a note on the unification of the akaike information criterion to measure the distance between a robust function evaluated under the true regression model and under a fitted model we propose generalized kullback leibler information using this generalization we have developed three robust model selection criteria aicr aiccr and aiccr that allow the selection of candidate models that not only fit the majority of the data but also take into account non normally distributed errors the aicr and aiccr criteria can unify most existing akaike information criteria three examples of such unification are given simulation studies are presented to illustrate the relative performance of each criterion

functional coefficient regression models with time trend abstract we consider the problem of estimating a varying coefficient regression model when regressors include a time trend we show that the commonly used local constant kernel estimation method leads to an inconsistent estimation result while a local polynomial estimator yields a consistent estimation result we establish the asymptotic normality result for the proposed estimator we also provide asymptotic analysis of the data driven least squares cross validation method of selecting the smoothing parameters in addition we consider a partially linear time trend model and establish the asymptotic distribution of our proposed estimator two test statistics are proposed to test the null hypotheses of a linear and of a partially linear time trend models simulations are reported to examine the finite sample performances of the proposed estimators and the test statistics

mdl denoising the so called denoising problem relative to normal models for noise is formalized such that noise is defined as the incompressible part in the data while the compressible part defines the meaningful information bearing signal such a decomposition is effected by minimization of the ideal code length called for by the minimum description length mdl principle and obtained by an application of the normalized maximum likelihood technique to the primary parameters their range and their number for any orthonormal regression matrix such as defined by wavelet transforms the minimization can be done with a threshold for the squared coefficients resulting from the expansion of the data sequence in the basis vectors defined by the matrix

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

comparative analysis of formulations for conservative transport in porous media through sensitivity based parameter calibration 1 we apply a general strategy based on global sensitivity analysis gsa and model discrimination criteria to a calibrate the parameters embedded in competing models employed to interpret laboratory scale tracer experiments b rank these models and c estimate the relative degree of likelihood of each model through a posterior probability weight we consider a conservative transport experiment in a uniform porous medium we apply gsa to three transport models based on the classical advection dispersion equation ade a dual porosity dp formulation with mass transfer between mobile and immobile regions and the continuous time random walk ctrw approach gsa is performed through polynomial chaos expansion of the governing equations treating key model parameters as independent random variables we show how this approach allows identification of a the relative importance of model dependent parameters and b the space time locations where the models are most sensitive to these parameters gsa is then employed to assist parameter estimates within a maximum likelihood framework finally formal model identification criteria are employed to a rank the alternative models and b associate each model with a posterior probability weight for the specific case study the gsa based calibration of each model returns an acceptable approximation remarkably accurate in the case of the ctrw model of all available concentration data with calibration being performed using minimum sets of observations corresponding to the most sensitive space time locations

estimation and statistical analysis of exponential polynomial signals we derive and analyze a suboptimal algorithm for estimating the unknown parameters of an exponential polynomial signal eps model the eps model represents a signal as an exponent raised to a complex polynomial of time that is the phase and the logarithm of the amplitude are approximated as finite order polynomials of time

a nonparametric multidimensional latent class irt model in a bayesian framework we propose a nonparametric item response theory model for dichotomously scored items in a bayesian framework the model is based on a latent class lc formulation and it is multidimensional with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class moreover an innovative system of prior distributions is proposed following the encompassing approach in which the largest model is the unconstrained lc model a reversible jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model by suitably post processing its output we then make inference on the number of dimensions i e number of groups of items measuring the same latent trait and we cluster items according to the dimensions when unidimensionality is violated the approach is illustrated by two examples on simulated data and two applications based on educational and quality of life data

variational bayesian learning for mixture autoregressive models with uncertain order autoregressive ar models are fundamental tools for modeling a variety of signals in many fields of study selecting the appropriate order for ar models is typically accomplished using an information criterion to compare the models learned for all orders under consideration the use of an information criterion for model order selection becomes increasingly computationally demanding when ar models are used as part of larger statistical models such as mixture models that have their own model order selection issues statistical models utilizing dirichlet process dp priors provide a mechanism for automatically selecting the number of components within a mixture model and have previously been utilized with ar components these previous investigations utilize different priors for the ar parameters to enable automatic selection of the ar order and each makes us of computationally expensive markov chain monte carlo mcmc sampling this paper develops and evaluates a variational bayesian vb inference procedure for the parameters of dp mixtures of ar components with uncertain order to enable rapid parameter inference for ar based statistical models that provide automatic model order selection and is suitable for large scale problems the previously utilized priors for ar models with uncertain order are evaluated to determine which is more appropriate for vb inference and the ability of the vb inference procedure for the developed model to correctly determine the number of mixture components and the ar order of each of the mixture components is shown to be comparable to computationally intensive mcmc inference the vb inference procedure is then applied to an acoustic signal classification problem to illustrate the efficacy of ar based statistical models utilizing automated model order selection for real world signal processing tasks

