Abstract
Spectrum estimates based on the raw periodogram (squared modulus of the Fourier transform) can be improved upon, at least according to criteria that matter to statisticians. Estimates based on averages of power spectrum estimates derived using orthogonal weight functions (multitaper estimates) can have better bias and variance properties. The raw periodogram also can be “post-processed,” using wavelet shrinkage or other smoothing techniques, to produce estimates that have more desirable statistical properties than the periodogram, and that are visually more pleasing. Subject to assumptions that can be difficult to test, these statistical techniques might improve inferences about the underlying physics, depending on which features of the spectrum matter physically. Differences between the periodogram and wavelet-shrinkage estimates are quite noticeable for the angular power spectrum of starlight from NGC 4622. However, estimates of the slope of a power law model for the spectrum are nearly identical.
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References
Buckheit, J., Chen, S., Donoho, D., Johnstone, I., and Scargle, J. (1995). WaveLab. Technical report, Stanford University.
Donoho, D. and Johnstone, I. (1998). Minimax estimation via wavelet shrinkage. Ann. Stat., 26: 879–921.
Donoho, D., Johnstone, I., Kerkyacharian, G., and Picard, D. (1995). Wavelet shrinkage: asymptopia? (with discussion). J. Roy. Stat. Soc., Ser. B, 57: 301–369.
Elmegreen, B., Kim, S., and Staveley-Smith, L. (2001). A fractal analysis of the H I emission from the Large Magellanic Cloud. Ap. J., 548: 749–769.
Elmegreen, D., Elmegreen, B., and Eberwein, K. (2002). Dusty acoustic turbulence in NGC 4450 and NGC 4736. Ap. J., 564: 234–243.
Fodor, I. and Stark, P. (2000). Multitaper spectrum estimation for time series with gaps. IEEE Trans. Signal Processing, 48: 3472–3483.
Gao, H.-Y. (1996). Choice of thresholds for wavelet shrinkage of the log spectrum. Technical report, MathSoft, Seattle, WA.
Komm, R., Gu, Y., Stark, P., and Fodor, I. (1999). Multitaper spectral analysis and wavelet denoising applied to helioseismic data. Ap. J., 519: 407–421.
Moulin, P. (1994). Wavelet thresholding techniques for power spectrum estimation. IEEE Trans. Signal Process., 42: 3126–3136.
Percival, D. and Walden, A. (1993). Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge, Cambridge.
Walden, A., E.McCoy, and Percival, D. (1995). Spectrum estimation by wavelet thresholding of multitaper estimates. Technical report, Dept. of Mathematics, Imperial College of Science, Technology and Medicine, London.
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Stark, P.B. (2004). Estimating Power Spectra of Galaxy Structure: Can Statistics Help?. In: Block, D.L., Puerari, I., Freeman, K.C., Groess, R., Block, E.K. (eds) Penetrating Bars through Masks of Cosmic Dust. Astrophysics and Space Science Library, vol 319. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2862-5_51
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DOI: https://doi.org/10.1007/978-1-4020-2862-5_51
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