Munich Personal RePEc Archive

Weak convergence of linear and quadratic forms and related statements on Lp-approximability

Mynbayev, Kairat and Darkenbayeva, Gulsim (2017): Weak convergence of linear and quadratic forms and related statements on Lp-approximability. Published in: Journal of Mathematical Analysis and Applications , Vol. 473, (2019): pp. 1305-1319.

[img]
Preview
PDF
MPRA_paper_101686.pdf

Download (168kB) | Preview

Abstract

In this paper we obtain central limit theorems for quadratic forms of non-causal short memory linear processes with independent identically distributed innovations. Nabeya and Tanaka (1988) suggested the format, which links the asymptotic distribution to integral operators. In their approach, integral operators had to have continuous symmetric kernels. Mynbaev (2001) employed the theory of approximations to get rid of the continuity requirement. Here we go one step further by lifting the kernel symmetry condition. Also, we establish Lp-approximability of the special sequences which arise in the theory of regressions with slowly varying regressors.

UB_LMU-Logo
MPRA is a RePEc service hosted by
the Munich University Library in Germany.