메뉴 건너뛰기




Volumn 41, Issue 6, 2013, Pages 2994-3021

Covariance and precision matrix estimation for high-dimensional time series

Author keywords

Consistency; Covariance matrix; Dependence; Functional dependence measure; High dimensional inference; Lasso; Nagaev inequality; Nonstationary time series; Precision matrix; Sparsity; Spatial temporal processes; Thresholding

Indexed keywords


EID: 84891934068     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1182     Document Type: Article
Times cited : (117)

References (48)
  • 2
    • 0032286356 scopus 로고    scopus 로고
    • Time-dependent spectral analysis of nonstationary time series
    • MR1666643
    • Honolulu, HI. ADAK, S. (1998). Time-dependent spectral analysis of nonstationary time series. J. Amer. Statist. Assoc. 93 1488-1501. MR1666643
    • (1998) J. Amer. Statist. Assoc , vol.93 , pp. 1488-1501
    • Honolulu, H.I.1    Adak, S.2
  • 4
    • 41549101939 scopus 로고    scopus 로고
    • Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data
    • MR2417243
    • BANERJEE, O., EL GHAOUI, L. and D'ASPREMONT, A. (2008). Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. J. Mach. Learn. Res. 9 485-516. MR2417243
    • (2008) J. Mach. Learn. Res , vol.9 , pp. 485-516
    • Banerjee, O.1    El Ghaoui, L.2    D'Aspremont, A.3
  • 5
    • 33745156863 scopus 로고    scopus 로고
    • Some theory of Fisher's linear discriminant function, "naive Bayes," and some alternatives when there are many more variables than observations
    • MR2108040
    • BICKEL, P. J. and LEVINA, E. (2004). Some theory of Fisher's linear discriminant function, "naive Bayes," and some alternatives when there are many more variables than observations. Bernoulli 10 989-1010. MR2108040
    • (2004) Bernoulli , vol.10 , pp. 989-1010
    • Bickel, P.J.1    Levina, E.2
  • 6
    • 62349112885 scopus 로고    scopus 로고
    • Covariance regularization by thresholding
    • MR2485008
    • BICKEL, P. J. and LEVINA, E. (2008a). Covariance regularization by thresholding. Ann. Statist. 36 2577-2604. MR2485008
    • (2008) Ann. Statist , vol.36 , pp. 2577-2604
    • Bickel, P.J.1    Levina, E.2
  • 7
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • MR2387969
    • BICKEL, P. J. and LEVINA, E. (2008b). Regularized estimation of large covariance matrices. Ann. Statist. 36 199-227. MR2387969
    • (2008) Ann. Statist , vol.36 , pp. 199-227
    • Bickel, P.J.1    Levina, E.2
  • 8
    • 79960110811 scopus 로고    scopus 로고
    • A constrained ℓ1 minimization approach to sparse precision matrix estimation
    • MR2847973
    • CAI, T., LIU, W. and LUO, X. (2011). A constrained ℓ1 minimization approach to sparse precision matrix estimation. J. Amer. Statist. Assoc. 106 594-607. MR2847973
    • (2011) J. Amer. Statist. Assoc , vol.106 , pp. 594-607
    • Cai, T.1    Liu, W.2    Luo, X.3
  • 9
    • 77955132618 scopus 로고    scopus 로고
    • Optimal rates of convergence for covariance matrix estimation
    • MR2676885
    • CAI, T. T., ZHANG, C.-H. and ZHOU, H. H. (2010). Optimal rates of convergence for covariance matrix estimation. Ann. Statist. 38 2118-2144. MR2676885
    • (2010) Ann. Statist , vol.38 , pp. 2118-2144
    • Cai, T.T.1    Zhang, C.-H.2    Zhou, H.H.3
  • 10
    • 84861177056 scopus 로고    scopus 로고
    • Minimax estimation of large covariance matrices under ℓ1-norm (with discussion)
    • MR3027084