statistical estimation in varying coefficient models varying coefficient models are a useful extension of classical linear models they arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age the appeal of these models is that the coef cient functions can easily be estimated via a simple local regression this yields a simple one step estimation procedure we show that such a one step method cannot be optimal when different coefficient functions admit different degrees of smoothness this drawback can be repaired by using our proposed two step estimation procedure the asymptotic mean squared error for the two step procedure is obtained and is shown to achieve the optimal rate of convergence a few simulation studies show that the gain by the two step procedure can be quite substantial the methodology is illustrated by an application to an environmental data set

fisher information and stochastic complexity by taking into account the fisher information and removing an inherent redundancy in earlier two part codes a sharper code length as the stochastic complexity and the associated universal process are derived for a class of parametric processes the main condition required is that the maximum likelihood estimates satisfy the central limit theorem the same code length is also obtained from the so called maximum likelihood code

model selection in the presence of nonstationarity abstract this paper studies model selection methods in the presence of nonstationarity we focus on the bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice first we derive each of these criteria in the presence of nonstationarity in particular we study the bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity one important feature of the bayesian model selection criterion bmsc is that bmsc gives different weights to the stationary and nonstationary components of a model while the other criteria do not this feature of bmsc is a desirable property for a model selection rule in the presence of possible nonstationarity second we compare these criteria with regard to parsimony and power we have found that bmsc shows the highest parsimony aic is the second and c p and r 2 having the same level of parsimony are the third with regard to power the order is not clearly established however for the size adjusted power bmsc becomes dominant as the sample size increases without size adjustment the order in the power is exactly the opposite to that in parsimony also we find that bmsc is a consistent selection rule while the other criteria are not third we consider four different cases of practical interest for which bmsc with some of the other criteria is applicable we discuss how our bmsc can be used in these cases of practical interest results of an extensive monte carlo simulation for models in these four cases show that overall the bmsc outperforms other criteria

on model selection criteria in multimodel analysis 1 hydrologic systems are open and complex rendering them prone to multiple conceptualizations and mathematical descriptions there has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to 1 rank these models 2 eliminate some of them and or 3 weigh and average predictions and statistics generated by multiple models this has led to some debate among hydrogeologists about the merits and demerits of common model selection also known as model discrimination or information criteria such as aic aicc bic and kic and some lack of clarity about the proper interpretation and mathematical representation of each criterion we examine the model selection literature to find that 1 all published rigorous derivations of aic and aicc require that the true model having generated the observational data be in the set of candidate models 2 though bic and kic were originally derived by assuming that such a model is in the set bic has been rederived by cavanaugh and neath 1999 without the need for such an assumption and 3 kic reduces to bic as the number of observations becomes large relative to the number of adjustable model parameters implying that it likewise does not require the existence of a true model in the set of alternatives we explain why kic is the only criterion accounting validly for the likelihood of prior parameter estimates elucidate the unique role that the fisher information matrix plays in kic and demonstrate through an example that it imbues kic with desirable model selection properties not shared by aic aicc or bic our example appears to provide the first comprehensive test of how aic aicc bic and kic weigh and rank alternative models in light of the models predictive performance under cross validation with real hydrologic data

an alternative quasi likelihood approach bayesian analysis and data based inference for model specification abstract this paper studies an alternative quasi likelihood approach under possible model misspecification we derive a filtered likelihood from a given quasi likelihood ql called a limited information quasi likelihood li ql that contains relevant but limited information on the data generation process our li ql approach in one hand extends robustness of the ql approach to inference problems for which the existing approach does not apply our study in this paper on the other hand builds a bridge between the classical and bayesian approaches for statistical inference under possible model misspecification we can establish a large sample correspondence between the classical ql approach and our li ql based bayesian approach an interesting finding is that the asymptotic distribution of an li ql based posterior and that of the corresponding quasi maximum likelihood estimator share the same sandwich type second moment based on the li ql we can develop inference methods that are useful for practical applications under possible model misspecification in particular we can develop the bayesian counterparts of classical ql methods that carry all the nice features of the latter studied in white 1982 in addition we can develop a bayesian method for analyzing model specification based on an li ql

