Pub Date : 2019-10-23DOI: 10.1142/S2010326319500138
L. Fu, Zhuoran Yang, Mingtao Zhao, Yan Zhou
A popular approach, generalized estimating equations (GEE), has been applied to the multivariate accelerated failure time (AFT) model of the clustered and censored data. However, this method needs to estimate the correlation parameters and calculate the inverse of the correlation matrix. Meanwhile, the efficiency of the parameter estimators is low when the correlation structure is misspecified and/or the marginal distribution is heavy-tailed. This paper proposes using the quadratic inference functions (QIF) with a mixture correlation structure to estimate the coefficients in the multivariate AFT model, which can avoid estimating the correlation parameters and computing the inverse matrix of the correlation matrix. Moreover, the estimator derived from the QIF is consistent and asymptotically normal. Simulation studies indicate that the proposed method outperforms the method based on GEE when the marginal distribution has a heavy tail. Finally, the proposed method is used to analyze a real dataset for illustration.
{"title":"Efficient parameter estimation for multivariate accelerated failure time model via the quadratic inference functions method","authors":"L. Fu, Zhuoran Yang, Mingtao Zhao, Yan Zhou","doi":"10.1142/S2010326319500138","DOIUrl":"https://doi.org/10.1142/S2010326319500138","url":null,"abstract":"A popular approach, generalized estimating equations (GEE), has been applied to the multivariate accelerated failure time (AFT) model of the clustered and censored data. However, this method needs to estimate the correlation parameters and calculate the inverse of the correlation matrix. Meanwhile, the efficiency of the parameter estimators is low when the correlation structure is misspecified and/or the marginal distribution is heavy-tailed. This paper proposes using the quadratic inference functions (QIF) with a mixture correlation structure to estimate the coefficients in the multivariate AFT model, which can avoid estimating the correlation parameters and computing the inverse matrix of the correlation matrix. Moreover, the estimator derived from the QIF is consistent and asymptotically normal. Simulation studies indicate that the proposed method outperforms the method based on GEE when the marginal distribution has a heavy tail. Finally, the proposed method is used to analyze a real dataset for illustration.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86359398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-23DOI: 10.1142/S201032631950014X
Yunlong Wang, Changliang Zou, Zhaojun Wang, G. Yin
Change-point detection is an integral component of statistical modeling and estimation. For high-dimensional data, classical methods based on the Mahalanobis distance are typically inapplicable. We propose a novel testing statistic by combining a modified Euclidean distance and an extreme statistic, and its null distribution is asymptotically normal. The new method naturally strikes a balance between the detection abilities for both dense and sparse changes, which gives itself an edge to potentially outperform existing methods. Furthermore, the number of change-points is determined by a new Schwarz’s information criterion together with a pre-screening procedure, and the locations of the change-points can be estimated via the dynamic programming algorithm in conjunction with the intrinsic order structure of the objective function. Under some mild conditions, we show that the new method provides consistent estimation with an almost optimal rate. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of power and estimation accuracy, and two real data examples are used for illustration.
