oriented distance function and its evolution equation for initial sets with thin boundary the central result of this paper is a new nonlinear equation which describes the evolution of the oriented distance function b omega of a set omega with thin boundary under the influence of a velocity field we relate it to equations and constructions used in the context of level set methods we further introduce a new moving narrow band method which not only can be readily implemented to solve our evolution equation but could also be used for equations of motion by curvatures in the process we review and sharpen the characterization of smooth sets and manifolds and sets of positive reach e g local semiconvexity in an extended sense of the oriented distance function of the closure of the set for w2 p sobolev domains a new characterization and a compactness theorem are given in terms of the laplacian of the oriented distance function rather than its whole hessian matrix

uncertainty in model based seasonal adjustment procedures and construction of minimax filters abstract unobserved component autoregressive integrated moving average models are often the cornerstone of model based seasonal adjustment procedures unfortunately these models are inherently underidentified and ad hoc assumptions must be made prior to the analysis this article investigates the effect of seasonal adjustment filters on a class of observationally equivalent models bounds on the mean squared error mse associated with arbitrary linear filters are derived the article also derives robust seasonal adjustment filters the filters are robust in the sense that they minimize the maximum mse from the set of observationally equivalent models the article shows that the minimax and minimum extraction filters are equivalent for a certain class of models empirical results for a number of economic time series are presented

research problems from the aveiro workshop on graph spectra abstract this is a collection of open problems presented at the aveiro workshop on graph spectra held at the university of aveiro portugal from april 10 12 2006

estimation prediction and interpolation for nonstationary series with the kalman filter abstract we show how our definition of the likelihood of an autoregressive integrated moving average arima model with missing observations alternative to that of kohn and ansley and based on the usual assumptions made in estimation of and forecasting with arima models permits a direct and standard state space representation of the nonstationary original data so that the ordinary kalman filter and fixed point smoother can be efficiently used for estimation forecasting and interpolation in this way the problem of estimating missing values in nonstationary series is considerably simplified the results are extended to regression models with arima errors and a computer program is available from the authors

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

dynamic stochastic models for time dependent ordered paired comparison systems abstract when paired comparisons are made sequentially over time as for example in chess competitions it is natural to assume that the underlying abilities do change with time previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities the parameters that determine the functions have to be specified a priori and are based on rational reasoning we suggest an alternative scheme for keeping track with the underlying abilities our approach is based on two components a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time the response model is a very general paired comparison model allowing for ties and ordered responses the transition model incorporates random walk models and local linear trend models taken together these two components form a non gaussian state space model based on recent results rec

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

fast computation of von neumann entropy for large scale graphs via quadratic approximations abstract the von neumann graph entropy vnge can be used as a measure of graph complexity which can be the measure of information divergence and distance between graphs however computing vnge is extensively demanding for a large scale graph we propose novel quadratic approximations for fast computing vnge various inequalities for error between the quadratic approximations and the exact vnge are found our methods reduce the cubic complexity of vnge to linear complexity computational simulations on random graph models and various real network datasets demonstrate superior performance

semiparametric inference in generalized mixed effects models summary the paper presents a study of the generalized partially linear model including random effects in its linear part we propose an estimator that combines likelihood approaches for mixed effects models with kernel methods following the methodology of hardie and co workers we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model the critical values are estimated by using a bootstrap procedure the asymptotic theory for the methods is provided as are the results of a simulation study these verify the feasibility and the excellent behaviour of the methods for samples of even moderate size the usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in galicia spain

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

the normalized laplacian spectrum of subdivisions of a graph determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and theoretical computer science the eigenvalues of the normalized laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects in particular those related to random walks in this paper we give the spectra of the normalized laplacian of iterated subdivisions of simple connected graphs as an example of application of these results we find the exact values of their multiplicative degree kirchhoff index kemeny s constant and number of spanning trees

on the second largest normalized laplacian eigenvalue of graphs abstract let g v e be a simple graph of order n with normalized laplacian eigenvalues 1 2 n 1 n 0 the normalized laplacian spread of graph g denoted by 1 n 1 is the difference between the largest and the second smallest normalized laplacian eigenvalues of graph g in this paper we obtain the first four smallest values on 2 of graphs moreover we give a lower bound on 2 of connected bipartite graph g except the complete bipartite graph and characterize graphs for which the bound is attained finally we present some bounds on the normalized laplacian spread of graphs and characterize the extremal graphs