adaptive estimation of stationary gaussian fields we study the nonparametric covariance estimation of a stationary gaussian field x observed on a regular lattice in the time series setting some procedures like aic are proved to achieve optimal model selection among autoregressive models however there exists no such equivalent results of adaptivity in a spatial setting by considering collections of gaussian markov random fields gmrf as approximation sets for the distribution of x we introduce a novel model selection procedure for spatial fields for all neighborhoods m in a given collection mathcal m this procedure first amounts to computing a covariance estimator of x within the gmrfs of neighborhood m then it selects a neighborhood m by applying a penalization strategy the so defined method satisfies a nonasymptotic oracle type inequality if x is a gmrf the procedure is also minimax adaptive to the sparsity of its neighborhood more generally the procedure is adaptive to the rate of approximation of the true distribution by gmrfs with growing neighborhoods

data driven calibration of penalties for least squares regression penalization procedures often suffer from their dependence on multiplying factors whose optimal values are either unknown or hard to estimate from data we propose a completely data driven calibration algorithm for these parameters in the least squares regression framework without assuming a particular shape for the penalty our algorithm relies on the concept of minimal penalty recently introduced by birge and massart 2007 in the context of penalized least squares for gaussian homoscedastic regression on the positive side the minimal penalty can be evaluated from the data themselves leading to a data driven estimation of an optimal penalty which can be used in practice on the negative side their approach heavily relies on the homoscedastic gaussian nature of their stochastic framework the purpose of this paper is twofold stating a more general heuristics for designing a data driven penalty the slope heuristics and proving that it works for penalized least squares regression with a random design even for heteroscedastic non gaussian data for technical reasons some exact mathematical results will be proved only for regressogram bin width selection this is at least a first step towards further results since the approach and the method that we use are indeed general

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

cramer rao bounds for ar parameter and reflection coefficient estimators the finite examples cramer rao bound for the autoregressive parameters of a gaussian autoregressive model is given in closed form quick algorithms for computing this bound for the autoregressive parameters and also for the reflection coefficients are presented the exact bounds are of interest since they can differ appreciably from the asymptotic bounds if replicated independent records are available as in some spatial array processing problems the exact bounds will be approached when the number of replications goes to infinity but the asymptotic bound will not since the record length remains finite

recursive maximum likelihood estimation of autoregressive processes a new method of autoregressive parameter estimation is presented the technique is a closer approximation to the true maximum likelihood estimator than that obtained using linear prediction techniques the advantage of the new algorithm is mainly for short data records and or sharply peaked spectra simulation results indicate that the parameter bias as well as the variance is reduced over the yule walker and the forward backward approaches of linear prediction also spectral estimates exhibit more resolution and less spurious peaks a stable all pole filter estimate is guaranteed the algorithm operates in a recursive model order fashion which allows one to successively fit higher order models to the data

bootstrap modeling of a class of nonstationary signals the problem of modeling polynomial phase signals is considered techniques based on the bootstrap and multiple hypotheses tests for optimal model selection of constant amplitude polynomial phase signals embedded in stationary noise are developed phase parameter estimators based on both the least squares method and the polynomial phase transform are used the proposed techniques are compared with existing ones including akaike s 1978 1974 information criterion and rissanen s 1978 minimum description length criterion and are shown to outperform these procedures for the considered small sample sizes

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

finite sample criteria for autoregressive order selection the quality of selected ar models depends on the true process in the finite sample practice on the number of observations on the estimation algorithm and on the order selection criterion samples are considered to be finite if the maximum candidate model order for selection is greater than n 10 where n denotes the number of observations finite sample formulae give empirical approximations for the statistical average of the residual energy and of the squared error of prediction for several autoregressive estimation algorithms this leads to finite sample criteria for order selection that depend on the estimation method the special finite sample information criterion fsic and combined information criterion cic are necessary because of the increase of the variance of the residual energy for higher model orders that has not been accounted for in other criteria only the expectation of the logarithm of the residual energy as a function of the model order has been the basis for the previous classes of asymptotical and finite sample criteria however the behavior of the variance causes an undesirable tendency to select very high model orders without the special precautions of fsic or cic

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

analysis of a nonlinear degenerating pde system for phase transitions in thermoviscoelastic materials abstract we address the analysis of a nonlinear and degenerating pde system proposed by m fremond for modelling phase transitions in viscoelastic materials subject to thermal effects the system features an internal energy balance equation governing the evolution of the absolute temperature an evolution equation for the phase change parameter and a stress strain relation for the displacement variable u the main novelty of the model is that the equations for and u are coupled in such a way as to take into account the fact that the properties of the viscous and of the elastic parts influence the phase transition phenomenon in different ways however this brings about an elliptic degeneracy in the equation for u which needs to be carefully handled in this paper we first prove a local in time well posedness result for a suitable initial boundary value problem for the above mentioned pde system in the spatially three dimensional setting secondly we restrict to the one dimensional case in which for the same initial boundary value problem we indeed obtain a global well posedness theorem

