### Citations

7720 |
Topics in Matrix Analysis
- Horn, Johnson
- 1991
(Show Context)
Citation Context ... in step 2 can be any matrix square root that converges to Σ −1/2 n at the same rate as ˆ Σ ɛ κ,l converges to Σn, such as those obtained by the Cholesky or spectral decompositions (see, for example, =-=Horn and Johnson, 1990-=-, p. 411). We conjecture that the same is true of the square root used in step 5, but our proof of Theorem 5 (below) is specific to the Cholesky decomposition. For reasons of symmetry, it seems prefer... |

4460 | Core Team. R: A language and environment for statistical computing - Development - 2005 |

1229 |
Time Series Theory and Methods
- Brockwell, Davis
- 1991
(Show Context)
Citation Context ... function which down-weighs the values of ˆγ |i−j| when |i − j| is large; this is desirable because estimated covariances with large values of |i − j| are known to be less reliable (see, for example, =-=Brockwell and Davis, 1991-=-). The motivation for our approach lies in the relationship between this problem and that of spectral density estimation. The spectral density is defined as f(ω) = 1 2π ∞∑ j=−∞ γje −iωj , 3and is non... |

509 | Toeplitz forms and their applications - Grenander, Szego - 1984 |

414 | The jackknife and the bootstrap for general stationary observations. - Kunsch - 1989 |

115 | Bootstraps for time series”, - Buhlmann - 2002 |

113 | Moving blocks jackknife and bootstrap capture weak dependence. Exploring the limits of bootstrap, - Liu, Singh - 1992 |

80 |
A Probability Path
- Resnick
- 2001
(Show Context)
Citation Context ...mate Σ 1/2 n term of (10). n −1/2 1 t (Ln,k) ˜ Z ∗ = n −1/2 (c1,n ˜ Z ∗ 1 + . . . + cn,n ˜ Z ∗ n). in the first 19We establish the desired result via the central limit theorem for triangular arrays (=-=Resnick, 1999-=-, p. 321) which is implied by the Liapunov condition 1 (c 2 1,n + . . . + c2 n,n) 1+δ/2 n∑ i=1 [ ∗ E |ci,n ˜ Z ∗ i | 2+δ] → 0, (11) for some δ > 0. Convergence (11) will be shown to hold for δ = 2. We... |

77 | Automatic block-length selection for the dependent bootstrap, - Politis, White - 2004 |

65 | Nonlinear system theory: another look at dependence - Wu - 2005 |

51 | The impact of bootstrap methods on time series analysis, - Politis - 2003 |

46 |
Bias-corrected nonparametric spectral estimation.
- Politis, Romano
- 1995
(Show Context)
Citation Context ...ts that play a role analogous to those used in the present problem. In the context of spectral density estimation, the weighting scheme we propose here has shown to provide optimal convergence rates (=-=Politis and Romano, 1995-=-) and to allow for a straightforward method of banding parameter selection (Politis, 2003a); we show that these advantages carry over to the present setting. With this motivation in mind, we denote ou... |

24 | Adaptive bandwidth choice. - Politis - 2003 |

23 |
Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices’,
- Politis
- 2011
(Show Context)
Citation Context ...thout knowing the MA coefficients. The LPB is also more general because one could, in principle, use a taper κ(·) that is not identically zero after a point, but just tends to zero, (see, for example =-=Politis, 2007-=-); in that case the LPB is generating linear MA(∞) rather than MA(q) processes. We prove the validity of the LPB for the mean, and we conjecture its validity for all statistics whose asymptotic distri... |

15 | Correction to ‘‘automatic block-length selection for the dependent bootstrap’’ by D Politis and H White. Economet Rev 2009; 28(4): 372–375 - Patton, DN, et al. |

13 | Resampling Methods for Dependent Data. Springer Series in Statistics. - Lahiri - 2003 |

13 | Nonparametric regression with infinite order flattop kernels - McMurry, Politis |

8 | Order identification statistics in stationary autoregressive movingaverage models: Vector autocorrelations and the bootstrap’, - Paparoditis, Streitberg - 1991 |

4 | Bootstrap procedures for AR (∞)—processes,” in Bootstrapping and Related - Kreiss - 1992 |

3 | boot: Bootstrap R (S-Plus) Functions, 2009. R package version - Canty, Ripley |