Time error estimate of minimum or maximum from a polynomial fit

[dbenn]

See Roy Axelson's request here: https://www.aavso.org/comment/162089#comment-162089

[dbenn]

Grant Foster's light curve analysis book briefly talks about uncertainty of minima/maxima when using a model, such as binned means or polynomials, but unlike his treatment of period error for which standard error of the frequency and FWHM are suggested, there is not a similar concrete suggestion for polynomials fits.

[dbenn]

This overview of methods by Tom Richards of Variable Stars South focusses on polynomial fitting and Kwee van Woerden and on balance seems to favour polynomials, especially low order polynomials:

https://www.variablestarssouth.org/wp-content/uploads/2020/01/nl_2020-1.pdf

It emphasises the importance of estimating "...which order of polynomial fits best without over-fitting, and what does that do for the vital polynomial curve-fit to minimum" (which VStar already provides, via RMS, AIC, BIC goodness of fit measures) and minima/maxima error estimates but doesn't examine that in any detail at least for polynomial fits. It also suggests the utility of a suite of methods, as found in Bob Nelson's Minima 25.

What's needed is equations, algorithms or source code though.

[dbenn]

This paper (via Brad Walter, who has pointed to a number of papers including Kwee van Woerden related papers) is useful re: polynomial extrema uncertainty:

https://www.researchgate.net/publication/227023900_On_Methods_for_the_Light_Curves_Extrema_Determination

See the equation in Section 2, page 2.

It makes sense that if the extrema determination method is derivative based, the uncertainty must be in terms of this.

Question: Could the term in the numerator simply be based upon the time resolution of the first derivative based extrema determination?

[dbenn]

See also https://www.aavso.org/tmaxmin which also provides some commentary on this, including mention of Bob Nelson's Minima software.

I also want to make note of the passing of Bob Nelson on November 2 2022 (3 days ago).