STT-Research Memoranda #693 On asymptotic distributions of weighted sums of periodograms
نویسندگان
چکیده
We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions of the quadratic forms involving integrals of weighted periodograms. Conditions for asymptotic normality of these weighted sums are simple and resemble Lindeberg-Feller condition for weighted sums of independent and identically distributed random variables. Our results are valid for short, long or negative memory processes. The proof is based on sharp bounds derived for Bartlett type approximation of these sums by the corresponding sums of weighted periodograms of independent and identically distributed random variables.
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