuming the abc conjecture and another conjecture

on the asymptotics of penalized splines summavry we study the asymptotic behaviour of penalized spline estimators in the univariate case we use b splines and a penalty is placed on mth order differences of the coefficients the number of knots is assumed to converge to infinity as the sample size increases we show that penalized splines behave similarly to nadaraya watson kernel estimators with equivalent kernels depending upon m the equivalent kernels we obtain for penalized splines are the same as those found by silverman for smoothing splines the asymptotic distribution of the penalized spline estimator is gaussian and we give simple expressions for the asymptotic mean and variance provided that it is fast enough the rate at which the number of knots converges to infinity does not affect the asymptotic distribution the optimal rate of convergence of the penalty parameter is given penalized splines are not design adaptive

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

how an erdos renyi type search approach gives an explicit code construction of rate 1 for random access with multiplicity feedback pippenger 1981 showed in a probabilistic way that the capacity of a collision channel with multiplicity feedback is one in this correspondence using an erdos renyi type search strategy we settle a long standing open problem by giving a constructive proof of this result moreover we prove that two different capacity definitions are equivalent thereby solving a problem posed by tsybakov 1985

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

a dynamic structure for high dimensional covariance matrices and its application in portfolio allocation abstractestimation of high dimensional covariance matrices is an interesting and important research topic in this article we propose a dynamic structure and develop an estimation procedure for high dimensional covariance matrices asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite by exploring a financial application an empirical study shows that portfolio allocation based on dynamic high dimensional covariance matrices can significantly outperform the market from 1995 to 2014 our proposed method also outperforms portfolio allocation based on the sample covariance matrix the covariance matrix based on factor models and the shrinkage estimator of covariance matrix supplementary materials for this article are available online

semiparametric gee analysis in partially linear single index models for longitudinal data in this article we study a partially linear single index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases a semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations gee is introduced to estimate the two parameter vectors as well as the unknown link function under some mild conditions we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios from which we find that the convergence rates and asymptotic variances of the proposed estimators for sparse longitudinal data would be substantially different from those for dense longitudinal data we also discuss the estimation of the covariance or weight matrices involved in the semiparametric gee method furthermore we provide some numerical studies including monte carlo simulation and an empirical application to illustrate our methodology and theory

cross covariance functions for multivariate random fields based on latent dimensions summary the problem of constructing valid parametric cross covariance functions is challenging we propose a simple methodology based on latent dimensions and existing covariance models for univariate random fields to develop flexible interpretable and computationally feasible classes of cross covariance functions in closed form we focus on spatio temporal cross covariance functions that can be nonseparable asymmetric and can have different covariance structures for instance different smoothness parameters in each component we discuss estimation of these models and perform a small simulation study to demonstrate our approach we illustrate our methodology on a trivariate spatio temporal pollution dataset from california and demonstrate that our cross covariance performs better than other competing models

a family of k 1 ary signature codes for noisy multiple access adder channel a coding scheme of k 1 ary error correcting signature codes for a noisy multiple access adder channel is proposed given a signature matrix a and a difference matrix d d d a priori a larger signature matrix is obtained by replacing each element in the hadamard matrix with a or d or d depending on the values of the elements and their locations in the hadamard matrix the set of rows in the proposed matrix gives an error correcting signature code introducing a difference matrix makes it possible to construct an error correcting signature code whose sum rate is increased with an increase in the order of the hadamard matrix either binary or non binary signature codes are constructed when the pairs of matrices a and d are given

variance function partially linear single index models we consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model we do not insist that the variance function depend only upon the mean function as happens in the classical generalized partially linear single index model we develop efficient and practical estimation methods for the variance function and for the mean function asymptotic theory for the parametric and nonparametric parts of the model is developed simulations illustrate the results an empirical example involving ozone levels is used to further illustrate the results and is shown to be a case where the variance function does not depend upon the mean function

bayesian prediction of spatial count data using generalized linear mixed models summary spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a bayesian approach and markov chain monte carlo informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling furthermore we demonstrate that so called langevin hastings updates are useful for efficient simulation of the posterior distributions and we discuss computational issues concerning prediction

motivic random variables and representation stability ii hypersurface sections abstract we prove geometric and cohomological stabilization results for the universal smooth degree d hypersurface section of a fixed smooth projective variety as d goes to infinity we show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed grothendieck ring of varieties and deduce from this the stabilization of the hodge euler characteristic of natural families of local systems constructed from the vanishing cohomology we prove explicit formulas for the stable values using a probabilistic interpretation along with the natural analogs in point counting over finite fields we explain how these results provide new geometric examples of a weak version of representation stability for symmetric symplectic and orthogonal groups this interpretation of representation stability was studied in the prequel 20 for configuration spaces

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

estimating the interest rate term structure of corporate debt with a semiparametric penalized spline model this article provides a new methodology for estimating the term structure of corporate debt using a semiparametric penalized spline model the method is applied to a case study of at t bonds typically very few data are available on individual corporate bond prices too little to find a nonparametric estimate of term structure from these bonds alone this problem is solved by borrowing strength from treasury bond data more specifically we combine a nonparametric model for the term structure of treasury bonds with a parametric component for the credit spread our methodology generalizes the work of fisher nychka and zervos in several ways first their model was developed for treasury bonds only and cannot be applied directly to corporate bonds second we more fully investigate the problem of choosing the smoothing parameter a problem that is complicated because the forward rate is the derivative log d t where the discount function d is the function fit to the data in our case study estimatio

generalized partially linear single index model for zero inflated count data count data often arise in biomedical studies while there could be a special feature with excessive zeros in the observed counts the zero inflated poisson model provides a natural approach to accounting for the excessive zero counts in the semiparametric framework we propose a generalized partially linear single index model for the mean of the poisson component the probability of zero or both we develop the estimation and inference procedure via a profile maximum likelihood method under some mild conditions we establish the asymptotic properties of the profile likelihood estimators the finite sample performance of the proposed method is demonstrated by simulation studies and the new model is illustrated with a medical care dataset

the topology of rational functions and divisors of surfaces segal studied the homotopy types of the spaces of holomorphic functions of the 2 sphere s 2 of closed surfaces of higher genus and of the spaces of divisors of these surfaces we continue segal s program by describing the entire stable homotopy types of these spaces in terms of the homotopy types of more familiar spaces

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

generalized t user codes for multiple access channels corresp large classes of t user codes for the binary adder channel are shown to be easily constructed by generalizing some previous results in two basic ways the first is an iterative procedure the second is by introducing an equivalence relation on such codes decoding algorithms are presented in both cases the number of codes in the equivalence class of some previously defined codes is determined exactly

parameter estimation of partial differential equation models partial differential equation pde models are commonly used to model complex dynamic systems in applied sciences such as biology and finance the forms of these pde models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system parameters in pde models often have interesting scientific interpretations but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors most pdes used in practice have no analytic solutions and can only be solved with numerical methods currently methods for estimating pde parameters require repeatedly solving pdes numerically under thousands of candidate parameter values and thus the computational load is high in this article we propose two methods to estimate parameters in pde models a parameter cascading method and a bayesian approach in both methods the underlying dynamic process modeled with the pde model is represented via basis function

a marginal approach to reduced rank penalized spline smoothing with application to multilevel functional data multilevel functional data are collected in many biomedical studies for example in a study of the effect of nimodipine on patients with subarachnoid hemorrhage sah patients underwent multiple 4 hr treatment cycles within each treatment cycle subjects vital signs were reported every 10 min these data have a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles most literature on nonparametric analysis of such multilevel functional data focuses on conditional approaches using functional mixed effects models however parameters obtained from the conditional models do not have direct interpretations as population average effects when population effects are of interest we may employ marginal regression models in this work we propose marginal approaches to fit multilevel functional data through penalized spline generalized estimating equation penalized spline gee the procedure is effective for modeling multilevel correlated generalized

a composite likelihood approach in fitting spatial point process models we propose a new likelihood based approach in fitting spatial point process models a composite likelihood is first formed by adding some pairwise composite likelihood functions that are defined in terms of the second order intensity function of the underlying process and then used for estimating the unknown parameters the estimation procedure is computationally simple and yields consistent and asymptotically normal estimators under some mild conditions we demonstrate through a simulation study and applications to two real data examples that the proposed approach may lead to improved estimations compared with the commonly used minimum contrast estimation approach

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

adapting for the missing link we consider the fitting of generalized linear models in wich the link function is assumed to be unknown and propose the following computational method first estimate regression coefficients using the canonical link then estimate the link via a kernel smoother treating the direction in the predictor space determined by the regression coefficients as known then reestimate the direction using the estimated link and alternate between these two steps we show that under fairly general conditions n 1 2 consistent estimates of the direction are obtained a small monte carlo study is presented

recursive constructions of detecting matrices for multiuser coding a unifying approach detecting matrices are a class of combinatorial objects originated from the coin weighing problem of soderberg and shapiro in the early 1960s in this paper various known recursive construction techniques for binary bipolar and ternary detecting matrices are reexamined in a unifying framework new general recursive constructions of detecting matrices which include previous recursive constructions as special cases are derived such matrices find applications in multiuser coding since they are equivalent to a certain class of uniquely decodable multiuser codes for the binary adder channel interestingly it is found that among the three kinds of detecting matrices ternary detecting matrices are of fundamental significance from the combinatorial theoretic as well as from the multiuser coding application point of view

fi modules and stability for representations of symmetric groups in this paper we introduce and develop the theory of fi modules we apply this theory to obtain new theorems about the cohomology of the configuration space of n distinct ordered points on an arbitrary connected oriented manifold the diagonal coinvariant algebra on r sets of n variables the cohomology and tautological ring of the moduli space of n pointed curves the space of polynomials on rank varieties of n n matrices the subalgebra of the cohomology of the genus n torelli group generated by h1 and more the symmetric group sn acts on each of these vector spaces in most cases almost nothing is known about the characters of these representations or even their dimensions we prove that in each fixed degree the character is given for n large enough by a polynomial in the cycle counting functions that is independent of n in particular the dimension is eventually a polynomial in n in this framework representation stability in the sense of church farb for a sequence of sn representations is converted to a finite generation property for a single fi module

spline based tests in survival analysis this paper examines a method for testing hypotheses on covariate effects in a proportional hazards model and also on how effects change over time in regression analysis of survival data the technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models the basic idea is to formulate a flexible parametric alternative using fixed knot splines together with a penalty function that penalizes noisy alternatives more than smooth ones to focus the power of the tests toward smooth alternatives the test statistics are the analogs of ordinary likelihood based statistics only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log likelihood large sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases numerical results suggest these approximations may be adequate with moderate sized samples

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

homological stability for configuration spaces of manifolds let cn m be the configuration space of n distinct ordered points in m we prove that if m is any connected orientable manifold closed or open the homology groups hi cn m are representation stable in the sense of church and farb arxiv 1008 1368 applying this to the trivial representation we obtain as a corollary that the unordered configuration space bn m satisfies classical homological stability for each i hi bn m hi bn 1 m for n i this improves on results of mcduff segal and others for open manifolds applied to closed manifolds this provides natural examples where rational homological stability holds even though integral homological stability fails

miscellanea on the optimal amount of smoothing in penalised spline regression summary the optimal amount of smoothing in penalised spline regression is investigated in particular a simple closed form approximation to the optimal smoothing parameter is derived comparisons with its exact counterpart show it to be a useful starting point for measuring the optimal amount of smoothing in penalised spline regression it also lends itself to the development of quick and simple rules for automatic smoothing parameter selection

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