estimation of finite population domain means a model assisted empirical best prediction approach in this article we introduce a general methodology for producing a model assisted empirical best predictor ebp of a finite population domain mean using data from a complex survey our method improves on the commonly used design consistent survey estimator by using a suitable mixed model such a model combines information from related sources such as census and administrative data unlike a purely model based ebp the proposed model assisted ebp converges in probability to the customary design consistent estimator as the domain and sample sizes increase the convergence in probability is shown to hold with respect to the sampling design irrespective of the assumed mixed model a property commonly known as design consistency this property ensures robustness of the proposed predictor against possible model failures in addition the convergence in probability is shown to be valid with respect to the assumed mixed model model consistency a new mean squared prediction error mspe estimator is proposed

some compact classes of open sets under hausdorff distance and application to shape optimization in this paper we introduce three new classes of open sets in a general euclidean space mathbb r n it is shown that every class of open sets is compact under the hausdorff distance the result is then applied to a shape optimization problem of elliptic equation the existence of the optimal solution is presented

missing observations in arima models skipping approach versus additive outlier approach optimal estimation of missing values in arma models is typically performed by using the kalman filter for likelihood evaluation skipping in the computations the missing observations obtaining the maximum likelihood ml estimators of the model parameters and using some smoothing algorithm the same type of procedure has been extended to nonstationary arima models in go mez and maravall 1994 an alternative procedure suggests filling in the holes in the series with arbitrary values and then performing ml estimation of the arima model with additive outliers ao when the model parameters are not known the two methods di er since the ao likelihood is a ected by the arbitrary values we develop the proper likelihood for the ao approach in the general non stationary case and show the equivalence of this and the skipping method finally the two methods are compared through simulation and their relative advantages assessed the comparison also includes the ao method with the uncorrected likelihood 1999 elsevier science s a all rights reserved

bayesian forecasting of multinomial time series through conditionally gaussian dynamic models abstract we consider inference in the class of conditionally gaussian dynamic models for nonnormal multivariate time series in such models data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series a key example the main focus here is time series of multinomial observations a common occurrence in sociological and demographic studies involving categorical count data however we present this development in a more general setting as the resulting methods apply beyond the multinomial context we discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing markov chain monte carlo algorithms for normal dynamic linear models and including metropolis hastings components we develop an analysis of time series of flows of students in the italian secondary education system as an illustration of the models and methods

the effect of seasonal adjustment filters on tests for a unit root abstract we consider the effect of seasonal adjustment filters in univariate dynamic models we concentrate our analysis on the behavior of the least squares estimator of the sum of the autoregressive coefficients in a regression we show the existence of a limiting upward bias with the x 11 filter when the process does not contain a unit root we quantify the extent of this bias for a range of models and filtering procedures the asymptotic bias has interesting implications with respect to the power of tests for a unit root in order to assess the importance of this effect we present an extensive simulation study of both the size and power of the usual dickey fuller 1979 and phillips perron 1988 statistics we show that in many cases there is considerable reduction in power compared to the benchmark cases where the data is unfiltered finally some practical implications of our study are addressed with respect to tests for unit roots with seasonally adjusted data

spectral distances of graphs abstract let 1 g 2 g n g be the adjacency spectrum of a graph g on n vertices the spectral distance g 1 g 2 between n vertex graphs g 1 and g 2 is defined by g 1 g 2 i 1 n i g 1 i g 2 here we provide some initial results regarding this quantity first we give some general results concerning the spectral distances between arbitrary graphs and compute these distances in some particular cases certain relation with the theory of graph energy is identified the spectral distances bounded by a given constant are also considered next we introduce the cospectrality measure and the spectral diameter and obtain specific results indicating their relevance for the theory of cospectral graphs finally we give and discuss some computational results and conclude the paper by a list of conjectures

