tracer model identification using artificial neural networks 1 the derivation of transport parameters from tracer tests conducted in geothermal systems will depend strongly on the conceptual and mathematical model that is fitted to the data depending on the model employed the estimation of transport parameters porosity and dispersivity of the fracture network porosity of the matrix may result in a significant variation in dispersivity if the results from such tracer tests are to be used in parameter selection for larger scale models it is crucial that the tracer test is itself interpreted with an appropriate model in order to tackle this problem artificial neural network ann technology is proposed a dual layer neural network model was trained using synthetic tracer test data generated using analytical one dimensional homogeneous double porosity pseudosteady state multifracture and fracture matrix models the developed model was then used to identify several actual tracer tests conducted in various geothermal reservoirs reported in the literature in most cases it was observed that the model successfully identified a wide variety of reservoir models in some cases the model decreased the number possible models to two it was also observed that ann results were in accord with least squares analysis

component selection and smoothing in multivariate nonparametric regression we propose a new method for model selection and model fitting in multivariate nonparametric regression models in the framework of smoothing spline anova the cosso is a method of regularization with the penalty functional being the sum of component norms instead of the squared norm employed in the traditional smoothing spline method the cosso provides a unified framework for several recent proposals for model selection in linear models and smoothing spline anova models theoretical properties such as the existence and the rate of convergence of the cosso estimator are studied in the special case of a tensor product design with periodic functions a detailed analysis reveals that the cosso does model selection by applying a novel soft thresholding type operation to the function components we give an equivalent formulation of the cosso estimator which leads naturally to an iterative algorithm we compare the cosso with mars a popular method that builds functional anova models in simulations and real examples the cosso method can be extended to classification problems and we compare its performance with those of a number of machine learning algorithms on real datasets the cosso gives very competitive performance in these studies

generalized point interactions in one dimensional quantum mechanics there is a four parameter family of point interactions in one dimensional quantum mechanics they represent all possible self adjoint extensions of the kinetic energy operator if time reversal invariance is imposed the number of parameters is reduced to three one of these point interactions is the familiar function potential but the other generalized ones do not seem to be widely known we present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so called interaction we emphasize that there is little resemblance between the interaction and what its name suggests

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

efficient empirical bayes variable selection and estimation in linear models we propose an empirical bayes method for variable selection and coefficient estimation in linear regression models the method is based on a particular hierarchical bayes formulation and the empirical bayes estimator is shown to be closely related to the lasso estimator such a connection allows us to take advantage of the recently developed quick lasso algorithm to compute the empirical bayes estimate and provides a new way to select the tuning parameter in the lasso method unlike previous empirical bayes variable selection methods which in most practical situations can be implemented only through a greedy stepwise algorithm our method gives a global solution efficiently simulations and real examples show that the proposed method is very competitive in terms of variable selection estimation accuracy and computation speed compared with other variable selection and estimation methods

on the non negative garrotte estimator summary we study the non negative garrotte estimator from three different aspects consistency computation and flexibility we argue that the non negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form in particular we consider using the lasso the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non negative garrotte we prove that the non negative garrotte has the nice property that with probability tending to 1 the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables whereas such a property may not be valid for the initial estimators in general we show that the non negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection we also show that the non negative garrotte has a piecewise linear solution path using this fact we propose an efficient algorithm for computing the whole solution path for the non negative garrotte simulations and a real example demonstrate that the non negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy

a new effective mass hamiltonian and associated lame equation bound states a new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wavefunctions are derived it is shown that in a mapping to an auxiliary constant mass schrodinger picture one obtains one period associated lame well bounded by two wells or barriers depending on the values of the ordering parameter the results for bound states of this new solvable model are provided for a wide variation of the parameters

