Estimating stellar parameters from spectra - 1. Goodness-of-fit parameters and lack-of-fit test

Estimating stellar parameters from spectrophotometric data is a key tool in the study of stellar structure and stellar evolution. Although many methods have been proposed to estimate stellar parameters from ultraviolet (UV), optical and infrared (IR) data using low, medium or high-resolution observational data of the target(s), only a few address the problem of the uncertainties in the stellar parameters. This information is critical for a meaningful comparison of the derived parameters with results obtained from other data and/or methods. Here we present a frequentist method to estimate these uncertainties. We demonstrate that the combined use of both a local and a global goodness-of-fit parameter alters the uncertainty intervals as determined from the use of only one of these deviation estimating parameters. This technique using both goodness-of-fit parameters is applied to the infrared 2.38-4.08 mum ISO-SWS data (Infrared Space Observatory - Short Wavelength Spectrometer) of alpha Boo yielding an effective temperature range from 4160 K to 4300 K, a logarithm of the gravity range from 1.35 to 1.65 dex and a metallicity from -0.30 to 0.00 dex. However, using a lack-of-fit test, it is shown that even the "best" theoretical models are still not capable of capturing all the structure in the data, and this is due to our incomplete knowledge and modelling of the full physical stellar structure or due to problems in the data reduction process.