高维周期向量自回归模型的精度矩阵的假设检验

doi:10.3969/j.issn.1000-5641.2023.02.007

华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (2): 48-59.doi: 10.3969/j.issn.1000-5641.2023.02.007

高维周期向量自回归模型的精度矩阵的假设检验

邹进()

上海交通大学数学科学学院, 上海　200240

收稿日期:2021-04-06 出版日期:2023-03-25 发布日期:2023-03-23
作者简介:邹　进, 男, 博士, 研究方向为回归模型中的参数估计和假设检验. E-mail: mathzj@alumni.sjtu.edu.cn
基金资助:
国家自然科学基金(11531001)

Hypothesis testing for the precision matrix of high-dimensional periodic vector autoregressive model

Jin ZOU()

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai　200240, China

Received:2021-04-06 Online:2023-03-25 Published:2023-03-23

摘要/Abstract

摘要：

由周期性向量自回归模型生成的精度矩阵(逆协方差矩阵)是一个块状三对角矩阵. 在此精度矩阵的基础上, 提出了一种新的块状迹函数, 用于检验两个精度矩阵的块状迹相等, 并研究了在零假设下的渐近行为. 数值实验表明, 这种块状迹函数检验方法与常用的检验方法相比, 具有简洁易算和功效优良的特点.

关键词: 假设检验, 周期性向量自回归模型, 精度矩阵, 块状三对角矩阵

Abstract:

The precision (inverse covariance) matrix generated by the periodic vector autoregressive model is a sparse block tridiagonal matrix. Based on this precision matrix, a new block trace function is proposed for testing the equality of block traces of two precision matrices, the asymptotic behavior under the null hypothesis is investigated. Numerical experiments show that the proposed testing procedure has both appropriate size and good power.

Key words: hypothesis testing, periodic vector autoregressive model, precision matrix, block tridiagonal matrix

中图分类号:

O212.1

邹进. 高维周期向量自回归模型的精度矩阵的假设检验[J]. 华东师范大学学报（自然科学版）, 2023, 2023(2): 48-59.

Jin ZOU. Hypothesis testing for the precision matrix of high-dimensional periodic vector autoregressive model[J]. Journal of East China Normal University(Natural Science), 2023, 2023(2): 48-59.

图/表 2

参考文献 27

1	TESFAYE Y G, MEERSCHAERT M M, ANDERSON P L. Identification of periodic autoregressive moving average models and their application to the modeling of river flows. Water Resources Research, 2006, 42, 87- 94.
2	GAUCHEREL C. Analysis of ENSO interannual oscillations using non-stationary quasi-periodic statistics: A study of ENSO memory. International Journal of Climatology, 2010, 30 (6): 926- 934.
3	KIM K Y, HAMLINGTON B, NA H. Theoretical foundation of cyclostationary EOF analysis for geophysical and climatic variables: Concepts and examples. Earth-Science Reviews, 2015, 150, 201- 218.
4	IQELAN B M. Periodically correlated time series: Models and examples [D]. Manchester, UK: The University of Manchester, 2007.
5	BROSZKIEWICZ-SUWAJ E, MAKAGON A, WERON R, et al. On detecting and modeling periodic correlation in financial data. Physica A, 2004, 336, 196- 205.
6	LUND R, SHAO Q, BASAWA I. Parsimonious periodic time series modeling. Australian & New Zealand Journal of Statistics, 2006, 48 (1): 33- 47.
7	HAN F, LU H, LIU H. A direct estimation of high dimensional stationary vector autoregressions. Journal of Machine Learning Research, 2015, 16, 3115- 3150.
8	DUBOIS P C A, TRYNKA G, FRANKE L, et al. Multiple common variants for celiac disease influencing immune gene expression. Nature Genetics, 2010, 42 (4): 295- 302.
9	FUKUSHIMA A. DiffCorr: An R package to analyze and visualize differential correlations in biological networks. Gene, 2013, 518, 209- 214.
10	DJAUHARI M A, GAN S L. Dynamics of correlation structure in stock market. Entropy, 2014, 16, 455- 470.
11	ANDERSON T W. An Introduction to Multivariate Statistical Analysis [M]. New York: John Wiley and Sons, 1962.
12	JOHN S. Some optimal multivariate tests. Biometrika, 1971, 58 (1): 123- 127.
13	JOHN S. The distribution of a statistic used for testing sphericity of normal distributions. Biometrika, 1972, 59 (1): 169- 173.
14	NAGAO H. On some test criteria for covariance matrix. The Annals of Statistics, 1973, 1 (4): 700- 709.
15	JOHNSTONE I M. On the distribution of the largest eigenvalue in principal components analysis. The Annals of Statistics, 2001, 29 (2): 295- 327.
16	BAI Z, JIANG D, YAO J F, et al. Corrections to LRT on large-dimensional covariance matrix by RMT. The Annals of Statistics, 2009, 37 (6B): 3822- 3840.
17	JIANG D, JIANG T, YANG F. Likelihood ratio tests for covariance matrices of high-dimensional normal distributions. Journal of Statistical Planning and Inference, 2012, 142 (8): 2241- 2256.
18	ZHENG S, BAI Z, YAO J. Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing. The Annals of Statistics, 2015, 43 (2): 546- 591.
19	LEDOIT O, WOLF M. Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. The Annals of Statistics, 2002, 30 (4): 1081- 1102.
20	CHEN S X, ZHANG L X, ZHONG P S. Tests for high-dimensional covariance matrices. Journal of the American Statistical Association, 2010, 105 (490): 810- 819.
21	FUJIKOSHI Y, ULYANOV V V, SHIMIZU R. Multivariate Statistics: High-Dimensional and Large-sample Approximations [M]. New York: John Wiley and Sons, 2010.
22	YAO J, ZHENG S, BAI Z D. Sample Covariance Matrices and High-Dimensional Data Analysis [M]. Cambridge: Cambridge University Press, 2015.
23	CAI T T. Global testing and large-scale multiple testing for high-dimensional covariance structures. Annual Review of Statistics and Its Application, 2017, (4): 423- 446.
24	SCHOTT J R. A test for the equality of covariance matrices when the dimension is large relative to the sample sizes. Computational Statistics & Data Analysis, 2007, 51 (12): 6535- 6542.
25	HE Y, XU G, WU C, et al. Asymptotically independent U-statistics in high-dimensional testing. The Annals of Statistics, 2021, 49, 154- 181.
26	HORN R A, JOHNSON C R. 矩阵分析 [M]. 杨奇, 译. 北京: 机械工业出版社, 2005.
27	GUPTA A K, NAGAR D K. Matrix Variate Distribution [M]. Boca Raton, Florida, USA: CRC Press, 2018.

(d, T, n)	ASL				势函数值
(d, T, n)	LRT	CLRT	UVW	ICT	LRT	CLRT	UVW	ICT
(2, 4, 300)	0.056	0.072	0.052	0.061	0.906	0.906	0.114	0.990
(2, 10, 300)	0.088	0.064	0.054	0.053	0.896	0.894	0.882	0.863
(10, 5, 300)	0.480	0.067	0.052	0.050	0.841	0.851	0.812	0.845
(10, 30, 300)			0.045	0.047			0.988	0.978
(10, 40, 300)			0.044	0.049			0.911	0.967
(30, 40, 1000)			0.051	0.048			0.776	0.883
(100, 20, 1000)			0.034	0.041			0.671	0.783

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高维周期向量自回归模型的精度矩阵的假设检验

Hypothesis testing for the precision matrix of high-dimensional periodic vector autoregressive model

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