I have recently interviewed for a statistical analysis job and was asked a question about why linear least squares regression fails when the data is heteroskedastic. The correct answer to this question, according to the interviewers, is that heteroskedastic data means that the equation of the regression line produced by least squares regression is an unbiased estimator of the true relationship, but that it is NOT efficient, essentially because the part of the dataset where the variance is smaller than average is effectively underweighted.
My question is which textbooks could I use to find more detail about this topic, and other similar topics at this level, e.g.
- the relationship between data being normally distributed and least-squares linear regression being the maximum likelihood estimator for the straight line fit
[I have a degree in mathematics but with minimal statistics background & understand general probability concepts such as the central limit theorem, random variables, etc, and I know high school level statistics up to the British A-level S4 statistics, however I lack a certain level of statistics knowledge and don't know what I don't know or where to find out more... ]