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

distance between the normalized laplacian spectra of two graphs abstract let g v e be a simple graph of order n the normalized laplacian eigenvalues of graph g are denoted by 1 g 2 g n 1 g n g 0 also let g and g be two nonisomorphic graphs on n vertices define the distance between the normalized laplacian spectra of g and g as n g g i 1 n i g i g p p 1 define the cospectrality of g by c s n g min n g g g not isomorphic to g let c s n n max c s n g g a graph on n vertices in this paper we give an upper bound on c s n g in terms of the graph parameters moreover we obtain an exact value of c s n n an upper bound on the distance between the normalized laplacian spectra of two graphs has been presented in terms of randic energy as an application we determine the class of graphs which are lying closer to the complete bipartite graph than to the complete graph regarding the distance of normalized laplacian spectra

trend estimation and de trending via rational square wave filters this paper gives an account of some techniques of linear filtering which can be used for extracting trends from economic time series of limited duration and for generating de trended series a family of rational square wave filters is described which enable designated frequency ranges to be selected or rejected their use is advocated in preference to other filters which are commonly used in quantitative economic analysis

outlier models and prior distributions in bayesian linear regression summary bayesian inference in regression models is considered using heavy tailed error distri butions to accommodate outliers the particular class of distributions that can be con structed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in bayesian linear modelling includ ing simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters the modelling of outliers in nominally normal linear regression models using alternative error distributions which are heavy tailed relative to the normal provides an automatic means of both detecting and accommodating possibly aberrant observations such realistic models do however often lead to analytically intractable analyses with complex posterior distributions in several dimensions that are difficult to summarize and understand in this paper we consider a special yet rather wide class of heavy tailed unimodal and symmetric error distributions for which the analyses though apparently intractable can be examined in some depth by exploiting certain properties of the assumed error form the distributions concerned are those that can be con structed as scale mixtures of normal distributions in his paper concerning location parameters de finetti 1961 discusses such distributions and suggests the hypothetical interpretation that each observation is taken using an instrument with normal error but each time chosen at random from a collection of instruments of different precisions the distribution of the

a closer look at combining data among a small number of binomial experiments in a regulatory environment the regulators and the regulated may not be able to agree on the use of subjective prior information for a clinical trial the use of a data based prior offers a greater possibility for agreement however the degree of importance given to the prior data may still be contentious the use of a hierarchical model to link the prior data and the current trial is shown to provide a relatively objective method for assigning weight to the prior data using a series of examples combining two binomial experiments the effect of a hierarchical model on estimating rates on the degree to which data is combined and on hypothesis testing is illustrated in addition the phenomenon in which combining data reduces the precision is explained simpler models based on finite mixtures of beta distributions are shown to work as well as the more computationally intensive continuous mixtures lastly an example combining three concurrent studies is illustrated published in 2001 by john wiley sons ltd

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

small area inference for binary variables in the national health interview survey abstract the national health interview survey is designed to produce precise estimates of finite population parameters for the entire united states but not for small geographical areas or subpopulations our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months to include all sources of variation in the model we carry out a bayesian hierarchical analysis for the desired finite population quantities first for each cluster county a separate logistic regression relates the individual s probability of a doctor visit to his or her characteristics second a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level we describe the numerical methods needed to obtain the desired posterior moments then we compare estimates produced using the exact numerical method with approximations finally we compare the hierarchical bayes estimates to empirical bayes estimates and to stand

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

estimation of median income of four person families a bayesian time series approach abstract this article develops a general methodology for small domain estimation based on data from repeated surveys the results are directly applied to the estimation of median income of four person families for the 50 states and the district of columbia these estimates are needed by the u s department of health and human services hhs to formulate its energy assistance program for low income families the u s bureau of the census by an informal agreement has provided such estimates to hhs through a linear regression methodology since the latter part of the 1970s the current method is an empirical bayes method eb that uses the current population survey cps estimates as well as the most recent decennial census estimates updated by the per capita income estimates of the bureau of economic analysis however with the existing methodology standard errors associated with these estimates are not easy to obtain the eb estimates when used naively can lead to underestimation of standard errors mo

an arima model based approach to seasonal adjustment abstract this article proposes a model based procedure to decompose a time series uniquely into mutually independent additive seasonal trend and irregular noise components the series is assumed to follow the gaussian arima model properties of the procedure are discussed and an actual example is given

