Pub Date : 2020-08-06DOI: 10.1142/s2010326320990014
{"title":"Author index Volume 9 (2020)","authors":"","doi":"10.1142/s2010326320990014","DOIUrl":"https://doi.org/10.1142/s2010326320990014","url":null,"abstract":"","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75043015","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 : 2020-07-01DOI: 10.1142/S2010326320500082
Xiaona Yang, Zhaojun Wang, Xuemin Zi
This paper develops an outlier detection procedure for multinomial data when the number of categories tends to infinity. Most of the outlier detection methods are based on the assumption that the observations follow multivariate normal distribution, while in many modern applications, the observations either are measured on a discrete scale or naturally have some categorical structures. For such multinomial observations, there are rather limited approaches for outlier detection. To overcome the main obstacle, the least trimmed distances estimator for multinomial data and a fast algorithm to identify the clean subset are introduced in this work. Also, a threshold rule is considered through the asymptotic distribution of measure distance to identify outliers. Furthermore, a one-step reweighting scheme is proposed to improve the efficiency of the procedure. Finally, the finite sample performance of our method is evaluated through simulations and is compared with that of available outlier detection methods.
{"title":"Outlier detection for multinomial data with a large number of categories","authors":"Xiaona Yang, Zhaojun Wang, Xuemin Zi","doi":"10.1142/S2010326320500082","DOIUrl":"https://doi.org/10.1142/S2010326320500082","url":null,"abstract":"This paper develops an outlier detection procedure for multinomial data when the number of categories tends to infinity. Most of the outlier detection methods are based on the assumption that the observations follow multivariate normal distribution, while in many modern applications, the observations either are measured on a discrete scale or naturally have some categorical structures. For such multinomial observations, there are rather limited approaches for outlier detection. To overcome the main obstacle, the least trimmed distances estimator for multinomial data and a fast algorithm to identify the clean subset are introduced in this work. Also, a threshold rule is considered through the asymptotic distribution of measure distance to identify outliers. Furthermore, a one-step reweighting scheme is proposed to improve the efficiency of the procedure. Finally, the finite sample performance of our method is evaluated through simulations and is compared with that of available outlier detection methods.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89242002","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 : 2020-07-01DOI: 10.1142/S2010326320500070
Xinbing Kong, Jinguan Lin, Guangying Liu
In this paper, we decompose the volatility of a diffusion process into systematic and idiosyncratic components, which are not identified with observations discretely sampled from univariate process. Using large dimensional high-frequency data and assuming a factor structure, we obtain consistent estimates of the Laplace transforms of the systematic and idiosyncratic volatility processes. Based on the discrepancy between realized bivariate Laplace transform of the pair of systematic and idiosyncratic volatility processes and the product of the two marginal Laplace transforms, we propose a Kolmogorov–Smirnov-type independence test statistics for the two components of the volatility process. A functional central limit theorem for the discrepancy is established under the null hypothesis that the systematic and idiosyncratic volatilities are independent. The limiting Gaussian process is realized by a simulated discrete skeleton process which can be applied to define an approximate critical region for an independence test.
{"title":"Asymptotics for the systematic and idiosyncratic volatility with large dimensional high-frequency data","authors":"Xinbing Kong, Jinguan Lin, Guangying Liu","doi":"10.1142/S2010326320500070","DOIUrl":"https://doi.org/10.1142/S2010326320500070","url":null,"abstract":"In this paper, we decompose the volatility of a diffusion process into systematic and idiosyncratic components, which are not identified with observations discretely sampled from univariate process. Using large dimensional high-frequency data and assuming a factor structure, we obtain consistent estimates of the Laplace transforms of the systematic and idiosyncratic volatility processes. Based on the discrepancy between realized bivariate Laplace transform of the pair of systematic and idiosyncratic volatility processes and the product of the two marginal Laplace transforms, we propose a Kolmogorov–Smirnov-type independence test statistics for the two components of the volatility process. A functional central limit theorem for the discrepancy is established under the null hypothesis that the systematic and idiosyncratic volatilities are independent. The limiting Gaussian process is realized by a simulated discrete skeleton process which can be applied to define an approximate critical region for an independence test.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"105 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79298126","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 : 2020-07-01DOI: 10.1142/S2010326320500069
Giorgio Cipolloni, L. Erdős
We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix [Formula: see text] and its minor [Formula: see text]. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of [Formula: see text] and [Formula: see text]. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.
{"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","authors":"Giorgio Cipolloni, L. Erdős","doi":"10.1142/S2010326320500069","DOIUrl":"https://doi.org/10.1142/S2010326320500069","url":null,"abstract":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix [Formula: see text] and its minor [Formula: see text]. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of [Formula: see text] and [Formula: see text]. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"87 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82457143","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 : 2020-05-28DOI: 10.1142/s2010326321500222
Boping Tian, Yangchun Zhang, Wang Zhou
In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference.
{"title":"Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA","authors":"Boping Tian, Yangchun Zhang, Wang Zhou","doi":"10.1142/s2010326321500222","DOIUrl":"https://doi.org/10.1142/s2010326321500222","url":null,"abstract":"In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"42 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85870496","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 : 2020-05-25DOI: 10.1142/s2010326322500198
Agnieszka Piliszek
We find the asymptotic spectral distribution of random Kummer matrix. Then we formulate and prove a free analogue of HV independence property, which is known for classical Kummer and Gamma random variables and for Kummer and Wishart matrices. We also prove a related characterization of free-Kummer and free-Poisson (Marchenko–Pastur) non-commutative random variables.