{"title":"Multiple change-points detection in high dimension","authors":"Yunlong Wang, Changliang Zou, Zhaojun Wang, G. Yin","doi":"10.1142/S201032631950014X","DOIUrl":"https://doi.org/10.1142/S201032631950014X","url":null,"abstract":"Change-point detection is an integral component of statistical modeling and estimation. For high-dimensional data, classical methods based on the Mahalanobis distance are typically inapplicable. We propose a novel testing statistic by combining a modified Euclidean distance and an extreme statistic, and its null distribution is asymptotically normal. The new method naturally strikes a balance between the detection abilities for both dense and sparse changes, which gives itself an edge to potentially outperform existing methods. Furthermore, the number of change-points is determined by a new Schwarz’s information criterion together with a pre-screening procedure, and the locations of the change-points can be estimated via the dynamic programming algorithm in conjunction with the intrinsic order structure of the objective function. Under some mild conditions, we show that the new method provides consistent estimation with an almost optimal rate. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of power and estimation accuracy, and two real data examples are used for illustration.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88141958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-01DOI: 10.1142/s2010326319990016
{"title":"Author index Volume 8 (2019)","authors":"","doi":"10.1142/s2010326319990016","DOIUrl":"https://doi.org/10.1142/s2010326319990016","url":null,"abstract":"","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80654816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-17DOI: 10.1142/s2010326322500149
D. Dai, P. Forrester, Shuai‐Xia Xu
We consider the singular linear statistic of the Laguerre unitary ensemble (LUE) consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generating function for this statistic can be written as a Toeplitz determinant with entries given in terms of particular [Formula: see text] Bessel functions. Earlier studies have identified the same determinant, but with the [Formula: see text] Bessel functions replaced by [Formula: see text] Bessel functions, as relating to the hard edge scaling limit of a generalized gap probability for the LUE, in the case of non-negative integer Laguerre parameter. We show that the Toeplitz determinant formed from an arbitrary linear combination of these two Bessel functions occurs as a [Formula: see text]-function sequence in Okamoto’s Hamiltonian formulation of Painlevé III[Formula: see text], and consequently the logarithmic derivative of both Toeplitz determinants satisfies the same [Formula: see text]-form Painlevé III[Formula: see text] differential equation, giving an explanation of a fact which can be observed from earlier results. In addition, some insights into the relationship between this characterization of the generating function, and its characterization in the [Formula: see text] limit, both with the Laguerre parameter [Formula: see text] fixed, and with [Formula: see text] (this latter circumstance being relevant to an application to the distribution of the Wigner time delay statistic), are given.
{"title":"Applications in random matrix theory of a PIII’ τ-function sequence from Okamoto’s Hamiltonian formulation","authors":"D. Dai, P. Forrester, Shuai‐Xia Xu","doi":"10.1142/s2010326322500149","DOIUrl":"https://doi.org/10.1142/s2010326322500149","url":null,"abstract":"We consider the singular linear statistic of the Laguerre unitary ensemble (LUE) consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generating function for this statistic can be written as a Toeplitz determinant with entries given in terms of particular [Formula: see text] Bessel functions. Earlier studies have identified the same determinant, but with the [Formula: see text] Bessel functions replaced by [Formula: see text] Bessel functions, as relating to the hard edge scaling limit of a generalized gap probability for the LUE, in the case of non-negative integer Laguerre parameter. We show that the Toeplitz determinant formed from an arbitrary linear combination of these two Bessel functions occurs as a [Formula: see text]-function sequence in Okamoto’s Hamiltonian formulation of Painlevé III[Formula: see text], and consequently the logarithmic derivative of both Toeplitz determinants satisfies the same [Formula: see text]-form Painlevé III[Formula: see text] differential equation, giving an explanation of a fact which can be observed from earlier results. In addition, some insights into the relationship between this characterization of the generating function, and its characterization in the [Formula: see text] limit, both with the Laguerre parameter [Formula: see text] fixed, and with [Formula: see text] (this latter circumstance being relevant to an application to the distribution of the Wigner time delay statistic), are given.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84011628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-02DOI: 10.1142/s2010326321500325
Shambhu Nath Maurya, Koushik Saha
We discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to [Formula: see text]. Our derivation is based on the trace formula of circulant matrix, method of moments and some combinatorial techniques.
{"title":"Process convergence of fluctuations of linear eigenvalue statistics of random circulant matrices","authors":"Shambhu Nath Maurya, Koushik Saha","doi":"10.1142/s2010326321500325","DOIUrl":"https://doi.org/10.1142/s2010326321500325","url":null,"abstract":"We discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to [Formula: see text]. Our derivation is based on the trace formula of circulant matrix, method of moments and some combinatorial techniques.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84252786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-12DOI: 10.1142/S2010326322500083
Taras Bodnar, H. Dette, Nestor Parolya, Erik Thorsén
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterize the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.
{"title":"Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions","authors":"Taras Bodnar, H. Dette, Nestor Parolya, Erik Thorsén","doi":"10.1142/S2010326322500083","DOIUrl":"https://doi.org/10.1142/S2010326322500083","url":null,"abstract":"Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterize the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87053006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1142/s2010326321500209
Octavio Arizmendi, Adrian Celestino
We provide a generalization and new proofs of the formulas of Collins et al. for the spectrum of polynomials in cyclic monotone elements. This is applied to Random Matrices with discrete spectrum.