    • CAI, T. and ZHOU, H. (2013). Minimax estimation of large covariance matrices under ℓ1-norm (with discussion). Statist. Sinica 22 1319-1349. MR3027084
    • (2013) Statist. Sinica , vol.22 , pp. 1319-1349
    • Cai, T.1    Zhou, H.2
  • 11
    • 84861177057 scopus 로고    scopus 로고
    • Optimal rates of convergence for sparse covariance matrix estimation
    • MR3097607
    • CAI, T. T. and ZHOU, H. H. (2012). Optimal rates of convergence for sparse covariance matrix estimation. Ann. Statist. 40 2389-2420. MR3097607
    • (2012) Ann. Statist , vol.40 , pp. 2389-2420
    • Cai, T.T.1    Zhou, H.H.2
  • 12
    • 79951831802 scopus 로고    scopus 로고
    • The sparse matrix transform for covariance estimation and analysis of high-dimensional signals
    • MR2799176
    • CAO, G., BACHEGA, L. R. and BOUMAN, C. A. (2011). The sparse matrix transform for covariance estimation and analysis of high-dimensional signals. IEEE Trans. Image Process. 20 625-640. MR2799176
    • (2011) IEEE Trans. Image Process , vol.20 , pp. 625-640
    • Cao, G.1    Bachega, L.R.2    Bouman, C.A.3
  • 14
    • 0031518090 scopus 로고    scopus 로고
    • Fitting time series models to nonstationary processes
    • MR1429916
    • DAHLHAUS, R. (1997). Fitting time series models to nonstationary processes. Ann. Statist. 25 1-37. MR1429916
    • (1997) Ann. Statist , vol.25 , pp. 1-37
    • Dahlhaus, R.1
  • 15
    • 64849095956 scopus 로고    scopus 로고
    • Quantile curve estimation and visualization for nonstationary time series
    • MR2511058
    • DRAGHICESCU, D., GUILLAS, S. and WU, W. B. (2009). Quantile curve estimation and visualization for nonstationary time series. J. Comput. Graph. Statist. 18 1-20. MR2511058
    • (2009) J. Comput. Graph. Statist , vol.18 , pp. 1-20
    • Draghicescu, D.1    Guillas, S.2    Wu, W.B.3
  • 16
    • 73949117731 scopus 로고    scopus 로고
    • Network exploration via the adaptive lasso and SCAD penalties
    • MR2750671
    • FAN, J., FENG, Y. and WU, Y. (2009). Network exploration via the adaptive lasso and SCAD penalties. Ann. Appl. Stat. 3 521-541. MR2750671
    • (2009) Ann. Appl. Stat , vol.3 , pp. 521-541
    • Fan, J.1    Feng, Y.2    Wu, Y.3
  • 18
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical lasso
    • FRIEDMAN, J., HASTIE, T. and TIBSHIRANI, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9 432441.
    • (2008) Biostatistics , vol.9 , pp. 432441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 19
    • 0033115889 scopus 로고    scopus 로고
    • Theory and application of covariance matrix tapers for robust adaptive beamforming
    • GUERCI, J. R. (1999). Theory and application of covariance matrix tapers for robust adaptive beamforming. IEEE Trans. Signal Process. 47 977985.
    • (1999) IEEE Trans. Signal Process , vol.47 , pp. 977985
    • Guerci, J.R.1
  • 20
    • 33644986127 scopus 로고    scopus 로고
    • Covariance matrix selection and estimation via penalised normal likelihood
    • MR2277742
    • HUANG, J. Z., LIU, N., POURAHMADI, M. and LIU, L. (2006). Covariance matrix selection and estimation via penalised normal likelihood. Biometrika 93 85-98. MR2277742
    • (2006) Biometrika , vol.93 , pp. 85-98
    • Huang, J.Z.1    Liu, N.2    Pourahmadi, M.3    Liu, L.4
  • 21
    • 3042777110 scopus 로고    scopus 로고
    • Bayesian analysis of stochastic volatility models with fat-tails and correlated errors
    • MR2083256
