cross validation for correlated data abstract k fold cross validation cv with squared error loss is widely used for evaluating predictive models especially when strong distributional assumptions cannot be taken however cv with sq

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

variable selection in linear mixed effects models this paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models we propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects to overcome the difficulty of unknown covariance matrix of random effects we propose to use a proxy matrix in the penalized profile likelihood we establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size we further propose a group variable selection strategy to simultaneously select and estimate important random effects where the unknown covariance matrix of random effects is replaced with a proxy matrix we prove that with the proxy matrix appropriately chosen the proposed procedure can identify all true random effects with asymptotic probability one where the dimension of random effects vector is allowed to increase exponentially with the sample size monte carlo simulation studies are conducted to examine the finite sample performance of the proposed procedures we further illustrate the proposed procedures via a real data example

asymptotically efficient selection of the order by the criterion autoregressive transfer function on montre que la propriete d optimalite obtenue par shibata 1980 1981 est valable pour l approche cat parzen 1974 cat parzen 1977 et cat 2 bhansali 1985

nonlinear functionals on c x and choquet integrals abstract we establish a retraction from monotone functionals defined on c x where x is a compact hausdorff space with pointwise convergence topology to functionals represented by choquet integrals with respect to monotone measures we prove an analogue of the riesz representation theorem in the case of choquet integrals

single index model selections we derive a new model selection criterion for single index models aicc by minimising the expected kullback leibler distance between the true and candidate models the proposed criterion selects not only relevant variables but also the smoothing parameter for an unknown link function thus it is a general selection criterion that provides a unified approach to model selection across both parametric and nonparametric functions monte carlo studies demonstrate that aicc performs satisfactorily in most situations we illustrate the practical use of aicc with an empirical example for modelling the hedonic price function for cars in addition we extend the applicability of aicc to partially linear and additive single index models language en

on the behaviour of marginal and conditional aic in linear mixed models in linear mixed models model selection frequently includes the selection of random effects two versions of the akaike information criterion aic have been used based either on the marginal or on the conditional distribution we show that the marginal aic is not an asymptotically unbiased estimator of the akaike information and favours smaller models without random effects for the conditional aic we show that ignoring estimation uncertainty in the random effects covariance matrix as is common practice induces a bias that can lead to the selection of any random effect not predicted to be exactly zero we derive an analytic representation of a corrected version of the conditional aic which avoids the high computational cost and imprecision of available numerical approximations an implementation in an r package r development core team 2010 is provided all theoretical results are illustrated in simulation studies and their impact in practice is investigated in an analysis of childhood malnutrition in zambia

traveling wave solutions of diffusive lotka volterra equations a heteroclinic connection in we establish the existence of traveling wave solutions for a reaction dif fusion system based on the lotka volterra differential equation model of a predator and prey interaction the waves are of transition front type analogous to the solutions discussed by fisher and kolmogorov et al for a scalar reaction diffusion equation the waves discussed here are not necessarily monotone there is a speed c 0 such that for c c there is a traveling wave moving with speed c the proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a liapunov function to guarantee the existence of the traveling wave solution the traveling wave solution is equivalent to a heteroclinic orbit in 4 dimensional phase space

model averaging and weight choice in linear mixed effects models this article studies model averaging for linear mixed effects models we establish an unbiased estimator of the squared risk for the model averaging and use the estimator as a criterion for choosing weights the resulting model average estimator is proved to be asymptotically optimal under some regularity conditions simulation experiments show it is superior or comparable to estimators based on the final models selected by the commonly used methods and some existing averaging procedures the proposed procedure is applied to data from an aids clinic trial

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

the accommodation of traveling waves of fisher s type to the dynamics of the leading tail traveling wave solutions for equations of fisher s type are given by a connection from a saddle point to a node and their velocity for large times is known to be determined by the spatial decay rate of the initial conditions far ahead of the wave to understand this phenomenon in simple terms initial conditions are considered that correspond to a traveling wave but with an exponential decay rate far ahead of the wave that varies slowly in the region referred to as the leading tail the wave that results is supersonic in the sense that the speed of the core of the traveling wave is greater than the velocity of the characteristics or group velocity in the leading tail consequently the speed of the core adjusts to accommodate the slowly varying decay rate in the leading tail a generalization is also considered that includes fisher s equation for which traveling waves with a stable exponential tail corresponding to a node are supersonic