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

inference after model selection typical modeling strategies involve model selection which has a significant effect on inference of estimated parameters common practice is to use a selected model ignoring uncertainty introduced by the process of model selection this could yield overoptimistic inferences resulting in false discovery in this article we develop a general methodology via optimal approximation for estimating the mean and variance of complex statistics that involve the process of model selection this allows us to make approximately unbiased inferences taking into account the selection process we examine the operating characteristics of the proposed methodology via asymptotic analyses and simulations these results show that the proposed methodology yields correct inferences and outperforms common alternatives

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

distribution theory for discontinuous test functions and differential operators with generalized coefficients investigation of the differential operators with the generalized coefficients having singular support on a disjoint set of points requires the consideration of the distribution theory with the set of discontinuous test functions such a distribution theory for test functions having discontinuity at one point is developed a four parameter family of schrodinger operators formed by the operators with singular potential singular metrics and singular gauge field is considered it is proved that this family of singular interactions describes all possible selfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point approximation by operators with smooth coefficients is discussed c 1996 academic press inc

probability inequalities for empirical processes and a law of the iterated logarithm given a class f of functions on x we can view vn as a stochastic process indexed by f and consider limit theorems for this process to prove such theorems it is often helpful to have bounds on the tail of the r v sup w i n f i see for example dudley 1978 kuelbs and dudley 1980 dudley and phillip 1983 or gine and zinn 1983 our main question of interest is for what classes f can best possible bounds be obtained so first we must ask what are these best possible bounds of course

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

the estimation of prediction error having constructed a data based estimation rule perhaps a logistic regression or a classification tree the statistician would like to know its performance as a predictor of future cases there are two main theories concerning prediction error 1 penalty methods such as cp akaike s information criterion and stein s unbiased risk estimate that depend on the covariance between data points and their corresponding predictions and 2 cross validation and related nonparametric bootstrap techniques this article concerns the connection between the two theories a rao blackwell type of relation is derived in which nonparametric methods such as cross validation are seen to be randomized versions of their covariance penalty counterparts the model based penalty methods offer substantially better accuracy assuming that the model is believable

hierarchically penalized cox regression with grouped variables summary in many biological and other scientific applications predictors are often naturally grouped for example in biological applications assayed genes or proteins are grouped by biological roles or biological pathways when studying the dependence of survival outcome on these grouped predictors it is desirable to select variables at both the group level and the within group level in this article we develop a new method to address the group variable selection problem in the cox proportional hazards model our method not only effectively removes unimportant groups but also maintains the flexibility of selecting variables within the identified groups we also show that the new method offers the potential for achieving the asymptotic oracle property

nonconcave penalized likelihood with a diverging number of parameters a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by fan and li to simultaneously estimate parameters and select important variables they demonstrated that this class of procedures has an oracle property when the number of parameters is finite however in most model selection problems the number of parameters should be large and grow with the sample size in this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators furthermore the consistency of the sandwich formula of the covariance matrix is demonstrated nonconcave penalized likelihood ratio statistics are discussed and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions the asymptotic results are augmented by a simulation study and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary

discussion of from fixed x to random x regression bias variance decompositions covariance penalties and prediction error estimation rosset and tibshirani are to be congratulated for addressing an important yet under studied topic of modern statistics so called random x prediction in regression analysis in statistics random x

optimal geostatistical model selection in many fields of science predicting variables of interest over a study region based on noisy data observed at some locations is an important problem two popular methods for the problem are kriging and smoothing splines the former assumes that the underlying process is stochastic whereas the latter assumes it is purely deterministic kriging performs better than smoothing splines in some situations but is outperformed by smoothing splines in others however little is known regarding selecting between kriging and smoothing splines in addition how to perform variable selection in a geostatistical model has not been well studied in this article we propose a general methodology for selecting among arbitrary spatial prediction methods based on approximately unbiased estimation of mean squared prediction errors using a data perturbation technique the proposed method accounts for estimation uncertainty in both kriging and smoothing spline predictors and is shown to be optimal in terms of two mean sq

