Gao, H.--Y. (1993) Choice of thresholds for wavelet estimation of the log spectrum. Technical Report 438, Department of Statistics, Stanford University.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... The threshold is selected by minimizing a cross validatory estimator of integrated squared error (ISE) Some possible generalizations of Nason s method have been developed by Wang (1996) Others who have addressed threshold selection and wavelet shrinkage applications include Bruce and Gao (1995) Gao (1993), and Saito (1993) A comprehensive overview of different thresholding methods was given by Nason (1995) Motivated by a body of work in nonparametric density estimation using orthogonal series and their intrinsic connections with Bayesian methods (e.g. Brunk 1978; Wahba 1981) I approached the ....

Gao, H-Y. (1993), "Choice of Thresholds for Wavelet Estimation of the Log-Spectrum," technical report, Stanford University, Dept. of Statistics.

....level of the hypothesis test, P F may be computed from the tail probabilities of the noise coefficients. Recently it has been recognized by Gao that the far tail probabilities are much heavier than Gaussian probabilities, and that with the thresholds s 2 lnN , P F tends to one for large N [21]. Larger thresholds are needed at fine scales, where the departure from the Gaussian model is greatest. Using a large deviations upper bound on the tail probabilities, Gao has proposed a threshold design for which P F tends to zero for large N. Here we show that for a specified P F , the ....

....limited due to the slow growth of the function 2 j 6 in the range of interest, e.g. 1 2 j 6 2 for the seven finest scales. At fine and moderate scales, the actual tail probability evaluated at (4. 2) is generally substantially larger than that given by the Gaussian approximation [21]. For instance, for N = 512, l 4.53 in (4.2) and P F 0.2 using the Gaussian approximation (4.3) However, a more accurate evaluation of (4.1) using the saddle point approximation of the next section reveals that, in fact, P F 0.7 for the wavelet RD6. 4.2. Saddle Point ....

H.-Y. Gao, "Choice of Thresholds for Wavelet Estimation of the Log Spectrum," preprint, UC Berkeley, Dept of Statistics, 1993.

....thresholding policies. Nason (1994) adjusted the well known cross validation method for use with wavelets. The threshold is selected by minimizing a cross validatory estimator of integrated square error (ISE) A few other references in threshold selection and wavelet shrinkage applications are Gao (1993) and Vidakovic (1994, 1995) 3 An Illustrative Example To illustrate our methodology we consider an artificial time series which is the sum of two perfect periodic series. Looking at the scalogram of the corresponding wavelet decomposition, we will be able to split the wavelet decomposition into ....

Gao, H-Y. (1993). Choice of thresholds for wavelets estimation of the log-spectrum, Tech. Report, Statistics, Stanford University.

.... are Chui (1992) and Daubechies (1992) References for uses of wavelets in statistics are Donoho and Johnstone (1990) Donoho (1993) Nason (1994) For uses in time series analysis see Brillinger (1994a, b) Neumann (1996) von Sachs and Schneider (1996) von Sachs, Nason and Kroisandt (1996) Gao (1997), Neumann and von Sachs (1997) and Chiann and Morettin (1998) In section 2 we give the basic ideas on locally stationary processes and the concept of evolutionary spectra. Section 3 presents two dimensional orthonormal wavelet bases. Wavelet estimators and kernel estimators of the evolutionary ....

Gao, H.Y. (1997). Choice of thresholds for wavelet estimation of the log spectrum. Journal of Time Series Analysis, Vol. 18, No. 3, 231-252.

....discuss a possible approach to the local spectral analysis of the series. Another approach, Stationary Wavelet Transforms 13 also using wavelets, is discussed by Sachs and Schneider [vSS] The use of wavelets in the estimation of the spectral density of a stationary series is considered by Gao [Ga1, Ga2]. 6.1 The wavelet periodogram and the wavelet spectrum For each fixed j, consider the sequence b j k as defined in (16) As was pointed out in Section 3.2 above, this sequence provides information about the original data at scale 2 J Gammaj . A way of seeing this more clearly is to recall ....

Gao, H.-Y.: Choice of thresholds for wavelet estimation of the log spectrum. Technical Report number 438, Department of Statistics, Stanford University. (1993).

....X represents the coefficients of the data after expressing the operator in the wavelet basis for signals . In this paper we have concentrated on estimation of a trend or signal in the presence of stationary correlated noise. This is thus a (non parametric) first moment setting. Other authors (Gao, 1993; Moulin, 1994; Neumann, 1996) have considered the application of wavelet shrinkage to the second moment setting of estimation of the spectral density of a stationary process of zero mean. These papers and ours may therefore be seen as addressing complementary problems. There has been much recent ....

Gao, H.--Y. (1993) Choice of thresholds for wavelet estimation of the log spectrum.

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Gao, H.--Y. (1993) Choice of thresholds for wavelet estimation of the log spectrum. Technical Report 438, Department of Statistics, Stanford University.

No context found.

Gao, H.Y.: Choice of thresholds for wavelet estimation of the log spectrum. Journal of Time Series Analysis 18(1997), No. 3, 231-252.

No context found.

Gao, H-Y. (1993). Choice of thresholds for wavelet estimation of the log-spectrum. Tech. Report, Statistics, Stanford University.

No context found.

Gao, H-Y. (1993). Choice of thresholds for wavelet estimation of the log-spectrum. Tech. Report, Statistics, Stanford University.

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