errors in variables and seasonal adjustment procedures abstract seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal and irregular factors in this article we consider a factor that has not been considered explicitly in previous treatments of seasonal adjustment measurement error because of the sample design used in the current population survey measurement error will not be a white noise process but instead it will be characterized by serial correlation of a known form we first consider what effect the serially correlated measurement error has on estimation of the nonseasonal component in seasonal adjustment models we also consider the effect of measurement error on the widely used seasonal adjustment process x 11 estimated unobserved components models are used to estimate the precision root mean squared error of the official and optimal seasonally adjusted data

the hierarchical logistic regression model for multilevel analysis abstract a hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable the group structure is defined by the presence of micro observations embedded within contexts macro observations and the specification is at both of these levels at the first micro level the usual logistic regression model is defined for each context the same regressors are used in each context but the micro regression coefficients are free to vary over contexts at the second level the micro coefficients are treated as functions of macro regressors an empirical bayes estimation procedure is proposed for estimating the micro and macro coefficients explicit formulas are provided that are computationally feasible for large scale data analyses these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within and between macro equation error variability the methodology is applied to world fertility survey data

signal extraction for finite nonstationary time series summary for a signal plus noise model where both signal and noise are generated by nonstation ary arima autoregressive integrated moving average models we use the transformation approach of ansley kohn 1985 to construct an estimate of the signal and obtain its mean squared error given a finite number of observations a method for efficient computa tion of the signal estimate and its mean squared error is also presented consider observations z t generated by the signal plus noise nmodel z t s t n t 1s1 where both signal s t and noise n t follow nonstationary arima processes we give a solution to the finite sample signal extraction problem by defining an estimate of the signal s t given observations z 1 z n and finding its mean squared error the major difficulty in handling the model with nonstationary components is that the distribution of the observations is not defined unless assumptions are made about the initial values of the series moreover it is usually very difficult to formulate reasonable assumptions about the initial values because they affect the correlation structure of the whole series see for example the discussion of bell 1984 p 652 kohn ansley 1986 use a transformation approach to overcome the initial value problem in defining the likelihood and obtaining predittors and interpolators for an arima model which may have missing values this approach does not require any assumptions about the initial values and generalizes the usual differencing approach of box jenkins 1976 for the case where there are no missing observations in the present paper we apply the transformation approach of kohn ansley 1986 and ansley kohn 1985 to solve the signal extraction problem we define a linear estimator a t of s t so that s t sa t is invariant to the initial values and furthermore is unbiased in the sense that e s t s t 0 moreover it has minimum mean squared error amongst all such estimators our approach allows missing observations and extends to signal extraction for several additive signals when each is an arima process we also show how to compute the signal estimate and its mean squared error efficiently by writing the model in state space form placing a diffuse prior on the initial values of the process and then using the modified kalman filter and the modified smoothing algorithm of ansley kohn 1985 and kohn ansley 1986 gersch kitagawa 1983 kitagawa gersch 1984 and harvey todd 1983 use

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

distance between spectra of graphs richard brualdi proposed in stevanivic 2007 10 the following problem problem awgs 4 let gngn and gn be two nonisomorphic graphs on n vertices with spectra 1 2 nand 1 2 n respectively define the distance between the spectra of gngn and gn as gn gn i 1n i i 2 or use i 1n i i define the cospectrality of gngn by cs gn min gn gn gn not isomorphic to gn let csn max cs gn gn a graph on n vertices problem a investigate cs gn cs gn for special classes of graphs problem b find a good upper bound on csncsn in this paper we completely answer problem b by proving that csn 2csn 2 for all n 2n 2 whenever csncsn is computed with respect to any lplp norm with 1 p 1 p and csn 1csn 1 with respect to the l l norm the cospectrality cs km n cs km n of the complete bipartite graph km nkm n for all positive integers m and n with m n m 1 2m 1 is computed as a consequence of the latter result it is proved that in general there is no constant upper bound on e e e e where e and e e denote the number of edges of the graphs g and g g respectively such that cs g g g cs g g g in contrast we show that for such graphs g and g g we have e e 1 in particular e e 3e e e 3e

robustness of maximum likelihood estimates for multi step predictions the exponential smoothing case summary we extend the argument initiated by cox 1961 that the exponential smoothing formula can be made more robust for multi step forecasts if the smoothing parameter is adjusted as a function of the forecast horizon 1 the consistency property of the estimator which minimizes the sum of squares of the sample 1 step ahead forecast errors makes the robustness result useful in practice we also generalize the consistency result to some other parsimonious nonstationary models which have been popular in use the asymptotic distribution of the estimated smoothing parameter adjusted for forecast horizon l leads to the development of diagnostic tools which are based on i step forecasts