shape optimization of thin walled structures governed by geometrically nonlinear mechanics this paper introduces a structural optimization strategy that combines fe based parametrization with nonlinear kinematics in order to optimize the shape of thin shell structures the optimization is based on gradient based strategies where the required derivatives are formulated by the adjoint approach the applied solution algorithm combines the well known nonlinear path following strategies with the design update procedure of the shape optimization this results in robust and flexible methods that require only a minimum of system evaluations the proposed optimization goals improve the load carrying behavior of the structure and minimize displacements and stresses it is shown that such efficient designs also exhibit an improved limit load this contribution illustrates the application of the proposed method by several shape optimization problems the presented results prove the exceptional performance of the optimized designs even if the optimal design is disturbed by unavoidable imperfections it is shown that the application of nonlinear kinematics in the shape optimization of thin shell structures allows for a much more realistic system response and gradient data the proposed approach is applicable to all kind of optimization strategies like topology sizing or material optimization respectively

minimal penalties for gaussian model selection this paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimiza tion of a penalized least squares type criterion within some general gaussian framework including the classical ones as compared to our previous paper on this topic birge and massart in j eur math soc 3 203 268 2001 more elaborate forms of the penalties are given which are shown to be in some sense optimal we indeed provide more precise upper bounds for the risk of the penalized estimators and lower bounds for the penalty terms showing that the use of smaller penalties may lead to disastrous results these lower bounds may also be used to design a practical strategy that allows to estimate the penalty from the data when the amount of noise is unknown we provide an illustra tion of the method for the problem of estimating a piecewise constant signal in gaussian noise when neither the number nor the location of the change points are known

model free variable selection computing power has encouraged the modelling of data sets of ever increasing size data mining applications in finance marketing and bioinformatics are obvious examples a limitation of nearly all existing variable selection methods is the need to specify the correct model before selection when the number of predictors is large model formulation and validation can be difficult or even infeasible on the basis of the theory of sufficient dimension reduction we propose a new class of model free variable selection approaches the methods proposed assume no model of any form require no nonparametric smoothing and allow for general predictor effects the efficacy of the methods proposed is demonstrated via simulation and an empirical example is given

a delta well with a mass jump in this paper it is shown that a one dimensional hamiltonian with an attractive delta potential at the origin plus a mass jump at the same point cannot have a bound state as is the case with the ordinary attractive delta potential with constant mass unless another term is added into the potential in the form of a derivative of the dirac delta at the origin the consistency of this singular potential with two terms is guaranteed by choosing suitable matching conditions at the singular point for the wavefunctions furthermore it is proved that the self adjointness of the hamiltonian with both singular interactions determines the coefficient of the derivative of the delta in a unique manner under these conditions the bound state and its energy are obtained and it is checked that the correct results in the limit of equal masses are obtained

the covariance inflation criterion for adaptive model selection we propose a new criterion for model selection in prediction problems the covariance inflation criterion adjusts the training error by the average covariance of the predictions and responses when the prediction rule is applied to permuted versions of the data set this criterion can be applied to general prediction problems e g regression or classification and to general prediction rules e g stepwise regression tree based models and neural nets as a by product we obtain a measure of the effective number of parameters used by an adaptive procedure we relate the covariance inflation criterion to other model selection procedures and illustrate its use in some regression and classification problems we also revisit the conditional bootstrap approach to model selection

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

preconditioning for feature selection and regression in high dimensional problems we consider regression problems where the number of predictors greatly exceeds the number of observations we propose a method for variable selection that first estimates the regression function yielding a preconditioned response variable the primary method used for this initial regression is supervised principal components then we apply a standard procedure such as forward stepwise selection or the lasso to the preconditioned response variable in a number of simulated and real data examples this two step procedure outperforms forward stepwise selection or the usual lasso applied directly to the raw outcome we also show that under a certain gaussian latent variable model application of the lasso to the preconditioned response variable is consistent as the number of predictors and observations increases moreover when the observational noise is rather large the suggested procedure can give a more accurate estimate than lasso we illustrate our method on some real problems including survival analysis with microarray data

