Some statistical aspects of estimating the local red clump absolute magnitude

Various statistical issues regarding estimation of the mean absolute magnitude of the red clump stars, using Hipparcos parallaxes, are discussed. The problem is put in the broader context of estimation of the functional dependence of the absolute magnitude on colour of local giant stars, as derived from Hipparcos observations. The methods used include calculation of the medians and modes of the absolute magnitudes of stars binned in narrow colour intervals. The modes are determined by kernel density estimation of the underlying distribution of absolute magnitudes. A weighted least trimmed squares procedure, which allows the incorporation of all information - including negative parallaxes - is described in detail. Standard errors are estimated by bootstrapping. Results are in good agreement with those of Paczynski & Stanek.