Nonparametric estimate of spectral density functions of sample covariance matrices generated by VARMA models

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.

Keywords:

• Limiting spectral distribution
• large dimension
• sample covariance matrices
• VARMA models
• kernel estimators

Additional information

Funding

Jiaqi Chen’s research is supported by National Natural Science Foundation of China, No. 11501147. Boping Tian and Yangchun Zhang’s research is supported by National Natural Science Foundation of China, No. 91646106.