### Citations

1321 | Probability: Theory and Examples - Durrett - 1996 |

1194 |
Time Series: Theory and Methods
- Brockwell, Davis
- 1991
(Show Context)
Citation Context ...(!F ; ) 1 4 @s!T ; ~Ut = (Ut; Ut1; : : : ; Ut+1p) 0, ~Vt = (Vt; Vt1; : : : ; Vt+1q) 0, and fUtg, fVtg are the processes Ut =Pp i=1 iUti + Zt and Vt + Pq i=1 iVti = Zt; with Zt N 0; 2 (=-=Brockwell & Davis, 1990-=-, p. 258). Our estimator of f(!), ~f(!), takes a similar form to that of Daniels and Cressie. Rather than use the fourth moment of a univariate normal distribution as our estimator for f , we use the ... |

441 |
Wavelet Methods for Time Series Analysis
- Percival, Walden
- 2000
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Citation Context ...andwidth smoother which was calculated using the glkerns function in R (Gasser et al., 1986, 1991; Hermann, 1997); the maximum likelihood estimator under each of the ARMA models; a wavelet estimator (=-=Percival & Walden, 2000-=-); and the Daniels-Cressie estimator given in equation (6) and the shrinkage estimator given in equation (12), which correspond to the correct parametric model. The adaptive bandwidth smoother, which ... |

115 |
The measurement of power spectra from the point of view of communication engineering
- Blackman, Tukey, et al.
- 1958
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Citation Context ...s lack of consistency is to smooth the periodogram across frequencies, and a large percentage of the research devoted to spectral density estimation focuses on how the periodogram should be smoothed (=-=Blackman & Tukey, 1958-=-; Hall et al., 1994; Ombao et al., 2001). Pawitan and Gangopadhyay (1991) related the spectral density and its second derivative to a smoothed version of the periodogram. Parameter estimates within th... |

70 |
Nonconjugate Bayesian Estimation of Covariance Matrices and Its Use in Hierarchical Models
- Daniels, Kass
- 1999
(Show Context)
Citation Context ...rtainty of the true spectral density around the ARMA model. The motivation behind this hierarchy was to obtain improved estimation in small samples by shrinking towards a parametric form (Chen, 1979; =-=Daniels & Kass, 1999-=-). With this model, the posterior distribution of the true spectral density at the Fourier frequencies, conditional on 2 and , is easy to calculate. The mean of the conditional posterior, p n f (!)... |

65 | A flexible and fast method for automatic smoothing - Gasser, Kneip, et al. - 1991 |

56 | Shrinkage estimators for covariance matrices - Daniels, Kass |

44 | On the nonparametric estimation of covariance functions - HALL, FISHER, et al. - 1994 |

37 |
Bayesian analysis of covariance matrices and dynamic models for longitudinal data
- DANIELS, POURAHMADI
- 2002
(Show Context)
Citation Context ...p,q) model. However, which 7 values of p and q should be selected? This has not been addressed in other work with this types of shrinkage prior for dependence (Chen, 1979; Daniels & Kass, 1999, 2001; =-=Daniels & Pourahmadi, 2002-=-). To avoid having to answer this question, we propose an estimator which averages over a class of parametric models. The estimator we propose averages over a class of ARMA(p; q) models, where p 2 f0;... |

19 |
Bayesian inference for a normal dispersion matrix and its application to stochastic multiple regression analysis
- Chen
- 1979
(Show Context)
Citation Context ...res the uncertainty of the true spectral density around the ARMA model. The motivation behind this hierarchy was to obtain improved estimation in small samples by shrinking towards a parametric form (=-=Chen, 1979-=-; Daniels & Kass, 1999). With this model, the posterior distribution of the true spectral density at the Fourier frequencies, conditional on 2 and , is easy to calculate. The mean of the conditiona... |

15 | Spectral analysis of replicated biomedical time series - Diggle, Wasel - 1997 |

12 | Bayesian inference on periodicities and component spectral structure in time series - Huerta, West - 1999 |

9 |
A Note on the Transformation of Chi-Squared Variables to Normality
- Hawkins, Wixley
- 1986
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Citation Context ...y time series has a 22 distribution, although the last periodogram ordinate has a 21 distribution if n is even. Since the fourth root of a 22 random variable is approximately normally distributed (=-=Hawkins & Wixley, 1986-=-), MjI(!j) 1 4 N n f(!j) 1 4 ; Vjf(!j) 1 2 o ; (3) where for n odd, Mj = 2 1 4 (1:25) and Vj = 2 1 2 (1:5) M 2j ; for j = 1; 2; : : : ; F; where F is the number of Fourier frequencies, and, for n... |

7 | A simple generalised crossvalidation method of span selection for periodogram smoothing - Ombao, Raz, et al. - 2001 |

5 | A hierarchical approach to Covariance function estimation for Time Series. Journal of Time Series Analysis 22, 253–266 - Daniels, Cressie - 2001 |

4 |
Local bandwidth choice in kernel regression
- Hermann
- 1997
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Citation Context ... new estimators to the following existing spectral density estimators: the periodogram; an adaptive bandwidth smoother which was calculated using the glkerns function in R (Gasser et al., 1986, 1991; =-=Hermann, 1997-=-); the maximum likelihood estimator under each of the ARMA models; a wavelet estimator (Percival & Walden, 2000); and the Daniels-Cressie estimator given in equation (6) and the shrinkage estimator gi... |

3 | Interpolating Vancouver's daily ambient PM10 - Sun, Zidek, et al. - 2000 |

2 | Asymptotically optimal estimation in misspeci…ed time series models - Dahlhaus, Wefelmeyer - 1996 |

2 |
Residual pattern in nonlinear regression
- Gasser, Sroka, et al.
- 1986
(Show Context)
Citation Context ...ckage of R. We compared the new estimators to the following existing spectral density estimators: the periodogram; an adaptive bandwidth smoother which was calculated using the glkerns function in R (=-=Gasser et al., 1986-=-, 1991; Hermann, 1997); the maximum likelihood estimator under each of the ARMA models; a wavelet estimator (Percival & Walden, 2000); and the Daniels-Cressie estimator given in equation (6) and the s... |

2 |
Periodograms and pulse detection methods for pulsatile hormone data
- Grambsch, Meller, et al.
- 2002
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Citation Context ...ensity estimation. In longitudinal studies, for example, time series are observed for multiple subjects, and a common periodic behavior within each series may be of interest, as in the example in x5 (=-=Grambsch et al., 2002-=-). Hierarchical models, similar to the one 14 proposed in this paper, might be adapted to such a setting by shrinking the subject-specic spectral densities to a population spectral density. The autho... |

1 | A Bayesian curve approach to power spectrum estimation - Denison, Mallick, et al. - 2002 |

1 | Ecient bias corrected nonparametric spectral estimation - Pawitan, Gangopadhyay - 1991 |

1 | Some Bayesian considerations in spectral estimation - Shaman - 1977 |