Astronomical (heteroscedastic) measurement errors: Statistical issues and problems

A statistical model for astronomical data with measurement errors is described and discussed. Attention is drawn to the distinction between two types of measurement errors according to whether or not the magnitude (variance) of the measurement error depends on the measurement. It is emphasized that when the magnitude of the measurement error does not depend on the measurement, more efficient procedures based on suitable weighting of the observations are possible. However, when the magnitude of the measurement error depends on the measurement, weighting biases the procedure. A method for comparing muItivariate data sets, valid for both kinds of measurement error, is described and a variety of other statistical problems are considered and solutions are proposed.