Approximate bias for first-order autoregressive model with uniform innovations. Small sample case

Karima Nouali; Hocine Fellag

Discussiones Mathematicae Probability and Statistics (2002)

  • Volume: 22, Issue: 1-2, page 15-26
  • ISSN: 1509-9423

Abstract

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The first-order autoregressive model with uniform innovations is considered. The approximate bias of the maximum likelihood estimator (MLE) of the parameter is obtained. Also, a formula for the approximate bias is given when a single outlier occurs at a specified time with a known amplitude. Simulation procedures confirm that our formulas are suitable. A small sample case is considered only.

How to cite

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Karima Nouali, and Hocine Fellag. "Approximate bias for first-order autoregressive model with uniform innovations. Small sample case." Discussiones Mathematicae Probability and Statistics 22.1-2 (2002): 15-26. <http://eudml.org/doc/287593>.

@article{KarimaNouali2002,
abstract = {The first-order autoregressive model with uniform innovations is considered. The approximate bias of the maximum likelihood estimator (MLE) of the parameter is obtained. Also, a formula for the approximate bias is given when a single outlier occurs at a specified time with a known amplitude. Simulation procedures confirm that our formulas are suitable. A small sample case is considered only.},
author = {Karima Nouali, Hocine Fellag},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {autoregressive model; bias; outlier; uniform distribution},
language = {eng},
number = {1-2},
pages = {15-26},
title = {Approximate bias for first-order autoregressive model with uniform innovations. Small sample case},
url = {http://eudml.org/doc/287593},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Karima Nouali
AU - Hocine Fellag
TI - Approximate bias for first-order autoregressive model with uniform innovations. Small sample case
JO - Discussiones Mathematicae Probability and Statistics
PY - 2002
VL - 22
IS - 1-2
SP - 15
EP - 26
AB - The first-order autoregressive model with uniform innovations is considered. The approximate bias of the maximum likelihood estimator (MLE) of the parameter is obtained. Also, a formula for the approximate bias is given when a single outlier occurs at a specified time with a known amplitude. Simulation procedures confirm that our formulas are suitable. A small sample case is considered only.
LA - eng
KW - autoregressive model; bias; outlier; uniform distribution
UR - http://eudml.org/doc/287593
ER -

References

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  1. [1] J. Andel, On AR(1) processes with exponential white noise, Communication in Statistics, A, Theory and Methods 17 (5) (1988), 1481-1495. Zbl0639.62082
  2. [2] C.B. Bell and E.P. Smith, Inference for non-negative autoregressive schemes, Communication in Statistics, Theory and Methods 15 (8) (1986), 2267-2293. Zbl0604.62087
  3. [3] P. Bickel and K. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Wiley: New York 1977. Zbl0403.62001
  4. [4] Y.J. Choi, Kolmogorov-Smirnov Test with Nuisance Parameters in Uniform Case, M.S. Thesis, University of Washington 1980. 
  5. [5] A.J. Fox, Outliers in time series, J. Roy. Stat. Soc. 34 (B) (1972), 350-363. Zbl0249.62089

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