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

regularity and separation from potential barriers for a non local phase field system abstract we show that solutions of a two phase model involving a non local interactive term become more regular immediately after the moment they separate from the pure phases this result allows us to prove stronger convergence to equilibria a new proof of the separation property is also given

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

functional coefficient autoregressive models in this article we propose a new class of models for nonlinear time series analysis investigate properties of the proposed model and suggest a modeling procedure for building such a model the proposed modeling procedure makes use of ideas from both parametric and nonparametric statistics a consistency result is given to support the procedure for illustration we apply the proposed model and procedure to several data sets and show that the resulting models substantially improve postsample multi step ahead forecasts over other models

fully bayes factors with a generalized g prior for the normal linear model variable selection problem we propose selection criteria based on a fully bayes formulation with a generalization of zellner s g prior which allows for p n a special case of the prior formulation is seen to yield tractable closed forms for marginal densities and bayes factors which reveal new model evaluation characteristics of potential interest

a note on impact factor distribution revisited abstract motivated by huang 2017 we analyze impact factor data in all subject categories for each year from 2010 to 2015 the results are provided by subject categories and by years the two exponent distribution due to mansilla et al 2007 and the normal distribution are shown to give the best fits for the data sets the best fits are assessed in terms of probability plots quantile plots and five other criteria

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

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

frequentist model average estimators the traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance without acknowledging the additional uncertainty introduced by model selection this often means underreporting of variability and too optimistic confidence intervals we build a general large sample likelihood apparatus in which limiting distributions and risk properties of estimators post selection as well as of model average estimators are precisely described also explicitly taking modeling bias into account this allows a drastic reduction in complexity as competing model averaging schemes may be developed discussed and compared inside a statistical prototype experiment where only a few crucial quantities matter in particular we offer a frequentist view on bayesian model averaging methods and give a link to generalized ridge estimators our work also leads to new model selection criteria the methods are illustrated with real data applications

model averaging by jackknife criterion in models with dependent data abstract the past decade witnessed a literature on model averaging by frequentist methods for the most part the asymptotic optimality of various existing frequentist model averaging estimators has been established under i i d errors recently hansen and racine hansen b e racine j 2012 jackknife model averaging journal of econometrics 167 38 46 developed a jackknife model averaging jma estimator which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors in this paper we broaden hansen and racine s scope of analysis to encompass models with i a non diagonal error covariance structure and ii lagged dependent variables thus allowing for dependent data we show that under these set ups the jma estimator is asymptotically optimal by a criterion equivalent to that used by hansen and racine a monte carlo study demonstrates the finite sample performance of the jma estimator in a variety of model settings

consistent model specification tests for time series econometric models in this paper we consider general hypothesis testing problems for nonparametric and semiparametric time series econometric models we apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model the proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses we also discuss the problems of testing portfolio conditional mean variance efficiency and testing a semiparametric single index model monte carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

twenty one ml estimators for model selection classical approaches to determine a suitable model structure from observed input output data are based on hypothesis tests and information based criteria recently the model structure has been considered as a stochastic variable and standard estimation techniques have been proposed the resulting estimators are closely related to the aforementioned methods however it turns out that there are a number of prior choices in the problem formulation which are crucial for the estimators behavior the contribution of this paper is to clarify the role of the prior choices to examine a number of possibilities and to show which estimators are consistent this is done in a linear regression framework for autoregressive models we also investigate a novel prior assumption on stability and give the estimator for the model order and the parameters themselves

exploring the model space and ranking a best class of models in surface wave dispersion inversion application at european strong motion sites abstractthe inversion of surface wave dispersion curve to derive shear wave velocity profile is a very delicate process dealing with a nonunique problem which is strongly dependent on the model space parameterization when independent and reliable information is not available the selection of most representative models within the ensemble produced by the inversion is often difficult we implemented a strategy in the inversion of dispersion curves able to investigate the influence of the parameterization of the model space and to select a best class of models we analyzed surface wave dispersion curves measured at 14 european strong motion sites within the neries ec project we focused on the inversion task exploring the model space by means of four distinct parameterization classes composed of layers progressively added over a half space the classes differ in the definition of the shear wave velocity profile we considered models with uniform velocity as well as models with increasing velocity with d

bias of the corrected aic criterion for underfitted regression and time series models summary the akaike information criterion aic akaike 1973 and a bias corrected version aicc sugiura 1978 hurvich tsai 1989 are two methods for selection of regression and autoregressive models both criteria may be viewed as estimators of the expected kullback leibler information the bias of aic and aicc is studied in the underfitting case where none of the candidate models includes the true model shibata 1980 1981 parzen 1978 both normal linear regression and autoregressive candidate models are considered the bias of aicc is typically smaller often dramatically smaller than that of aic a simulation study in which the true model is an infinite order autoregression shows that even in moderate sample sizes aicc provides substantially better model selections than aic

