Nonparametric estimate of spectral density functions of sample covariance matrices generated by VARMA models. Issue 4 (16th February 2022)

• Record Type: Journal Article
• Authors: Zhang, Yangchun; Chen, Jiaqi; Cui, Bosen; Tian, Boping
• Is Part Of: Communications in statistics. Volume 51:Issue 4(2022)
• Page Start: 943
• Page End: 952
• Publication Date: 2022-02-16
• Subjects: Limiting spectral distribution -- large dimension -- sample covariance matrices -- VARMA models -- kernel estimators; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2020.1745842
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: The density function of the limiting spectral distribution(LSD) of sample covariance matrices is widely used in large scale statistical inference when the sample size and dimension both tend to infinity. However, there are no explicit expressions for the density function generated by vector autoregressive moving average(VARMA) models. For such models whose sample covariance matrices do not have independence structure in columns, we propose to use modified kernel estimators which are proved to be consistent. A simulation study is also conducted to show the performance of the estimators.