Linear models

MATH-341

Weighted sum CLT proof

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Description

Some students asked for a reference where a proof of the weighted CLT theorem can be found (slide 45). The theorem is attributed to Hájek & Šidák, and a proof (via a series of intermediate results) can be found in:

Sen & Singer (1993). Large Sample Methods in Statistics. Chapman & Hall.

See pages 108-119. In particular, the result is not a simple consequence of the classical CLT, but rather it hinges on Lyapunov's CLT.