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

properties and estimation of asymmetric exponential power distribution the new distribution class asymmetric exponential power distribution aepd proposed in this paper generalizes the class of skewed exponential power distributions sepd in a way that in addition to skewness introduces different decay rates of density in the left and right tails our parametrization provides an interpretable role for each parameter we derive moments and moment based measures skewness kurtosis expected shortfall it is demonstrated that a maximum entropy property holds for the aepd distributions we establish consistency asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix where the results apply to the sepd class they enlarge on the current literature also we give a convenient stochastic representation of the distribution our monte carlo study illustrates the theoretical results we also provide some empirical evidence for the usefulness of employing aepd errors in garch type models for predicting downside market risk of financial assets

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

vector autoregressive models a gini approach abstract in this paper it is proven that the usual var models may be performed in the gini sense that is on a l 1 metric space the gini regression is robust to outliers as a consequence when data are contaminated by extreme values we show that semi parametric var gini regressions may be used to obtain robust estimators the inference about the estimators is made with the l 1 norm also impulse response functions and gini decompositions for prevision errors are introduced finally granger s causality tests are properly derived based on u statistics

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

on a doubly nonlinear model for the evolution of damaging in viscoelastic materials we consider a model describing the evolution of damage in visco elastic materials where both the stiffness and the viscosity properties are assumed to degenerate as the damaging is complete the equation of motion ruling the evolution of macroscopic displacement is hyperbolic the evolution of the damage parameter is described by a doubly nonlinear parabolic variational inclusion due to the presence of two maximal monotone graphs involving the phase parameter and its time derivative existence of a solution is proved in some subinterval of time in which the damage process is not complete uniqueness is established in the case when one of the two monotone graphs is assumed to be lipschitz continuous

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

hybridization of intelligent techniques and arima models for time series prediction traditionally the autoregressive moving average arma model has been one of the most widely used linear models in time series prediction recent research activities in forecasting with artificial neural networks anns suggest that anns can be a promising alternative to the traditional arma structure these linear models and anns are often compared with mixed conclusions in terms of the superiority in forecasting performance in this paper we propose a hybridization of intelligent techniques such as anns fuzzy systems and evolutionary algorithms so that the final hybrid arima ann model could outperform the prediction accuracy of those models when used separately more specifically we propose the use of fuzzy rules to elicit the order of the arma or arima model without the intervention of a human expert and the use of a hybrid arima ann model that combines the advantages of the easy to use and relatively easy to tune arima models and the computational power of anns

strong optimality of the normalized ml models as universal codes and information in data we show that the normalized maximum likelihood nml distribution as a universal code for a parametric class of models is closest to the negative logarithm of the maximized likelihood in the mean code length distance where the mean is taken with respect to the worst case model inside or outside the parametric class we strengthen this result by showing that when the data generating models are restricted to be the most benevolent ones in that they incorporate all the constraints in the data and no more the bound cannot be beaten in essence by any code except when the mean is taken with respect to the data generating models in a set of vanishing size these results allow us to decompose the code of the data into two parts the first having all the useful information in the data that can be extracted with the family in question and the rest which has none and we obtain a measure for the useful information in data

bootstrap choice of estimators in parametric and semiparametric families an extension of eic ishiguro sakamoto et kitagawa 1997 ont propose le eic comme une extension du critere d akaike aic le eic est construit en corrigeant le biais de la log vraisemblance consideree comme un estimateur de l information de kullback leibler par la technique du bootstrap nous developpons ce critere dans un cadre d estimation semi parametrique multivarie et nous montrons qu il peut etre utilise pour choisir un estimateur parmi une famille d estimateurs parametriques et semi parametriques une etude de simulation basee sur un modele de regression montre que l eic est meilleur que les criteres usuels bien que la validation croisee appliquee a la vraisemblance donne des resulats tres proches sauf dans le cas d echantillons de faible taille nous avons applique le eic afin d estimer l evolution moyenne de la charge virale d enfants infectes par le vih

maximum likelihood estimation analysis and applications of exponential polynomial signals we model complex signals by approximating the phase and the logarithm of the time varying amplitude of the signal as a finite order polynomial we refer to a signal that has this form as an exponential polynomial signal eps we derive an iterative maximum likelihood ml estimation algorithm to estimate the unknown parameters of the eps model the initialization of the ml algorithm can be performed by using the result of a related paper a statistical analysis of the ml algorithm is performed using a finite order taylor expansion of the mean squared error mse of the estimate about the variance of the additive noise this perturbation analysis gives a method of predicting the mse of the estimate for any choice of the signal parameters the mse from the perturbation analysis is compared with the mse from a monte carlo simulation and the cramer rao bound crb the crb for this model is also derived