    • JACQUIER, E., POLSON, N. G. and ROSSI, P. E. (2004). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. J. Econometrics 122 185-212. MR2083256
    • (2004) J. Econometrics , vol.122 , pp. 185-212
    • Jacquier, E.1    Polson, N.G.2    Rossi, P.E.3
  • 22
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • MR1863961
    • JOHNSTONE, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295-327. MR1863961
    • (2001) Ann. Statist , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 23
    • 66549088006 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high-dimensions
    • MR2751448
    • JOHNSTONE, I. M. and LU, A. Y. (2009). On consistency and sparsity for principal components analysis in high-dimensions. J. Amer. Statist. Assoc. 104 682-693. MR2751448
    • (2009) J. Amer. Statist. Assoc , vol.104 , pp. 682-693
    • Johnstone, I.M.1    Lu, A.Y.2
  • 26
    • 73949122606 scopus 로고    scopus 로고
    • Sparsistency and rates of convergence in large covariance matrix estimation
    • MR2572459
    • LAM, C. and FAN, J. (2009). Sparsistency and rates of convergence in large covariance matrix estimation. Ann. Statist. 37 4254-4278. MR2572459
    • (2009) Ann. Statist , vol.37 , pp. 4254-4278
    • Lam, C.1    Fan, J.2
  • 27
    • 0041841552 scopus 로고    scopus 로고
    • Improved estimation of the covariance matrix of stock returns with an application to portfolio selection
    • LEDOIT, O. and WOLF, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance 10 603621.
    • (2003) Journal of Empirical Finance , vol.10 , pp. 603621
    • Ledoit, O.1    Wolf, M.2
  • 28
    • 0038036818 scopus 로고    scopus 로고
    • On robust capon beamforming and diagonal loading
    • LI, J., STOCIA, P. and WANG, Z. (2003). On robust capon beamforming and diagonal loading. IEEE Trans. Signal Process. 51 17021715.
    • (2003) IEEE Trans. Signal Process , vol.51 , pp. 17021715
    • Li, J.1    Stocia, P.2    Wang, Z.3
  • 30
    • 84883866253 scopus 로고    scopus 로고
    • Probability and moment inequalities under dependence
    • To appear. DOI: 10.5705/ss.2011.287
    • LIU, W., XIAO, H. and WU, W. B. (2013). Probability and moment inequalities under dependence. Statist. Sinica. To appear. DOI: 10.5705/ss.2011.287.
    • (2013) Statist. Sinica
    • Liu, W.1    Xiao, H.2    Wu, W.B.3
  • 31
    • 0000263239 scopus 로고
    • Distribution of eigenvalues in certain sets of random matrices
    • MR0208649
    • MARČENKO, V. A. and PASTUR, L. A. (1967). Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. 72 507-536. MR0208649
    • (1967) Mat. Sb , vol.72 , pp. 507-536
    • Marčenko, V.A.1    Pastur, L.A.2
  • 32
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the lasso
    • MR2278363
    • MEINSHAUSEN, N. and BÜHLMANN, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436-1462. MR2278363
    • (2006) Ann. Statist , vol.34 , pp. 1436-1462
    • Meinshausen, N.1    Bühlmann, P.2
  • 34
    • 80555142374 scopus 로고    scopus 로고
    • High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence
    • MR2836766
    • RAVIKUMAR, P., WAINWRIGHT, M. J., RASKUTTI, G. and YU, B. (2011). High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence. Electron. J. Stat. 5 935-980. MR2836766
    • (2011) Electron. J. Stat , vol.5 , pp. 935-980
    • Ravikumar, P.1    Wainwright, M.J.2    Raskutti, G.3    Yu, B.4
  • 35
    • 62349119614 scopus 로고    scopus 로고