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

comparison of partially measured latent traits across nominal subgroups abstract this article presents a method for estimating the subgroup distributions of a latent trait measured as a normal variate in the population this problem occurs in large scale assessments such as the national assessment of educational progress the national adult literacy survey and other programs where proficiencies are estimated via marginal maximum likelihood through a model based on item response theory heretofore estimates of subgroup means were often estimated using ad hoc assumptions about within group distributions which conflicted with concurrent assumptions about normality of the population distributions the method presented here removes the conflict using consistent distributional assumptions for population and subgroup estimates

stochastic linear trends models and estimators abstract the paper considers stochastic linear trends in series with a higher than annual frequency of observation using an approach based on arima models some of the trend models or the model interpretation of trend estimation filters most often found in statistics and econometrics are analysed and compared the properties of the trend optimal estimator are derived and the analysis is extended to seasonally adjusted and or detrended series it is seen that under fairly general conditions the estimator of the unobserved component is noninvertible and will not accept a convergent autoregressive representation this has implications concerning unit root testing and vad model fitting

empirical likelihood for small area estimation abstract small areaestimation has become a topic of growingimportance inrecent years due to increasing demand for small area statistics fromboth the public and private sectors the current methodologies inthis area with possibly a handful of exceptions are all parametric be it bayesian or frequentist even the so called nonparamet ric procedures based on empirical best linear unbiased predictors eblup assume linearity of the estimators of small area means resampling methods like jacknife and bootstrap are used mostlyfor mean squared error estimation in this paper we propose analternative bayesian approach based on empirical likelihood whichdoes not require the assumption of either a parametric likelihoodor linearity of estimators the proposed method can also handleboth discrete and continuous data in a uni ed manner empiricallikelihood for both area and unit level models are introduced theimproved performance of our estimator is illustrated through twoexamples involving both discrete and continuous data key words and phrases area level exponentially tilted t prior unit level

consistent estimators in generalized linear mixed models abstract a simple method based on simulated moments is proposed for estimating the fixed effects and variance components in a generalized linear mixed model glmm it is shown that the method is not only computationally attractive but also leads to consistent estimators on the other hand simulation shows that the method can be quite inefficient

the normalized laplacians on both k triangle graph and k quadrilateral graph with their applications abstract the k triangle graph tk g is obtained from a graph g by replacing each edge in g with k 1 parallel paths in which one is of length 1 and each of the rest k paths is of length 2 whereas the k quadrilateral graph qk g is obtained from g by replacing each edge in g with k 1 parallel paths in which one is of length 1 and each of the rest k paths is of length 3 in this paper we completely determine the normalized laplacian spectrum on tk g resp qk g for any connected graph g k 2 as applications the correlation between the degree kirchhoff index the kemeny s constant and the number of spanning trees of tk g resp qk g the r th iterative k triangle graph t r k g the r th iterative k quadrilateral graph q r k g and those of g are derived our results extend those main results obtained in xie et al 2016 and li and hou 2017

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

free boundary problems and density perimeter we introduce a new concept the density perimeter which substitutes the measure of length of the perimeter of a set in free boundary problems we deduce some links between the hausdorff convergence and the char convergence for a family of domains with bounded density perimeter if this perimeter is considered as a penalty term we give existence results for the variational problem which appears in computer vision and in a bernoulli like free boundary problem we also make some considerations concerning a convergence property of the density perimeter

on the spectrum of the normalized laplacian of iterated triangulations of graphs the eigenvalues of the normalized laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects specifically in relation to random walks in this paper we determine the spectra of the normalized laplacian of iterated triangulations of a generic simple connected graph as an application we also find closed forms for their multiplicative degree kirchhoff index kemeny s constant and number of spanning trees

mathematical framework for pseudo spectra of linear stochastic difference equations although spectral analysis of stationary stochastic processes has solid mathematical foundations this is not always so for some non stationary cases here we establish a rigorous mathematical extension of the classic fourier spectrum to the case in which there are ar roots in the unit circle i e the transfer function of the linear time invariant filter has poles on the unit circle to achieve it we embed the classical problem in a wider framework extend the discrete time fourier transform and defined a new extended fourier transform pair pseudo covariance function pseudo spectrum our approach is a proper extension of the classical spectral analysis within which the fourier transform pair auto covariance function spectrum is a particular case consequently spectrum and pseudo spectrum coincide when the first one is defined

