Suprihatin, Bambang and Guritno, Suryo and Haryatmi, Sri (2012) *Delta Method for Deriving the Consistency of Bootstrap Estimator for Parameter of Autoregressive Model.* Proceeding of the 8th World Congress on Probability and Statistics, Istanbul. (Submitted)

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## Abstract

Let be the first order of autoregressive model and let be the sample that satisfies such model, i.e. the sample follows the relation where is a zero mean white noise process with constant variance . Let be the estimator for parameter . Brockwell and Davis (1991) showed that and . Meantime, Central Limit Theorem asserts that the distribution of converges to Normal distribution with mean 0 and variance as . In bootstrap view, the key of bootstrap terminology says that the population is to the sample as the sample is to the bootstrap samples. Therefore, when we want to investigate the consistency of the bootstrap estimator for sample mean, we investigate the distribution of contrast to , where is a bootstrap version of computed from sample bootstrap . Asymptotic theory of the bootstrap sample mean is useful to study the consistency for many other statistics. Let be the bootstrap estimator for . In this paper we study the consistency of using delta Method. After all, we construct a measurable map such that = conditionally almost surely, by applying the fact that , where G is a normal distribution. We also present the Monte Carlo simulations to emphisize the conclusions.

Item Type: | Article |
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Subjects: | H Social Sciences > HA Statistics |

Divisions: | Faculty of Mathematics and Natural Sciences > Department of Mathematics |

Depositing User: | Mr. Bambang Suprihatin |

Date Deposited: | 22 Apr 2014 18:38 |

Last Modified: | 22 Apr 2014 18:38 |

URI: | http://eprints.unsri.ac.id/id/eprint/4322 |

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