MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe~cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.     

Control charts based on randomized quantile residuals

In practice, quality characteristics do not always follow a normal distribution, and quality control processes sometimes generate non‐normal response outcomes, including continuous non‐normal data and discrete count data. Thus, achieving better results in such situations requires a new control chart derived from various types of response variables. This study proposes a procedure for monitoring response variables that uses control charts based on randomized quantile residuals obtained from a fitted regression model. Simulation studies demonstrate the performance of the proposed control charts under various situations. We illustrate the procedure using two real‐data examples, based on normal and negative binomial regression models, respectively. The simulation and real‐data results support our proposed procedure.     

Model selection of copulas: AIC versus a cross validation copula information criterion

Akaike Information Criterion (AIC) is frequently employed in the semiparametric setting of selection of copula models, even though as a model selection tool it was developed in a parametric setting. Recently a Copula Information Criterion (CIC) has been especially designed for copula model selection. In this paper we examine the two approaches and present a simulation study where the performance of a cross-validated version of CIC is compared with the AIC criterion. Only minor differences are observed.     

Model selection via information criteria

Summary This is a survey of the information criterion approach to model selection problems. New results about context tree estimation and the estimation of the basic neighborhood of Markov random fields are also mentioned.     

A new method of solving the coefficient inverse problem

This paper is concerned with the new method for solving the coefficient inverse problem in the reproducing kernel space. It is different from the previous studies. This method gives accurate results and shows that it is valid by the numerical example.     

Vector valued bilinear maximal operator and method of rotations

In this paper we obtain a bilinear analogue of Fefferman-Stein?s vector valued inequality for classical Hardy-Littlewood maximal function. Also, we prove the boundedness of bilinear Hardy-Littlewood maximal operator from Lp₁(Rn)×Lp₂(Rn)→L¹(Rn), where , by applying the method of rotations.     

Model detection and variable selection for varying coefficient models with longitudinal data

In this paper, we consider the problem of variable selection and model detection in varying coefficient models with longitudinal data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.     

Conditional information for an inverse Gaussian distribution with known coefficient of variation

Conditional inference about a mean of an inverse Gaussian distribution with known coefficient of variation is discussed. For a random sample from the distribution, sufficient statistics with respect to the mean parameter include an ancillary statistic. The effects of conditioning on the ancillary statistic are investigated. It is shown that the model provides a good illustration of R. A. Fisher's recommendation concerning use of the observed second derivative of the log likelihood function in normal approximations.This work was started while Ksei Iwase was visiting the Institute of Statistical Mathematics in Spring, 1987, and was partly supported by the ISM Cooperative Research Program (88-ISM·CRP-7), and by Scientific Research Fund No. 62540173 from the Ministry of Education, Science and Culture of Japan.     

Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment

A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under intuitionistic fuzzy environment for some situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a set of criteria represented by intuitionistic fuzzy sets (IFSs), we establish an entropy weight model, which can be used to get the criteria weights, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the weighted correlation coefficients. Finally, two illustrative examples demonstrate the practicality and effectiveness of the proposed method.     

A proximal point method for the sum of maximal monotone operators

In this paper, we concentrate on the maximal inclusion problem of locating the zeros of the sum of maximal monotone operators in the framework of proximal point method. Such problems arise widely in several applied mathematical fields such as signal and image processing. We define two new maximal monotone operators and characterize the solutions of the considered problem via the zeros of the new operators. The maximal monotonicity and resolvent of both of the defined operators are proved and calculated, respectively. The traditional proximal point algorithm can be therefore applied to the considered maximal inclusion problem, and the convergence is ensured. Furthermore, by exploring the relationship between the proposed method and the generalized forward‐backward splitting algorithm, we point out that this algorithm is essentially the proximal point algorithm when the operator corresponding to the forward step is the zero operator. Copyright © 2013 John Wiley & Sons, Ltd.     

An asymptotic method for calculating limits of maximal means

For a continuous almost periodic function , we show that the function

Evaluation of diffusion coefficient based on multiple forward solutions

This note is concerned with the identification of the unknown diffusion coefficient for a parabolic equation. It introduces an iterative algorithm that can be used to recover the unknown function. The algorithm assumes an initial guess for the unknown function and obtains a background field. It obtains an equation for the error field. It then formulates three forward problems for the error field. These three formulations share the same unknown function which is the correction to the assumed value of the unknown diffusion coefficient. By equating the responses of these three formulations, the algorithm obtains two working equations for the unknown function. A number of numerical examples are also used to study the performance of the algorithm.     

基于直觉模糊规划的多目标投资组合选择模型

将直觉模糊集合的概念引入投资组合模型中,并将多目标投资组合模型中的收益、方差和偏度三个目标模糊化,用隶属函数与非隶属函数作为新的目标函数.针对该模糊多目标投资组合模型,提出了一个动态遗传算法,算例给出了该模型的一个实例的最优解.     

Spherical maximal operator on symmetric spaces of constant curvature

We prove an endpoint weak-type maximal inequality for the spherical maximal operator applied to radial funcions on symmetric spaces of constant curvature and dimension . More explicitly, in the Lorentz space associated with the natural isometry-invariant measure, we show that, for every radial function ,

The proof uses only geometric arguments and volume estimates, and applies uniformly in every dimension.

     

Global statistical information in exponential experiments and selection of exponential models

The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion.     

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

We will prove that for 1相似文献   

Two versions of the Nikodym maximal function on the Heisenberg group

The classical Nikodym maximal function on the Euclidean plane R² is defined as the supremum over averages over rectangles of eccentricity N; its operator norm in L²(R²) is known to be O(logN). We consider two variants, one on the standard Heisenberg group H¹ and the other on the polarized Heisenberg group . The latter has logarithmic L² operator norm, while the former has the L² operator norm which grows essentially of order O(N1/4). We shall imbed these two maximal operators in the family of operators associated to the hypersurfaces {(x₁,x₂,αx₁x₂)} in the Heisenberg group H¹ where the exceptional blow up in N occurs when α=0.     

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