    • Sparse permutation invariant covariance estimation
    • MR2417391
    • ROTHMAN, A. J., BICKEL, P. J., LEVINA, E. and ZHU, J. (2008). Sparse permutation invariant covariance estimation. Electron. J. Stat. 2 494-515. MR2417391
    • (2008) Electron. J. Stat , vol.2 , pp. 494-515
    • Rothman, A.J.1    Bickel, P.J.2    Levina, E.3    Zhu, J.4
  • 39
    • 78449244115 scopus 로고    scopus 로고
    • A general science-based framework for dynamical spatio-temporal models
    • MR2745992
    • WIKLE, C. K. and HOOTEN, M. B. (2010). A general science-based framework for dynamical spatio-temporal models. TEST 19 417-451. MR2745992
    • (2010) TEST , vol.19 , pp. 417-451
    • Wikle, C.K.1    Hooten, M.B.2
  • 40
    • 26444450641 scopus 로고    scopus 로고
    • Nonlinear system theory: Another look at dependence
    • (electronic). MR2172215
    • WU, W. B. (2005). Nonlinear system theory: Another look at dependence. Proc. Natl. Acad. Sci. USA 102 14150-14154 (electronic). MR2172215
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 14150-14154
    • Wu, W.B.1
  • 41
    • 34547951595 scopus 로고    scopus 로고
    • Strong invariance principles for dependent random variables
    • MR2353389
    • WU, W. B. (2007). Strong invariance principles for dependent random variables. Ann. Probab. 35 2294-2320. MR2353389
    • (2007) Ann. Probab , vol.35 , pp. 2294-2320
    • Wu, W.B.1
  • 42
    • 84861372960 scopus 로고    scopus 로고
    • Asymptotic theory for stationary processes
    • MR2812816
    • WU, W. B. (2011). Asymptotic theory for stationary processes. Stat. Interface 4 207-226. MR2812816
    • (2011) Stat. Interface , vol.4 , pp. 207-226
    • Wu, W.B.1
  • 43
    • 3843104546 scopus 로고    scopus 로고
    • Nonparametric estimation of large covariance matrices of longitudinal data
    • MR2024760
    • WU, W. B. and POURAHMADI, M. (2003). Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika 90 831-844. MR2024760
    • (2003) Biometrika , vol.90 , pp. 831-844
    • Wu, W.B.1    Pourahmadi, M.2
  • 44
    • 3242813749 scopus 로고    scopus 로고
    • Limit theorems for iterated random functions
    • MR2052582
    • WU, W. B. and SHAO, X. (2004). Limit theorems for iterated random functions. J. Appl. Probab. 41 425-436. MR2052582
    • (2004) J. Appl. Probab , vol.41 , pp. 425-436
    • Wu, W.B.1    Shao, X.2
  • 45
    • 84866867488 scopus 로고    scopus 로고
    • Covariance matrix estimation for stationary time series
    • MR3014314
    • XIAO, H. and WU, W. B. (2012). Covariance matrix estimation for stationary time series. Ann. Statist. 40 466-493. MR3014314
    • (2012) Ann. Statist , vol.40 , pp. 466-493
    • Xiao, H.1    Wu, W.B.2
  • 46
    • 77956916683 scopus 로고    scopus 로고
    • High dimensional inverse covariance matrix estimation via linear programming
    • MR2719856
    • YUAN, M. (2010). High dimensional inverse covariance matrix estimation via linear programming. J. Mach. Learn. Res. 11 2261-2286. MR2719856
    • (2010) J. Mach. Learn. Res , vol.11 , pp. 2261-2286
    • Yuan, M.1
  • 48
    • 77955601966 scopus 로고    scopus 로고
    • Time varying undirected graphs
    • MR3108169
    • ZHOU, S., LAFFERTY, J. and WASSERMAN, L. (2010). Time varying undirected graphs. Mach. Learn. 80 295-319. MR3108169
    • (2010) Mach. Learn , vol.80 , pp. 295-319
    • Zhou, S.1    Lafferty, J.2    Wasserman, L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.