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

is there an optimal forecast combination abstract we consider several geometric approaches for combining forecasts in large samples a simple eigenvector approach a mean corrected eigenvector and trimmed eigenvector approach we give conditions where geometric approach yields identical result as the regression approach we also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination monte carlos are conducted to compare the finite sample performance of these and some popular forecast combination and information combination methods and to shed light on the issues of forecast combination vs information combination we also try to shed light on whether there exists an optimal forecast combination method by comparing various forecast combination methods to predict us real output growth rate and excess equity premium

computation of the exact information matrix of gaussian time series with stationary random components the paper presents an algorithm for efficient recursive computation of the fisher information matrix of gaussian time series whose random components are stationary and whose means and covariances are functions of a parameter vector the algorithm is first developed in a general framework and then specialized to the case of autoregressive moving average processes with possible additive white noise the asymptotic behavior of the algorithm is explored and a termination criterion is derived finally the algorithm is used to demonstrate the behavior of the exact cramer rao bound for unbiased estimates for some arma processes as a function of the number of data points it is shown that for processes with zeros near the unit circle and short data records the exact cramer rao bound differs dramatically from its common approximation based on asymptotic theory

extended aic model based on high order moments and its application in the financial market abstract in this paper an extended method of traditional akaike information criteria aic is proposed to detect the volatility of time series by combining it with higher order moments such as skewness and kurtosis since measures considering higher order moments are powerful in many aspects the properties of asymmetry and flatness can be observed furthermore in order to reduce the effect of noise and other incoherent features we combine the extended aic algorithm with multiscale wavelet analysis in which the newly extended aic algorithm is applied to wavelet coefficients at several scales and the time series are reconstructed by wavelet transform after that we create aic planes to derive the relationship among aic values using variance skewness and kurtosis respectively when we test this technique on the financial market the aim is to analyze the trend and volatility of the closing price of stock indices and classify them and we also adapt multiscale analysis to measure complexity of time series over a range of scales empirical results show that the singularity of time series in stock market can be detected via extended aic algorithm

accumulated prediction errors information criteria and optimal forecasting for autoregressive time series the predictive capability of a modification of rissanen s accumulated prediction error ape criterion ape n is investigated in infinite order autoregressive ar oo models instead of accumulating squares of sequential prediction errors from the beginning ape n is obtained by summing these squared errors from stage n n where n is the sample size and 1 n n 1 1 n may depend on n under certain regularity conditions an asymptotic expression is derived for the mean squared prediction error mspe of an ar predictor with order determined by ape n this expression shows that the prediction performance of ape n can vary dramatically depending on the choice of n another interesting finding is that when n approaches 1 at a certain rate ape n can achieve asymptotic efficiency in most practical situations an asymptotic equivalence between ape n and an information criterion with a suitable penalty term is also established from the mspe point of view this offers new perspectives for understanding the information and prediction based model selection criteria finally we provide the first asymptotic efficiency result for the case when the underlying ar oo model is allowed to degenerate to a finite autoregression

forecasting seasonal time series based on fuzzy techniques abstract this paper is devoted to a method for the forecasting of seasonal time series the core of our approach is based on the fuzzy transform and fuzzy natural logic fnl techniques under the assumption that a time series can be additively decomposed into a trend cycle a seasonal component and an irregular fluctuation the forecasting is a combination of individual forecasting of each of these constituents more precisely the trend cycle and the seasonal component are predicted with the help of fuzzy transform pattern recognition and fuzzy natural logic techniques to model the irregular component we apply the box jenkins approach in the paper we compare the suggested method with two other well known methods namely stl see 14 and arima ones