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

a generalization of the kalman filter for models with state dependent observation variance abstract the kalman filter is generalized to cover state space models in which the variance of the observation error depends on the state vector derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints linear bayes theory and gauss markov theory the results are applied to a model for which y t t 1 2 n follow a poisson distribution with corresponding intensities t t 1 2 n that are assumed to follow an autoregressive process of order 1 namely the steady state generalized kalman filter algorithm in the case for which 1 gives a generalization of exponential smoothing for a poisson process with time varying intensity

existence for shape optimization problems in arbitrary dimension we discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous neumann boundary conditions or with the interior transmission conditions we show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions which in turn guarantees convergence of any minimizing sequences for the first problem in the second case weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution we impose no restriction on the dimension of the underlying euclidean space

modeling of time series arrays by multistep prediction or likelihood methods abstract an estimation theory is provided for the fitting of possibly incorrect invertible short memory models to short or long memory time series or time series arrays by multistep prediction error minimization or gaussian likelihood maximization by array we mean data y t t 1 t t that depend on the number of observations t such as regression or other estimated model residuals or the outputs of time varying filters for example seasonal adjustments our theory only requires the modeled array to have basic properties for a s i p convergence of parameter estimates the array s sample lagged second moments must converge a s i p and its end values y 1 j t and y t j t must be of order less than t 1 2 or an appropriately differenced version of the observed array must have these properties in findley et al ann statist 29 2001 815 broad classes of arrays were shown to have these properties even for the special case of autoregressive moving average models fit to stationary gaussian time series data our result on the convergence of parameter estimates minimizing p step ahead prediction error sums of squares is new

cospectrality of graphs richard brualdi proposed in stevanivic 2007 6 the following problem problem awgs 4 let gngn and gn be two nonisomorphic graphs on n vertices with spectra 1 2 nand 1 2 n respectively define the distance between the spectra of gngn and gn as gn gn i 1n i i 2 or use i 1n i i define the cospectrality of gngn by cs gn min gn gn gn not isomorphic to gn let csn max cs gn gn a graph on n vertices problem a investigate cs gn cs gn for special classes of graphs problem b find a good upper bound on csncsn in this paper we study problem a and determine the cospectrality of certain graphs by the euclidian distance let knkn denote the complete graph on n vertices nk1nk1 denote the null graph on n vertices and k2 n 2 k1k2 n 2 k1 denote the disjoint union of the k2k2 with n 2n 2 isolated vertices where n 2n 2 in this paper we find cs kn cs kn cs nk1 cs nk1 cs k2 n 2 k1 cs k2 n 2 k1 n 2n 2 and cs kn n cs kn n

robust estimation in generalised linear mixed models summary we propose robust methods for estimation of parameters of interest in an extended generalised linear mixed model in which only the conditional means of the responses given the random effects are specified a first step estimator 0 of the vector 0 of parameters is obtained by solving a system of estimating equations it is shown that 9 is consistent if furthermore the conditional variances are correctly specified a second step estimator 0 can be obtained by solving a system of optimal estimating equations whose coefficients a are estimated by 0 it is shown that 0 maintains the asymptotic optimality simulations a also indicate solid improvement of 0 over 0 two examples involving real data analysis are considered the methods are developed under a more general framework so that they may be applied to more general estimation problems

a bayesian approach to nonlinear random effects models nonlinear random effects models are considered from the bayesian point of view the method of analysis follows closely that of lindley and smith 1972 journal of the royal statistical society series b 34 1 42 the numerical method is related to the em algorithm