penalized model based clustering with application to variable selection variable selection in clustering analysis is both challenging and important in the context of model based clustering analysis with a common diagonal covariance matrix which is especially suitable for high dimension low sample size settings we propose a penalized likelihood approach with an l1 penalty function automatically realizing variable selection via thresholding and delivering a sparse solution we derive an em algorithm to fit our proposed model and propose a modified bic as a model selection criterion to choose the number of components and the penalization parameter a simulation study and an application to gene function prediction with gene expression profiles demonstrate the utility of our method

adaptive model selection and assessment for exponential family distributions in many scientific and engineering problems selecting the optimal model from a large pool of candidate models is important particularly in data mining in the literature model assessment in the context of nonnormal distributions has not yet received a lot of attention indeed many existing model selection criteria such as the bayes information criterion and cp may not be suitable for a situation in which the conditional mean and variance of the response are dependent such as in generalized linear model regression in this article we propose a new adaptive model selection criterion and construct an approximately unbiased kullback leibler loss estimator for model assessment in the context of exponential family distributions this permits comparing any arbitrary complex modeling procedures our proposal uses a concept called generalized degrees of freedom that generalizes the concept originally proposed for the normal distribution the proposed procedure is implemented for the binomial and poisson distr

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

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

simultaneous grouping pursuit and feature selection over an undirected graph in high dimensional regression grouping pursuit and feature selection have their own merits while complementing each other in battling the curse of dimensionality to seek a parsimonious model we perform simultaneous grouping pursuit and feature selection over an arbitrary undirected graph with each node corresponding to one predictor when the corresponding nodes are reachable from each other over the graph regression coefficients can be grouped whose absolute values are the same or close this is motivated from gene network analysis where genes tend to work in groups according to their biological functionalities through a nonconvex penalty we develop a computational strategy and analyze the proposed method theoretical analysis indicates that the proposed method reconstructs the oracle estimator that is the unbiased least square estimator given the true grouping leading to consistent reconstruction of grouping structures and informative features as well as to optimal parameter estimation sim

two point one dimensional delta delta prime interactions non abelian addition law and decoupling limit in this contribution to the study of one dimensional point potentials we prove that if we take the limit on a potential of the type we obtain a new point potential of the type when u0 and u1 are related to v0 v1 w0 and w1 by a law with the structure of a group this is the borel subgroup of we also obtain the non abelian addition law from the scattering data the spectra of the hamiltonian in the decoupling cases emerging in the study are also described in full it is shown that for the values of the couplings the singular kurasov matrices become equivalent to dirichlet at one side of the point interaction and robin boundary conditions at the other side

towards data driven selection of a penalty function for data driven neyman tests the data driven neyman statistic consists of two elements a score statistic in a finite dimensional submodel and a selection rule to determine the best fitted submodel for instance schwarz bic and akaike aic rules are often applied in such constructions for moderate sample sizes aic is sensitive in detecting complex models while bic works well for relatively simple structures when the sample size is moderate the choice of selection rule for determining a best fitted model from a number of models has a substantial influence on the power of the related data driven neyman test this paper proposes a new solution in which the type of penalty aic or bic is chosen on the basis of the data the resulting refined data driven test combines the advantages of these two selection rules

regularized finite mixture models for probability trajectories finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time in practice trajectories are usually modeled as polynomials which may fail to capture important features of the longitudinal pattern focusing on dichotomous response measures we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates we show how parameter estimation and inference for whether trajectories are time invariant linear time varying or nonlinear time varying can be carried out for such models to illustrate the method we use simulation studies and data from a long term longitudinal study of children at high risk for substance abuse

variable selection for model based high dimensional clustering and its application to microarray data variable selection in high dimensional clustering analysis is an important yet challenging problem in this article we propose two methods that simultaneously separate data points into similar clusters and select informative variables that contribute to the clustering our methods are in the framework of penalized model based clustering unlike the classical l1 norm penalization the penalty terms that we propose make use of the fact that parameters belonging to one variable should be treated as a natural group numerical results indicate that the two new methods tend to remove noninformative variables more effectively and provide better clustering results than the l1 norm approach

