Mynbaev, Kairat
(2000):
*$L_p$-Approximable sequences of vectors and limit distribution of quadratic forms of random variables.*
Published in: Advances in Applied Mathematics
, Vol. 26,
(2001): pp. 302-329.

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## Abstract

The properties of $L_2$-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are "two-wing" averages of martingale differences. The results constitute the first significant advancement in the theory of $L_2$-approximable sequences since 1976 when Moussatat introduced a narrower notion of $L_2$-generated sequences. The method relies on a study of certain linear operators in the spaces $L_p$ and $l_p$. A criterion of $L_p$-approximability is given. The results are new even when the weights generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.

Item Type: | MPRA Paper |
---|---|

Original Title: | $L_p$-Approximable sequences of vectors and limit distribution of quadratic forms of random variables |

Language: | English |

Keywords: | linear operators in $L_p$ spaces; central limit theorem; quadratic forms of random variables |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics |

Item ID: | 18447 |

Depositing User: | Kairat Mynbaev |

Date Deposited: | 08 Nov 2009 06:36 |

Last Modified: | 28 Sep 2019 02:57 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/18447 |