robust sequential approximate bayesian estimation summary an approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non normal observations the behaviour of the resulting non linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non normal error distributions illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned we consider here the problem of sequential estimation of the location vector of a linear time series model termed the dynamic linear model by harrison and stevens 1976 the straightforward exact analysis obtained by assuming normal error and prior structure is generally lost when alternative error distributions are adopted and yet considerations of realism or robustness may strongly suggest such non normal assumptions the multi state model of harrison and stevens provides an approximate analysis based on a discrete variance mixture of normal distributions an approach which has been extensively investigated in the engineering literature under the name of gaussian sum approximations see for example alspach and sorenson 1971 our aim in this paper is to provide an approximate tractible recursive updating procedure for the location parameters which is applicable to a wide range of symmetric unimodal error distributions and is both more realistic and more elegant than the discrete gaussian sum approach in particular for heavy tailed distributions our procedures provide approximate bayesian methods for time series analysis which extend considerably the work of masreliez and martin 1977 and have close connections with classical robustness ideas such as m estimation and influence functions

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

six classes of trees with largest normalized algebraic connectivity abstract the normalized algebraic connectivity of a graph g denoted by 2 g is the second smallest eigenvalue of its normalized laplacian matrix in this paper we firstly determine all trees with 2 g 1 6 3 then we classify such trees into six classes c 1 c 6 and prove that 2 t i 2 t j for 1 i j 6 where t i c i and t j c j at the same time the values of the normalized algebraic connectivity for the six classes of trees are provided respectively these results are similar to those on the algebraic connectivity which were obtained by yuan et al 2008 8

design consistent versus model dependent estimation for small domains abstract for small domains we have a choice between design consistent estimators that make the strongest possible use of auxiliary information and model dependent design biased alternatives such as the synthetic estimator in this article a design consistent method is developed that borrows strength in the same way that the design biased synthetic estimator does the latter has a design based mean squared error mse advantage in small samples under the supposition that domains resemble each other under deviations from that model however and with moderate to large samples the design consistent method gives a smaller mse it also has the advantage that design based variance estimators and design based confidence intervals can be easily obtained this article emphasizes that the choice of estimation method depends on a complex interaction of factors that include sample size sampling fraction domain size and departures from the model

on the linearity of bayesian interpolators for non gaussian continuous time ar 1 processes bayesian estimation problems involving gaussian distributions often result in linear estimation techniques nevertheless there are no general statements as to whether the linearity of the bayesian estimator is restricted to the gaussian case the two common strategies for non gaussian models are either finding the best linear estimator or numerically evaluating the bayesian estimator by monte carlo methods in this paper we focus on bayesian interpolation of non gaussian first order autoregressive ar processes where the driving innovation can admit any symmetric infinitely divisible distribution characterized by the levy khintchine representation theorem we redefine the bayesian estimation problem in the fourier domain with the help of characteristic forms by providing analytic expressions we show that the optimal interpolator is linear for all symmetric stable distributions the bayesian interpolator can be expressed in a convolutive form where the kernel is described in terms of exponential splines we also show that the limiting case of levy type ar 1 processes the system of which has a pole at the origin always corresponds to a linear bayesian interpolator made of a piecewise linear spline irrespective of the innovation distribution finally we show the two mentioned cases to be the only ones within the family for which the bayesian interpolator is linear

comparing large scale graphs based on quantum probability theory abstract in this paper a new measurement to compare two large scale graphs based on the theory of quantum probability is proposed an explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established our proposed distance between two graphs is defined as the distance between the corresponding moment matrices of their spectral distributions it is shown that the spectral distributions of their adjacency matrices in a vector state includes information not only about their eigenvalues but also about the corresponding eigenvectors moreover we prove that the proposed distance is graph invariant and sub structure invariant examples with various graphs are given and distances between graphs with few vertices are checked computational results for real large scale graphs show that its accuracy is better than any existing methods and time cost is extensively cheap

estimation error and the specification of unobserved component models abstract the paper deals with the problem of identifying stochastic unobserved two component models as in seasonal adjustment or trend cycle decompositions solutions based on the properties of the unobserved component estimation error are considered and analytical expressions for the variance of the errors in the final preliminary and concurrent estimators are obtained these expressions are straightforwardly derived from the arima model for the observed series the estimation error variance is always minimized at a canonical decomposition i e at a decomposition with one of the components noninvertible and a simple procedure to determine that decomposition is presented on occasion however the most precise final estimator may be obtained at a canonical decomposition different from the one that yields the most precise preliminary estimator two examples are presented first a simple trend plus cycle type model is used to illustrate the derivations the second example presents results for a class of models often encountered in actual time series

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due