How to Derive Asymptotic Distribution of Sum of Squares

In this video I cover two approaches to derive the asymptotic distribution of a sum of squares statistic. First method is a normal approximation which is not very good, and second method is a chi-squared approximation which is essentially 1-for-1.

Link to delta method video if you're unfamiliar: https://www.youtube.com/watch?v=YVQtTQRs6ls