{"title":"Polynomial with cyclic monotone elements with applications to Random Matrices with discrete spectrum","authors":"Octavio Arizmendi, Adrian Celestino","doi":"10.1142/s2010326321500209","DOIUrl":"https://doi.org/10.1142/s2010326321500209","url":null,"abstract":"We provide a generalization and new proofs of the formulas of Collins et al. for the spectrum of polynomials in cyclic monotone elements. This is applied to Random Matrices with discrete spectrum.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79122051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-26DOI: 10.1142/S2010326319500102
Guangren Yang, Songshan Yang, Wang Zhou
In this paper, we study whether two networks arising from two stochastic block models have the same connection structures by comparing their adjacency matrices. We conduct Monte Carlo simulations study to examine the finite sample performance of the proposed method. A real data example is used to illustrate the proposed methodology.
{"title":"Adjacency matrix comparison for stochastic block models","authors":"Guangren Yang, Songshan Yang, Wang Zhou","doi":"10.1142/S2010326319500102","DOIUrl":"https://doi.org/10.1142/S2010326319500102","url":null,"abstract":"In this paper, we study whether two networks arising from two stochastic block models have the same connection structures by comparing their adjacency matrices. We conduct Monte Carlo simulations study to examine the finite sample performance of the proposed method. A real data example is used to illustrate the proposed methodology.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75321123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-26DOI: 10.1142/S2010326321500362
F. Lehner, K. Szpojankowski
Subordination is the basis of the analytic approach to free additive and multiplicative convolution. We extend this approach to a more general setting and prove that the conditional expectation [Formula: see text] for free random variables [Formula: see text] and a Borel function [Formula: see text] is a resolvent again. This result allows the explicit calculation of the distribution of noncommutative polynomials of the form [Formula: see text]. The main tool is a new combinatorial formula for conditional expectations in terms of Boolean cumulants and a corresponding analytic formula for conditional expectations of resolvents, generalizing subordination formulas for both additive and multiplicative free convolutions. In the final section, we illustrate the results with step by step explicit computations and an exposition of all necessary ingredients.
{"title":"Boolean cumulants and subordination in free probability","authors":"F. Lehner, K. Szpojankowski","doi":"10.1142/S2010326321500362","DOIUrl":"https://doi.org/10.1142/S2010326321500362","url":null,"abstract":"Subordination is the basis of the analytic approach to free additive and multiplicative convolution. We extend this approach to a more general setting and prove that the conditional expectation [Formula: see text] for free random variables [Formula: see text] and a Borel function [Formula: see text] is a resolvent again. This result allows the explicit calculation of the distribution of noncommutative polynomials of the form [Formula: see text]. The main tool is a new combinatorial formula for conditional expectations in terms of Boolean cumulants and a corresponding analytic formula for conditional expectations of resolvents, generalizing subordination formulas for both additive and multiplicative free convolutions. In the final section, we illustrate the results with step by step explicit computations and an exposition of all necessary ingredients.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73892130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-01DOI: 10.1142/S2010326321500386
J. Campbell, Z. Yin
We consider the three finite free convolutions for polynomials studied in a recent paper by Marcus, Spielman and Srivastava. Each can be described either by direct explicit formulae or in terms of operations on randomly rotated matrices. We present an alternate approach to the equivalence between these descriptions, based on combinatorial Weingarten methods for integration over the unitary and orthogonal groups. A key aspect of our approach is to identify a certain quadrature property, which is satisfied by some important series of subgroups of the unitary groups (including the groups of unitary, orthogonal, and signed permutation matrices), and which yields the desired convolution formulae.
{"title":"Finite free convolutions via Weingarten calculus","authors":"J. Campbell, Z. Yin","doi":"10.1142/S2010326321500386","DOIUrl":"https://doi.org/10.1142/S2010326321500386","url":null,"abstract":"We consider the three finite free convolutions for polynomials studied in a recent paper by Marcus, Spielman and Srivastava. Each can be described either by direct explicit formulae or in terms of operations on randomly rotated matrices. We present an alternate approach to the equivalence between these descriptions, based on combinatorial Weingarten methods for integration over the unitary and orthogonal groups. A key aspect of our approach is to identify a certain quadrature property, which is satisfied by some important series of subgroups of the unitary groups (including the groups of unitary, orthogonal, and signed permutation matrices), and which yields the desired convolution formulae.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79565252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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