{"title":"Regression conditions that characterize free-Poisson and free-Kummer distributions","authors":"Agnieszka Piliszek","doi":"10.1142/s2010326322500198","DOIUrl":"https://doi.org/10.1142/s2010326322500198","url":null,"abstract":"We find the asymptotic spectral distribution of random Kummer matrix. Then we formulate and prove a free analogue of HV independence property, which is known for classical Kummer and Gamma random variables and for Kummer and Wishart matrices. We also prove a related characterization of free-Kummer and free-Poisson (Marchenko–Pastur) non-commutative random variables.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76026438","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 : 2020-04-01DOI: 10.1142/S2010326320500033
Lei Chen, Shaochen Wang
Let [Formula: see text] be respectively the largest and smallest eigenvalues of beta-Laguerre ensembles with parameters [Formula: see text]. For fixed [Formula: see text], under the condition that [Formula: see text] is much larger than [Formula: see text], we obtain the full moderate deviation principles for [Formula: see text] and [Formula: see text] by using the asymptotic expansion technique. Interestingly, under this regime, our results show that asymptotically the exponential tails of the extreme eigenvalues are Gaussian-type distribution tail rather than the Tracy–Widom-type distribution tail.
{"title":"Moderate deviations for extreme eigenvalues of beta-Laguerre ensembles","authors":"Lei Chen, Shaochen Wang","doi":"10.1142/S2010326320500033","DOIUrl":"https://doi.org/10.1142/S2010326320500033","url":null,"abstract":"Let [Formula: see text] be respectively the largest and smallest eigenvalues of beta-Laguerre ensembles with parameters [Formula: see text]. For fixed [Formula: see text], under the condition that [Formula: see text] is much larger than [Formula: see text], we obtain the full moderate deviation principles for [Formula: see text] and [Formula: see text] by using the asymptotic expansion technique. Interestingly, under this regime, our results show that asymptotically the exponential tails of the extreme eigenvalues are Gaussian-type distribution tail rather than the Tracy–Widom-type distribution tail.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89929851","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}
We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.
{"title":"Estimation and testing for panel data partially linear single-index models with errors correlated in space and time","authors":"Jian-Qiang Zhao, Yan-Yong Zhao, Jinguan Lin, Zhang-Xiao Miao, Waled Khaled","doi":"10.1142/s2010326321500052","DOIUrl":"https://doi.org/10.1142/s2010326321500052","url":null,"abstract":"We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85284857","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 : 2020-04-01DOI: 10.1142/S2010326320500045
Long Feng, Haojie Ren, Changliang Zou
The monitoring of high-dimensional data streams has become increasingly important for real-time detection of abnormal activities in many statistical process control (SPC) applications. Although the multivariate SPC has been extensively studied in the literature, the challenges associated with designing a practical monitoring scheme for high-dimensional processes when between-streams correlation exists are yet to be addressed well. Classical [Formula: see text]-test-based schemes do not work well because the contamination bias in estimating the covariance matrix grows rapidly with the increase of dimension. We propose a test statistic which is based on the “divide-and-conquer” strategy, and integrate this statistic into the multivariate exponentially weighted moving average charting scheme for Phase II process monitoring. The key idea is to calculate the [Formula: see text] statistics on low-dimensional sub-vectors and to combine them together. The proposed procedure is essentially distribution-free and computation efficient. The control limit is obtained through the asymptotic distribution of the test statistic under some mild conditions on the dependence structure of stream observations. Our asymptotic results also shed light on quantifying the size of a reference sample required. Both theoretical analysis and numerical results show that the proposed method is able to control the false alarm rate and deliver robust change detection.
{"title":"A setwise EWMA scheme for monitoring high-dimensional datastreams","authors":"Long Feng, Haojie Ren, Changliang Zou","doi":"10.1142/S2010326320500045","DOIUrl":"https://doi.org/10.1142/S2010326320500045","url":null,"abstract":"The monitoring of high-dimensional data streams has become increasingly important for real-time detection of abnormal activities in many statistical process control (SPC) applications. Although the multivariate SPC has been extensively studied in the literature, the challenges associated with designing a practical monitoring scheme for high-dimensional processes when between-streams correlation exists are yet to be addressed well. Classical [Formula: see text]-test-based schemes do not work well because the contamination bias in estimating the covariance matrix grows rapidly with the increase of dimension. We propose a test statistic which is based on the “divide-and-conquer” strategy, and integrate this statistic into the multivariate exponentially weighted moving average charting scheme for Phase II process monitoring. The key idea is to calculate the [Formula: see text] statistics on low-dimensional sub-vectors and to combine them together. The proposed procedure is essentially distribution-free and computation efficient. The control limit is obtained through the asymptotic distribution of the test statistic under some mild conditions on the dependence structure of stream observations. Our asymptotic results also shed light on quantifying the size of a reference sample required. Both theoretical analysis and numerical results show that the proposed method is able to control the false alarm rate and deliver robust change detection.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"36 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86808695","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 : 2020-04-01DOI: 10.1142/S2010326320500057
Xue Ding
In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.
{"title":"Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0","authors":"Xue Ding","doi":"10.1142/S2010326320500057","DOIUrl":"https://doi.org/10.1142/S2010326320500057","url":null,"abstract":"In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86457899","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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