a mathematical model for spatially varying extracellular matrix alignment orientation of extracellular matrix fibers in the skin is a keyingredient of tissue appearance and function and differences in fiber alignment are one of the main distinctions between scar tissue and normal skin in this paper the authors develop a mathematical model for alignment of collagen fibers and the fibroblast cells that remodel them the model extends previous work in which spatial variation was excluded numerical simulations of the model are presented which show spatial variations in alignment over long transients but with spatiallyuniform behavior in the long term this is investigated further via asymptotic analysis using the angular diffusion coefficient as a small parameter this method enables calculation of the form of the steadystate orientation peaks observed numerically by considering behavior at large times the rate of approach to these peaks is shown to be exponential extension of this analysis to the spatially varying model confirms that long time behavior will be spatiallyuniform except in one special and biologicallyunrealistic case the authors conclude that the spatiallyvary ing alignment patterns observed in skin are in fact slow transients and biological implications of the modeling are discussed

fixed and random effects selection in mixed effects models summary we consider selecting both fixed and random effects in a general class of mixed effects models using maximum penalized likelihood mpl estimation along with the smoothly clipped absolute deviation scad and adaptive least absolute shrinkage and selection operator alasso penalty functions the mpl estimates are shown to possess consistency and sparsity properties and asymptotic normality a model selection criterion called the icq statistic is proposed for selecting the penalty parameters ibrahim zhu and tang 2008 journal of the american statistical association 103 1648 1658 the variable selection procedure based on icq is shown to consistently select important fixed and random effects the methodology is very general and can be applied to numerous situations involving random effects including generalized linear mixed models simulation studies and a real data set from a yale infant growth study are used to illustrate the proposed methodology

quasi states and quasi measures abstract it is shown that in general non linear quasi states will exist on c x where x is a compact hausdorff space we introduce the concept of a quasi measure in x and establish the connection between quasi states and quasi measures

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

conditions for choquet integral representation of the comonotonically additive and monotone functional if the universal set x is not compact but locally compact a comonotonically additive and monotone functional for short c m on the class of continuous functions with compact support is not represented by one choquet integral but represented by the difference of two choquet integrals the conditions for which a c m functional can be represented by one choquet integral are discussed

nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogenesis with chemical diffusion abstract we consider a simplified chemotaxis model of tumor angiogenesis described by a keller segel system on the two dimensional infinite cylindrical domain x y r s where s is the circle of perimeter 0 the domain models a virtual channel where newly generated blood vessels toward the vascular endothelial growth factor will be located the system is known to allow planar traveling wave solutions of an invading type in this paper we establish the nonlinear stability of these traveling invading waves when chemical diffusion is present if is sufficiently small the same result for the corresponding system in one dimension was obtained by li li wang 2014 17 our result solves the problem remained open in chae choi kang lee 2018 3 at which only linear stability of the planar traveling waves was obtained under certain artificial assumption

traveling wave solutions of a mathematical model for tumor encapsulation the formation of a capsule of dense fibrous extracellular matrix around a solid tumor is a key prognostic indicator in a wide range of cancers however the cellular mechanisms underlying capsule formation remain unclear one hypothesized mechanism is the expansive growth hypothesis which suggests that a capsule may form by the rearrangement of existing extracellular matrix without new matrix production a mathematical model was recently proposed to study the implications of this hypothesis perumpanani sherratt and norbury nonlinearity 10 1997 pp 1599 1614 the model consists of conservation equations for tumor cells and extracellular matrix and exhibits traveling wave solutions in which a pulse of extracellular matrix corresponding to a capsule moves in parallel with the advancing front of the tumor in this paper the author presents a detailed study of traveling wave behavior in the model deriving conditions for the existence of traveling waves and their key properties numerical meth

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on measuring and correcting the effects of data mining and model selection abstract in the theory of linear models the concept of degrees of freedom plays an important role this concept is often used for measurement of model complexity for obtaining an unbiased estimate of the error variance and for comparison of different models i have developed a concept of generalized degrees of freedom gdf that is applicable to complex modeling procedures the definition is based on the sum of the sensitivity of each fitted value to perturbation in the corresponding observed value the concept is nonasymptotic in nature and does not require analytic knowledge of the modeling procedures the concept of gdf offers a unified framework under which complex and highly irregular modeling procedures can be analyzed in the same way as classical linear models by using this framework many difficult problems can be solved easily for example one can now measure the number of observations used in a variable selection process different modeling procedures such as a tree based regression and a

conditional akaike information for mixed effects models summary this paper focuses on the akaike information criterion aic for linear mixed effects models in the analysis of clustered data we make the distinction between questions regarding the population and questions regarding the particular clusters in the data we show that the aic in current use is not appropriate for the focus on clusters and we propose instead the conditional akaike information and its corresponding criterion the conditional aic caic the penalty term in caic is related to the effective degrees of freedom p for a linear mixed model proposed by hodges sargent 2001 p reflects an intermediate level of complexity between a fixed effects model with no cluster effect and a corresponding model with fixed cluster effects the caic is defined for both maximum likelihood and residual maximum likelihood estimation a pharmacokinetics data appli cation is used to illuminate the distinction between the two inference settings and to illustrate the use of the conditional aic in model selection

