empirical bayes estimates of cancer mortality rates using spatial models we give results of empirical bayes eb estimation of mortality rates designed to smooth observed smr when random fluctuation of the observed deaths is important we have specially studied the case where the prior distributions of the eb method have a spatial structure the need for spatial modelling of cancer mortality rates in france is first shown with testing autocorrelation and fitting autoregressive spatial models conditional car or simultaneous sar a positive autocorrelation of the rates is shown for most cancer sites studied as expected eb estimates of mortality rates for common tumours are similar to smrs for rare tumours the eb method identifies the extreme rates more clearly than smrs by smoothing the smrs with large variances car or sar models are adequate prior distributions for autocorrelated rates and produce quite similar rate estimates

a regression method for spatial disease rates an estimating function approach abstract epidemiologists commonly study the geographical variation of disease rates to generate and refine testable hypotheses regarding etiology poisson regression is often used to estimate the parameters that characterize the effects of risk factors on disease hierarchical models have been proposed to utilize spatial locations and neighbors as surrogates for unknown or unmeasured risk factors in the analysis of disease rates although hierarchical models are useful in modeling spatial disease rates in a scientifically meaningful way the analytic tools for them are generally computationally intensive we overcome this issue by applying a conditional spatial modeling technique using unbiased estimating functions the resulting estimator of regression coefficients is consistent and asymptotically normally distributed under mild conditions a simulation study compares the performance of the proposed scheme with the approximate inference methods for hierarchical models we apply the proposed scheme to sco

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

archimedean non vanishing cohomological test vectors and standard l functions of gl2n complex case abstract the purpose of this paper is to study the local zeta integrals of friedberg jacquet at complex place and to establish similar results to the recent work 4 joint with c chen and d jiang in this paper we will 1 give a necessary and sufficient condition on an irreducible essentially tempered cohomological representation of gl 2 n c with a non zero shalika model 2 construct a new twisted linear period s and give a different expression of the linear model for 3 give a necessary and sufficient condition on the character such that there exists a uniform cohomological test vector v v which we construct explicitly for s as a consequence we obtain the non vanishing of local friedberg jacquet integral at complex place all of the above are essential preparations for attacking a global period relation problem in the forthcoming paper 11

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

on the problem of permissible covariance and variogram models the covariance and variogram models ordinary or generalized are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems for example the efficacy of kriging a method for interpolating filtering or averaging spatial phenomena depends to a large extent on the covariance or variogram model chosen the aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem and is not included among the known covariance or variogram models is permissible as such a model this is done by investigating the properties of the candidate model in both the space and frequency domains in the present article this investigation covers stationary random functions as well as intrinsic random functions i e nonstationary functions for which increments of some order are stationary then based on the theoretical results obtained a procedure is outlined and successfully applied to a number of candidate models in order to give to this procedure a more practical context we employ stereological equations that essentially transfer the investigations to one dimensional space together with approximations in terms of polygonal functions and fourier bessel series expansions there are many benefits and applications of such a procedure polygonal models can be fit arbitrarily closely to the data also the approximation of a particular model in the frequency domain by a fourier bessel series expansion can be very effective this is shown by theory and by example

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

generalized harish chandra descent gelfand pairs and an archimedean analog of jacquet rallis s theorem in the first part of the paper we generalize a descent technique due to harish chandra to the case of a reductive group acting on a smooth affine variety both defined over an arbitrary local field f of characteristic zero our main tool is the luna slice theorem in the second part of the paper we apply this technique to symmetric pairs in particular we prove that the pairs gln k f gln f glk f and gln e gln f are gelfand pairs for any local field f and its quadratic extension e in the non archimedean case the first result was proven earlier by jacquet and rallis and the second by flicker we also prove that any conjugation invariant distribution on gln f is invariant with respect to transposition for non archimedean f the latter is a classical theorem of gelfand and kazhdan

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

archimedean non vanishing cohomological test vectors and standard l functions of mathrm gl _ 2n gl2n real case the standard l functions of mathrm gl 2n expressed in terms of the friedberg jacquet global zeta integrals have better structure for arithmetic applications due to the relation of the linear periods with the modular symbols the most technical obstacles towards such arithmetic applications are 1 non vanishing of modular symbols at infinity and 2 the existence or construction of uniform cohomological test vectors problem 1 is also called the non vanishing hypothesis at infinity which was proved by sun duke math j 168 1 85 126 2019 theorem 5 1 by establishing the existence of certain cohomological test vectors in this paper we explicitly construct an archimedean local integral that produces a new type of a twisted linear functional lambda s chi which when evaluated with our explicitly constructed cohomological vector is equal to the local twisted standard l function l s pi otimes chi for all complex values s with the relations between linear models and shalika models we establish 1 with an explicitly constructed cohomological vector using classical invariant theory and hence proves the non vanishing results of sun 24 theorem 5 1 via a completely different method

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

cohomologically induced distinguished representations and cohomological test vectors let g be a real reductive group and let be a character of a reductive subgroup h of g we construct invariant linear functionals on certain cohomologically induced representations of g and we show that these linear functionals do not vanish on the bottom layers applying this construction we prove two archimedean nonvanishing hypotheses which are vital to the arithmetic study of special values of certain l functions via modular symbols

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

a latent process regression model for spatially correlated count data summary this paper proposes a regression model for spatially correlated count data that generalizes the work spatially correlated count data arise in a variety of settings frequently it is of interest to make marginal inferences about spatial trends and effects of explanatory variables on spatially correlated counts an example application described in this paper involves an examination of the distribution of neuronal cells in a laboratory culture well our motivation for examining the distribution of cells was due to the implications of the distribution for the choice of an efficient sampling method to estimate total cell count total neuronal cell counts in a culture well are ordinarily estimated using data from multiple sampled subregions viewed under the microscope or with the aid of an image analysis system because counting all cells in a culture well is prohibitively time consuming as routine practice these sampling methods typically involve recording from multiple randomly selected fields the area of the field and number of cells visible in the field a cell per unit area density is estimated from the data and the total cell count estimate for the well is obtained by multiplication by the total well area these methods implicitly assume that cells are distributed completely at random throughout the well experience would suggest that there could be trends in neuron density and clustering tendencies for example neurons can tend to a higher density in the center of a well due to a slight vortex that occurs when the cultures are moved before the neurons have attached themselves to the substratum neurons also may distribute in higher density around the edges of a culture well due to a meniscus and slightly greater depth of medium at the edge of a well spatial clustering may result if neural cell bodies migrate along the cell body s neuritic processes or if the tissue culture tray is

a generalized estimating equations approach for spatially correlated binary data applications to the analysis of neuroimaging data this paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects this approach is useful when the scientific focus is on modeling the marginal mean structure proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed the use of semivariogram models for parameterizing the correlation structure is discussed and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation the methodology is illustrated with neuroimaging data collected as part of the national institute of neurological disorders and stroke ninds stroke data bank a simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies