Lomb: statistical analysis of least-squares spectra for irregular observations

What changed

Lomb analyzes sinusoidal least-squares spectra for unequally spaced observations, deriving fixed-frequency Gaussian-noise behavior and the correlation of spectral heights at different frequencies, with astronomical numerical illustrations.

Scientific scope

Lomb analyzes sinusoidal least-squares spectra for unequally spaced observations, deriving fixed-frequency Gaussian-noise behavior and the correlation of spectral heights at different frequencies, with astronomical numerical illustrations. The target is the 1976 Astrophysics and Space Science 39(2), pages 447-462 paper. The formulas are not an independently certified executable transcription. Fits sine/cosine coefficients at a given frequency with zero-mean observations, independent zero-mean equal-variance errors and a nonsingular two-column design. Fixed-frequency Gaussian-noise reduction is scaled chi-square with two degrees of freedom; subtracting a sample mean or estimating variance requires the corresponding covariance/distribution treatment. Numerical examples use an observed-variance approximation; normalized power is not automatically that same chi-square variable. Cross-frequency correlation and aliases remain; searched-maximum significance does not follow from independent fixed-frequency tests. Section 5 approximations and the reported 11 noise/10 signal simulations are not universal guarantees. A noise-free pattern match need not identify a unique period: integer-time aliases can coincide. Earlier Barning/Vanicek and later Scargle work remain distinct; no complete proof certification.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• N. R. Lomb · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Lomb: statistical analysis of least-squares spectra for irregular observations; exact original technical journal scan
• Publisher-deposited exact 1976 Lomb journal identity

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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