smoothing parameter and model selection for general smooth models abstractthis article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates gaussian random effects and parametric terms may also be present by construction the method is numerically stable and convergent and enables smoothing parameter uncertainty to be quantified the latter enables us to fix a well known problem with aic for such models thereby improving the range of model selection tools available the smooth functions are represented by reduced rank spline like smoothers with associated quadratic penalties measuring function smoothness model estimation is by penalized likelihood maximization where the smoothing parameters controlling the extent of penalization are estimated by laplace approximate marginal likelihood the methods cover for example generalized additive models for nonexponential family responses e g beta ordered categorical scaled t distribution negative binomial a

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

conditional akaike information under generalized linear and proportional hazards mixed models we study model selection for clustered data when the focus is on cluster specific inference such data are often modelled using random effects and conditional akaike information was proposed in vaida blanchard 2005 and used to derive an information criterion under linear mixed models here we extend the approach to generalized linear and proportional hazards mixed models outside the normal linear mixed models exact calculations are not available and we resort to asymptotic approximations in the presence of nuisance parameters a profile conditional akaike information is proposed bootstrap methods are considered for their potential advantage in finite samples simulations show that the performance of the bootstrap and the analytic criteria are comparable with bootstrap demonstrating some advantages for larger cluster sizes the proposed criteria are applied to two cancer datasets to select models when the cluster specific inference is of interest

counting degrees of freedom in hierarchical and other richly parameterised models summary drawing on linear model theory we rigorously extend the notion of degrees of freedom to richly parameterised models including linear hierarchical and random effect models some smoothers and spatial models and combinations of these the number of degrees of freedom is often much smaller than the number of parameters our notion of degrees of freedom is compatible with similar ideas long associated with smoothers but is applicable to new classes of models and can be interpreted using the projection theory of linear models we use an example to illustrate the two applications of setting prior distributions for variances and fixing model complexity by fixing degrees of freedom

stability of planar traveling waves in a keller segel equation on an infinite strip domain abstract we consider a simplified model of tumor angiogenesis described by a keller segel equation on the two dimensional domain x y r s where s is the circle of perimeter it is known that the system allows planar traveling wave solutions of an invading type in case that is sufficiently small we establish the nonlinear stability of traveling wave solutions in the absence of chemical diffusion if the initial perturbation is sufficiently small in some weighted sobolev space when chemical diffusion is present it can be shown that the system is linearly stable lastly we prove that any solution with our front condition eventually becomes planar under certain regularity conditions

metrizability of the levy topology on the space of nonadditive measures on metric spaces we formalize the levy prokhorov metric and the fortet mourier metric for nonadditive measures on a metric space and show that the levy topology on every uniformly equi autocontinuous set of radon nonadditive measures can be metrized by such metrics this result is proved using the uniformity for levy convergence on a bounded subset of lipschitz functions we describe some applications to stochastic convergence of a sequence of measurable mappings on a nonadditive measure space

signed integral representations of comonotonic additive functionals we establish integral representation results for suitably pointwise continuous and comonotonic additive functionals of bounded variation de ned on stone lattices as an application we prove a comonotonic version of the daniell stone theorem 2000 mathematics subject classi cation primary 28a12 28a25 46g12 secondary 91b06

a note on conditional aic for linear mixed effects models the conventional model selection criterion aic has been applied to choose candidate models in mixed effects models by the consideration of marginal likelihood vaida and blanchard 2005 demonstrated that such a marginal aic and its small sample correction are inappropriate when the research focus is on clusters correspondingly these authors suggested to use conditional aic the conditional aic is derived under the assumptions of the variance covariance matrix or scaled variance covariance matrix of random effects being known we develop a general conditional aic but without these strong assumptions this allows vaida and blanchard s conditional aic to be applied in a wide range simulation studies show that the proposed method is promising

a group analysis via weak equivalence transformations for a model of tumour encapsulation a symmetry reduction of a pdes system describing the expansive growth of a benign tumour is obtained via a group analysis approach the presence in the model of three arbitrary functions suggests the use of lie symmetries by using the weak equivalence transformations an invariant classification is given which allows us to reduce the initial pdes system to an odes system numerical simulations show a realistic enough description of the physical process

biclustering models for two mode ordinal data the work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two mode ordinal categorical response data such as those resulting from likert scale responses we use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data model fitting is performed using the em algorithm and a fuzzy allocation of rows and columns to corresponding clusters is obtained the clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets

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

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates