On the Asymptotic Distribution of a Weighted Least Absolute Deviation Estimate for a Bifurcating Autoregressive Process

被引：0

作者：

Terpstra, Jeff T. ^{[1
]}

机构：

[1] Western Michigan Univ, Dept Stat, Kalamazoo, MI 49008 USA

来源：

ROBUST RANK-BASED AND NONPARAMETRIC METHODS | 2016年 / 168卷

关键词：

Asymptotic normality; Bifurcating autoregressive model; L1-estimates; Median; Schweppe weights;

D O I：

10.1007/978-3-319-39065-9_5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces a new class of estimates for estimating the parameter vector of a first-order bifurcating autoregressive model. The estimates minimize a sum of weighted absolute deviations where the weights are of the Schweppe variety. Asymptotic linearity properties are derived for the so called WL1-estimate. Based on these properties, the WL1-estimate is shown to be asymptotically normal at rate n(1/2). The results hinge on two new law of large numbers theorems for bifurcating processes. As an application of the theory, some asymptotic relative efficiency comparisons are made.

引用

页码：81 / 100

页数：20

共 37 条

[21] On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)
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[23] A DERIVATION OF THE ASYMPTOTIC-DISTRIBUTION OF THE PARTIAL AUTOCORRELATION FUNCTION OF AN AUTOREGRESSIVE PROCESS
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[26] ASYMPTOTIC-DISTRIBUTION OF THE MOVING AVERAGE COEFFICIENTS OF AN ESTIMATED VECTOR AUTOREGRESSIVE PROCESS
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[29] Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors
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[30] A WEIGHTED LEAST SQUARES PROCEDURE TO APPROXIMATE LEAST ABSOLUTE DEVIATION ESTIMATION IN TIME SERIES WITH SPECIFIC REFERENCE TO INFINITE VARIANCE UNIT ROOT PROBLEMS
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