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.

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## 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.

Item Type: | MPRA Paper |
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Original Title: | Weak convergence of linear and quadratic forms and related statements on Lp-approximability |

Language: | English |

Keywords: | central limit theorem, Lp-approximability, quadratic forms |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General |

Item ID: | 101686 |

Depositing User: | Kairat Mynbaev |

Date Deposited: | 17 Jul 2020 11:50 |

Last Modified: | 17 Jul 2020 11:50 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/101686 |