TY - JOUR
AB - We consider quadratic forms [GRAPHICS] where X-j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q(n), and the distribution of the same quadratic forms with X-j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well. as to nonstationary AR(1) processes.
AU - GĂ¶tze, Friedrich
AU - Tikhomirov, AN
ID - 1622394
IS - 2
JF - ANNALS OF PROBABILITY
KW - limit theorems
KW - asymptotic distribution
KW - quadratic forms
KW - independent random variables
KW - Berry-Esseen bounds
SN - 0091-1798
TI - Asymptotic distribution of quadratic forms
VL - 27
ER -