parametric or nonparametric a parametricness index for model selection in model selection literature two classes of criteria perform well asymptotically in different situations bayesian information criterion bic as a representative is consistent in selection when the true model is finite dimensional parametric scenario akaike s information criterion aic performs well in an asymptotic efficiency when the true model is infinite dimensional nonparametric scenario but there is little work that addresses if it is possible and how to detect the situation that a specific model selection problem is in in this work we differentiate the two scenarios theoretically under some conditions we develop a measure parametricness index pi to assess whether a model selected by a potentially consistent procedure can be practically treated as the true model which also hints on aic or bic is better suited for the data for the goal of estimating the regression function a consequence is that by switching between aic and bic based on the pi the resulting regression estimator is simultaneously asymptotically efficient for both parametric and nonparametric scenarios in addition we systematically investigate the behaviors of pi in simulation and real data and show its usefulness

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 proximal iteration for deconvolving poisson noisy images using sparse representations we propose an image deconvolution algorithm when the data is contaminated by poisson noise the image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms our key contributions are as follows first we handle the poisson noise properly by using the anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive gaussian noise second the deconvolution problem is formulated as the minimization of a convex functional with a data fidelity term reflecting the noise properties and a nonsmooth sparsity promoting penalty over the image representation coefficients e g lscr1 norm an additional term is also included in the functional to ensure positivity of the restored image third a fast iterative forward backward splitting algorithm is proposed to solve the minimization problem we derive existence and uniqueness conditions of the solution and establish convergence of the iterative algorithm finally a gcv based model selection procedure is proposed to objectively select the regularization parameter experimental results are carried out to show the striking benefits gained from taking into account the poisson statistics of the noise these results also suggest that using sparse domain regularization may be tractable in many deconvolution applications with poisson noise such as astronomy and microscopy

adaptive model selection most model selection procedures use a fixed penalty penalizing an increase in the size of a model these nonadaptive selection procedures perform well only in one type of situation for instance bayesian information criterion bic with a large penalty performs well for small models and poorly for large models and akaike s information criterion aic does just the opposite this article proposes an adaptive model selection procedure that uses a data adaptive complexity penalty based on a concept of generalized degrees of freedom the proposed procedure combining the benefit of a class of nonadaptive procedures approximates the best performance of this class of procedures across a variety of different situations this class includes many well known procedures such as aic bic mallows s cp and risk inflation criterion ric the proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression simulation results and an asymptotic

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

efficient estimation of semiparametric multivariate copula models we propose a sieve maximum likelihood estimation procedure for a broad class of semiparametric multivariate distributions a joint distribution in this class is characterized by a parametric copula function evaluated at nonparametric marginal distributions this class of distributions has gained popularity in diverse fields due to its flexibility in separately modeling the dependence structure and the marginal behaviors of a multivariate random variable and its circumvention of the curse of dimensionality associated with purely nonparametric multivariate distributions we show that the plug in sieve maximum likelihood estimators mles of all smooth functionals including the finite dimensional copula parameters and the unknown marginal distributions are semiparametrically efficient and that their asymptotic variances can be estimated consistently moreover prior restrictions on the marginal distributions can be easily incorporated into the sieve maximum likelihood estimation procedure to achieve fu

ejiim for the stationary schrodinger equations with delta potential wells we investigate the bound state problems for the 1d stationary schrodinger equations with a class of singular potentials i e the delta potential wells by using the explicit jump immersed interface method ejiim either in the single delta case or in the double delta case numerical results show the feasibility efficiency and convergence of ejiim with applications to the eigenvalue problems just as to numerous boundary value and initial boundary value differential equations comparisons with peskin s ib method reveal the superiority of ejiim in calculating the bound eigenfunctions and particularly the corresponding eigenvalues for the stationary schrodinger equations