If one repeats a least squares fit a large number of times one would expect the means of the slope and intercept to converge to a particular value and so we should be able to determine if ordinary least squares and transverse least squares give different results. The average values for a batch of 20 trial fits of 25 data points for a given line with random errors couldn't resolve the issue. However the process can be repeated by generating a new set of 1000 normal random for each batch of 20 lines, the values for the fit averages saved and a cumulative average can be computed as the number of batches increases. Transverse least squares appears to show a better convergence to the true values.
The estimate given by ordinary least squares for the slope and intercept of the line appears to be biased.
No comments:
Post a Comment