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By
Li, Weiming
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1 Citations
This paper discusses the relationship between the population spectral distribution and the limit of the empirical spectral distribution in highdimensional situations. When the support of the limiting spectral distribution is split into several intervals, the population one gains a meaningful division, and general functional expectations of each part from the division, referred as local expectations, can be formulated as contour integrals around these intervals. Basing on these knowledge we present consistent estimators of the local expectations and prove a central limit theorem for them. The results are then used to analyze an estimator of the population spectral distribution in recent literature.
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By
Gao, Xiaoli
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1 Citations
Existing grouped variable selection methods rely heavily on prior group information, thus they may not be reliable if an incorrect group assignment is used. In this paper, we propose a family of shrinkage variable selection operators by controlling the kth largest norm (KAN). The proposed KAN method exhibits some flexible groupwise variable selection naturally even though no correct prior group information is available. We also construct a group KAN shrinkage operator using a composite of KAN constraints. Neither ignoring nor relying completely on prior group information, the group KAN method has the flexibility of controlling within group strength and therefore can reduce the effect caused by incorrect group information. Finally, we investigate an unbiased estimator of the degrees of freedom for (group) KAN estimates in the framework of Stein’s unbiased risk estimation. Extensive simulation studies and real data analysis are performed to demonstrate the advantage of KAN and group KAN over the LASSO and group LASSO, respectively.
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By
Meintanis, Simos G.; Allison, James; Santana, Leonard
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1 Citations
We investigate the finitesample properties of certain procedures which employ the novel notion of the probability weighted empirical characteristic function. The procedures considered are: (1) Testing for symmetry in regression, (2) Testing for multivariate normality with independent observations, and (3) Testing for multivariate normality of random effects in mixed models. Along with the new tests alternative methods based on the ordinary empirical characteristic function as well as other more well known procedures are implemented for the purpose of comparison.
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Meskaldji, DjalelEddine; Van De Ville, Dimitri; Thiran, JeanPhilippe; Morgenthaler, Stephan
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Over the last two decades, a large variety of type I error rates and control procedures have been proposed in the field of multiple hypotheses testing. This paper proposes a framework that includes many existing proposals by investigating procedures in which the ordered pvalues are compared to an arbitrary positive and nondecreasing threshold sequence. For this case, we derive the error rate being controlled under different assumptions on the pvalues. Our focus will be on stepup procedures. The new formulation gives insight into the relations between existing error rates and opens new perspectives for the whole field of multiple testing.
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By
Li, Zhaoyuan; Yao, Jianfeng
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In this paper, we generalize two criteria, the determinantbased and tracebased criteria proposed by Saranadasa (J Multivar Anal 46:154–174, 1993), to general populations for high dimensional classification. These two criteria compare some distances between a new observation and several different known groups. The determinantbased criterion performs well for correlated variables by integrating the covariance structure and is competitive to many other existing rules. The criterion however requires the measurement dimension be smaller than the sample size. The tracebased criterion, in contrast, is an independence rule and effective in the “large dimensionsmall sample size” scenario. An appealing property of these two criteria is that their implementation is straightforward and there is no need for preliminary variable selection or use of turning parameters. Their asymptotic misclassification probabilities are derived using the theory of large dimensional random matrices. Their competitive performances are illustrated by intensive Monte Carlo experiments and a real data analysis.
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By
Kopčová, Veronika; Žežula, Ivan
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In this paper the growth curve model, with the data correlated according to uniform structure, is considered. It represents a useful statistical model for a variety of areas. Our aim is to present various estimators of unknown variance parameters and compare their statistical properties. In the first part the review of known results for different estimators of
$$\rho $$
and
$$\sigma ^2$$
and their properties is given. The aim is to compare and order these estimators based on biasedness and mean square error.
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By
Wang, Lihong; Wang, Jinde
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In this paper we study the estimation of the spatial long memory parameter for stationary long range dependent random fields using wavelet methods. We first show the relation between the wavelet coefficients of the random fields and its long memory parameter. Based on this relation, we construct a logregression wavelet estimator of the long memory parameter. Under some mild regularity assumptions, the asymptotic properties of the estimators are investigated. Finally, a small simulation study illustrates the method.
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By
Belopolskaya, Yana
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Stochastic differential equations give a constructive way to obtain a large number of stochastic processes. They can be used as well to simulate these processes numerically. As a byproduct we can construct numerically solutions of the Cauchy problem for some parabolic equations and systems. In this paper we derive systems of stochastic equations for stochastic processes underlying systems of coupled parabolic equations which are particular cases of crossdiffusion systems of PDEs. Stochastic processes satisfying these stochastic systems allow to obtain probabilistic representations of classical and weak solutions of the Cauchy problem for original PDE systems and can be used to simulate the PDE solutions.
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By
Li, KimHung; Lau, TaiShing; Zhang, Chongqi
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3 Citations
In this paper we give a sufficient condition under which theDoptimal design for a regression model without an intercept can be obtained from theDoptimal design for the corresponding model with an intercept by simply removing the origin from its support points. Examples are given to demonstrate the applications of the results.
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