Other
Scientific paper
Nov 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991mnras.253..198s&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 253, Nov. 15, 1991, p. 198-206.
Other
102
Analysis Of Variance, Least Squares Method, Power Spectra, Signal To Noise Ratios, Stellar Spectra, Autocorrelation, Curve Fitting, Iteration, Maximum Likelihood Estimates
Scientific paper
Periods of oscillation are frequently found using one of two methods: least-squares (LSQ) fit or power spectrum. Their errors are estimated using the LSQ correlation matrix or the Rayleigh resolution criterion, respectively. In this paper, it is demonstrated that both estimates are statistically incorrect. On the one hand, the LSQ covariance matrix does not account for correlation of residuals from the fit. Neglect of the correlations may cause large underestimation of the variance. On the other hand, the Rayleigh resolution criterion is insensitive to signal-to-noise ratio and thus does not reflect quality of observations. The correct variance estimates are derived for the two methods.
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