exact sensitivity matrix and influence of the number of pilot points in the geostatistical inversion of moment equations of groundwater flow received 3 august 2009 revised 12 july 2010 accepted 21 july 2010 published 4 november 2010 1 we present novel equations for the exact sensitivity matrix of the ensemble mean hydraulic head under steady state groundwater flow conditions these equations are embedded in a geostatistical inverse procedure to condition approximations of stochastic moment equations of flow on measured hydraulic conductivities and heads our formulation allows considerable improvement of the methodology proposed by hernandez et al 2003 2006 and renders the inversion of moment equations feasible for a large number of unknown hydraulic parameters the spatial distribution of the natural logarithm y of conductivity is parameterized within the pilot points framework whereas prior values of y at pilot points are obtained by a variant of kriging posterior estimates at pilot points are obtained through a maximum likelihood fit of computed to measured heads the maximum likelihood function also includes a regularization term by means of a synthetic example and upon adopting formal model information criteria we explore the influence of 1 the number of pilot points and 2 the order of approximation of the governing mean flow equation on our ability to properly estimate the log conductivity and head fields and identify the relative weight of the regularization term and the parameters of the underlying y variogram we find that none of the adopted information criteria can identify the optimum number of pilot points and the plausibility weight and variogram parameters values can be determined by the kashyap s bayesian measure

estimating the order of an autoregressive model using normalized maximum likelihood this paper examines the estimation of the order of an autoregressive model using the minimum description length principle a closed form for an approximation of the parametric complexity of the autoregressive model class is derived by exploiting a relationship between coefficients and partial autocorrelations the parametric complexity over the complete parameter space is found to diverge a model selection criterion is subsequently derived by bounding the parameter space and simulations suggest that it compares well against standard autoregressive order selection techniques in terms of correct order identification and prediction error

is first order vector autoregressive model optimal for fmri data we consider the problem of selecting the optimal orders of vector autoregressive var models for fmri data many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions subjects tasks and experimental designs in addition the classical information criteria ic used e g the akaike ic aic are biased and inappropriate for the high dimensional fmri data typically with a small sample size we examine the mixed results on the optimal var orders for fmri especially the validity of the order one hypothesis by a comprehensive evaluation using different model selection criteria over three typical data types a resting state an event related design and a block design data set with varying time series dimensions obtained from distinct functional brain networks we use a more balanced criterion kullback s ic kic based on kullback s symmetric divergence combining two directed divergences we also consider the bias corrected versions aicc and kicc to improve var model selection in small samples simulation results show better small sample selection performance of the proposed criteria over the classical ones both bias corrected ics provide more accurate and consistent model order choices than their biased counterparts which suffer from overfitting with kicc performing the best results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions particularly from small specific networks such as the resting state default mode network and the task related motor networks whereas low orders close to one but not necessarily one were chosen for the large dimensions of full brain networks

a semi nonparametric estimator of regression discontinuity design with discrete duration outcomes abstract we consider the regression discontinuity rd design with the duration outcome which has discrete support the parameters of policy interest are treatment effects on unconditional duration effect and conditional hazard effect exiting probabilities for each discrete level we propose a novel semi nonparametric estimator which exploits a flexible separability structure of the underlying continuous time duration process simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank the peculiarity is delivered by the nature of the rd estimand and we provide solutions random censoring and competing risks can also be allowed in our framework

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

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

optimal model assessment selection and combination central to statistical theory and application is statistical modeling which typically involves choosing a single model or combining a number of models of different sizes and from different sources whereas model selection seeks a single best modeling procedure model combination combines the strength of different modeling procedures in this article we look at several key issues and argue that model assessment is the key to model selection and combination most important we introduce a general technique of optimal model assessment based on data perturbation thus yielding optimal selection in particular model selection and combination from a frequentist perspective we advocate model combination over a selected subset of modeling procedures because it controls bias while reducing variability hence yielding better performance in terms of the accuracy of estimation and prediction to realize the potential of model combination we develop methodologies for determining the optimal tuning parameter such

a small sample model selection criterion based on kullback s symmetric divergence the kullback information criterion kic is a recently developed tool for statistical model selection kic serves as an asymptotically unbiased estimator of a variant within a constant of the kullback symmetric divergence known also as j divergence between the generating model and the fitted candidate model in this paper a bias correction to kic is derived for linear regression 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 for linear regression models the corrected criterion called kicc is an exactly unbiased estimator of the variant of the kullback symmetric divergence assuming that the true model is correctly specified or overfitted furthermore when applied to polynomial regression and autoregressive time series modeling kicc is found to estimate the model order more accurately than any other asymptotically efficient method finally kicc is tested on real data to forecast foreign currency exchange rate the result is very interesting in comparison to classical techniques

high snr consistent linear model order selection and subset selection high snr consistency of model order selection criteria in linear regression models has attracted a lot of attention in the signal processing community recently it is now known that exponentially embedded family versions of minimum description length etc are high snr consistent however a general framework for high snr consistency in linear regression is still missing this paper fills this gap by deriving necessary and sufficient conditions nscs for model order selection criteria in both known and unknown noise variance situations to be high snr consistent many popular model order selection criteria are proved to be high snr consistent using these nscs we also provide a convergence rate analysis to discriminate between various high snr consistent model order selection criteria a direct application of model order selection techniques to the very important subset selection problem is computationally infeasible this paper establish the high snr consistency of an existing t statistics based index ordering scheme that allows the conversion of a subset selection problem into a model order selection problem combining this index ordering with high snr consistent model order selection criteria leads to a novel subset selection procedure ssp that is numerically shown to outperform existing high snr consistent ssps

