메뉴 건너뛰기




Volumn 18, Issue 6, 2008, Pages 2337-2366

The asymptotic distribution and Berry-Esseen bound of a new test for independence in high dimension with an application to stochastic optimization

Author keywords

Berry Esseen bound; Correlation matrices; Extreme distribution; Independence test; Stochastic optimization

Indexed keywords


EID: 63049106197     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/08-AAP527     Document Type: Article
Times cited : (75)

References (21)
  • 1
    • 63049092630 scopus 로고    scopus 로고
    • ARRATIA, R., GOLDSTEIN, L. and GORDON, L. (1989). Two moments suffice for Poisson approximations: The Chen-Stein method. Ann. Probab. 17 9-25. MR972770
    • ARRATIA, R., GOLDSTEIN, L. and GORDON, L. (1989). Two moments suffice for Poisson approximations: The Chen-Stein method. Ann. Probab. 17 9-25. MR972770
  • 2
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • MR2236170
    • CANDES, E. J., ROMBERG, J. and TAO, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 489-509. MR2236170
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 489-509
    • CANDES, E.J.1    ROMBERG, J.2    TAO, T.3
  • 3
    • 33646800236 scopus 로고    scopus 로고
    • CHEN, J. and X. HUO, X. (2005). Sparse representations for multiple measurement vectors (MMV) in an over-complete dictionary. In International Conference on Acoustics, Speech and Signal Processing (ICASSP-2005). Philadelphia, PA.
    • CHEN, J. and X. HUO, X. (2005). Sparse representations for multiple measurement vectors (MMV) in an over-complete dictionary. In International Conference on Acoustics, Speech and Signal Processing (ICASSP-2005). Philadelphia, PA.
  • 5
    • 33646365077 scopus 로고    scopus 로고
    • 1 -norm solution is also the sparsest solution
    • MR2217606
    • 1 -norm solution is also the sparsest solution. Comm. Pure Appl. Math. 59 797-829. MR2217606
    • (2006) Comm. Pure Appl. Math , vol.59 , pp. 797-829
    • DONOHO, D.L.1
  • 7
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse over-complete representations in the presence of noise
    • MR2237332
    • DONOHO, D. L., ELAD, M. and TEMLYAKOV, V. N. (2006). Stable recovery of sparse over-complete representations in the presence of noise. IEEE Trans. Inform. Theory 52 6-18. MR2237332
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 6-18
    • DONOHO, D.L.1    ELAD, M.2    TEMLYAKOV, V.N.3
  • 8
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • MR1872845
    • DONOHO, D. L. and HUO, X. (2001). Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47 2845-2862. MR1872845
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2845-2862
    • DONOHO, D.L.1    HUO, X.2
  • 9
    • 63049093526 scopus 로고    scopus 로고
    • DONOHO, D. L. and STARK, P. B. (1989). Uncertainty principles and signal recovery. SIAM J. Appl. Math. 49 906-931. MR997928
    • DONOHO, D. L. and STARK, P. B. (1989). Uncertainty principles and signal recovery. SIAM J. Appl. Math. 49 906-931. MR997928
  • 10
    • 63049107752 scopus 로고    scopus 로고
    • Characterization of LIL behavior in Banach space
    • EINMAHL, U. and LI, D. (2008). Characterization of LIL behavior in Banach space. Trans. Amer. Math. Soc. 360 6677-6693.
    • (2008) Trans. Amer. Math. Soc , vol.360 , pp. 6677-6693
    • EINMAHL, U.1    LI, D.2
  • 11
    • 84878031768 scopus 로고    scopus 로고
    • FAN, J. and LI, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. In International Congress of Mathematicians III 595-622. Eur. Math. Soc., Zurich. MR2275698
    • FAN, J. and LI, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. In International Congress of Mathematicians III 595-622. Eur. Math. Soc., Zurich. MR2275698
  • 12
    • 63049131235 scopus 로고    scopus 로고
    • GALAMBOS, J., LECHNER, J. and SIMIU, E., EDS. (1994). Extreme Value Theory and Applications. I. Kluwer Academic, Dordrecht.
    • GALAMBOS, J., LECHNER, J. and SIMIU, E., EDS. (1994). Extreme Value Theory and Applications. I. Kluwer Academic, Dordrecht.
  • 13
    • 0018481132 scopus 로고    scopus 로고
    • HALL, P. (1979). On the rate of convergence of normal extremes. J. Appl. Probab. 16 433-439. MR531778
    • HALL, P. (1979). On the rate of convergence of normal extremes. J. Appl. Probab. 16 433-439. MR531778
  • 14
    • 11244330494 scopus 로고    scopus 로고
    • The asymptotic distributions of the largest entries of sample correlation matrices
    • MR2052906
    • JIANG, T. (2004). The asymptotic distributions of the largest entries of sample correlation matrices. Ann. Appl. Probab. 14 865-880. MR2052906
    • (2004) Ann. Appl. Probab , vol.14 , pp. 865-880
    • JIANG, T.1
  • 15
    • 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
  • 16
    • 84869241304 scopus 로고    scopus 로고
    • LEADBETTER, M. R., LINDGREN, G. and ROOTZÉN, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York. MR691492
    • LEADBETTER, M. R., LINDGREN, G. and ROOTZÉN, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York. MR691492
  • 17
    • 0036392431 scopus 로고    scopus 로고
    • Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size
    • MR1926169
    • LEDOIT, O. and WOLF, M. (2002). Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann. Statist. 30 1081-1102. MR1926169
    • (2002) Ann. Statist , vol.30 , pp. 1081-1102
    • LEDOIT, O.1    WOLF, M.2
  • 18
    • 63049117783 scopus 로고    scopus 로고
    • PETROV, V. V. (1975). Sums of Independent Random Variables. Springer, New York. MR0388499
    • PETROV, V. V. (1975). Sums of Independent Random Variables. Springer, New York. MR0388499
  • 19
    • 0040234620 scopus 로고
    • Estimates of Berry-Esseen type for the probabilities of large deviations
    • MR1142075
    • SAKHANENKO, A. I. (1991). Estimates of Berry-Esseen type for the probabilities of large deviations. Sibirsk. Mat. Zh. 32 133-142, 228. MR1142075
    • (1991) Sibirsk. Mat. Zh , vol.32 , Issue.133-142 , pp. 228
    • SAKHANENKO, A.I.1
  • 20
    • 27944479075 scopus 로고    scopus 로고
    • Testing for complete independence in high dimensions
    • MR2234197
    • SCHOTT, J. R. (2005). Testing for complete independence in high dimensions. Biometrika 92 951-956. MR2234197
    • (2005) Biometrika , vol.92 , pp. 951-956
    • SCHOTT, J.R.1
  • 21
    • 63049085100 scopus 로고    scopus 로고
    • Asymptotic distribution of the largest off-diagonal entry of correlation matrices
    • MR2327033
    • ZHOU, W. (2007). Asymptotic distribution of the largest off-diagonal entry of correlation matrices. Trans. Amer. Math. Soc. 359 5345-5363. MR2327033
    • (2007) Trans. Amer. Math. Soc , vol.359 , pp. 5345-5363
    • ZHOU, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.