selecting a separable parametric spatiotemporal covariance structure for longitudinal imaging data longitudinal imaging studies allow great insight into how the structure and function of a subject s internal anatomy changes over time unfortunately the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation the temporal from the repeated measures and the spatial from the outcomes of interest being observed at multiple points in a patients body we propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data the model makes use of spatial exponential spherical and matern and temporal compound symmetric autoregressive 1 toeplitz and unstructured parametric correlation functions a simulation study inspired by a longitudinal cardiac imaging study on mitral regurgitation patients compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on type i and ii error rates for inference on fixed effects when the specified model is incorrect information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures misspecification of the covariance structure was found to have the ability to inflate the type i error or have an overly conservative test size which corresponded to decreased power an example with clinical data is given illustrating how the covariance structure procedure can be done in practice as well as how covariance structure choice can change inferences about fixed effects

wavelet based estimation of a semiparametric generalized linear model of fmri time series addresses the problem of detecting significant changes in fmri time series that are correlated to a stimulus time course this paper provides a new approach to estimate the parameters of a semiparametric generalized linear model of the fmri time series the fmri signal is described as the sum of two effects a smooth trend and the response to the stimulus the trend belongs to a subspace spanned by large scale wavelets the wavelet transform provides an approximation to the karhunen loeve transform for the long memory noise and we have developed a scale space regression that permits one to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend in order to demonstrate that our approach outperforms the state of the art detrending technique we evaluated our method against a smoothing spline approach experiments with simulated data and experimental fmri data demonstrate that our approach can infer and remove drifts that cannot be adequately represented with splines

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

bandwidth selection in nonparametric kernel testing we propose a sound approach to bandwidth selection in nonparametric kernel testing the main idea is to find an edgeworth expansion of the asymptotic distribution of the test concerned due to the involvement of a kernel bandwidth in the leading term of the edgeworth expansion we are able to establish closed form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions for example when a significance level is given we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level both asymptotic theory and methodology are established in addition we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example

weak solutions to the penrose fife phase field model for a class of admissible heat flux laws abstract this paper is concerned with a thermodynamically consistent model for diffusive phase transitions proposed by penrose and fife the model has recently received a good deal of attention and the related initial boundary value problems have been investigated from the mathematical point of view in the case where the order parameter is not conserved the common working assumption for the heat flow was that such a flux is proportional to the gradient of the inverse absolute temperature this position seems to be helpful for the analysis due to the coupling term in the phase field equation which depends right on the inverse temperature here we prove the existence of weak solutions in a wide setting of constitutive laws for the heat flux different from the previous ones and considerably more significant owing to their behaviour for high temperatures we also discuss the limiting situation of zero interfacial energy for the order parameter

functional coefficient regression models for nonlinear time series abstract the local linear regression technique is applied to estimation of functional coefficient regression models for time series data the models include threshold autoregressive models and functional coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross validatory estimation for the expected forecasting errors the proposed methodology is data analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality the asymptotic properties of the proposed estimators are investigated under the mixing condition both simulated and real data examples are used for illustration

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

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

variable selection with incomplete covariate data summary application of classical model selection methods such as akaike s information criterion aic becomes problematic when observations are missing in this article we propose some variations on the aic which are applicable to missing covariate problems the method is directly based on the expectation maximization em algorithm and is readily available for em based estimation methods without much additional computational efforts the missing data aic criteria are formally derived and shown to work in a simulation study and by application to data on diabetic retinopathy

evaluating frequency wise directed connectivity of bold signals applying relative power contribution with the linear multivariate time series models in this article we propose a statistical method to evaluate directed interactions of functional magnetic resonance imaging fmri data the multivariate autoregressive mar model was combined with the relative power contribution rpc in this analysis the mar model was fitted to the data to specify the direction of connections and the rpc quantifies the strength of connections as the rpc is computed in the frequency domain we can evaluate the connectivity for each frequency component from this we can establish whether the specified connections represent low or high frequency connectivity which cannot be examined solely using the estimated mar coefficients we applied this analysis method to fmri data obtained during visual motion tasks confirming previous reports of bottom up connectivity around the frequency corresponding to the block experimental design furthermore we used the mar model with exogenous variables marx to extend our understanding of these data and to show how the input to v1 transfers to higher cortical areas