### Abstract

The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE.

Original language | English |
---|---|

Pages (from-to) | 20-29 |

Number of pages | 10 |

Journal | Journal of Econometrics |

Volume | 165 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 Nov 3 |

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### Keywords

- Control variate method
- Nonparametric spectral estimator
- Spectral density matrix
- Stationary processes

### ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics
- History and Philosophy of Science

### Cite this

*Journal of Econometrics*,

*165*(1), 20-29. https://doi.org/10.1016/j.jeconom.2011.05.003

**Control variate method for stationary processes.** / Amano, Tomoyuki; Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Journal of Econometrics*, vol. 165, no. 1, pp. 20-29. https://doi.org/10.1016/j.jeconom.2011.05.003

}

TY - JOUR

T1 - Control variate method for stationary processes

AU - Amano, Tomoyuki

AU - Taniguchi, Masanobu

PY - 2011/11/3

Y1 - 2011/11/3

N2 - The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE.

AB - The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE.

KW - Control variate method

KW - Nonparametric spectral estimator

KW - Spectral density matrix

KW - Stationary processes

UR - http://www.scopus.com/inward/record.url?scp=80053306600&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053306600&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2011.05.003

DO - 10.1016/j.jeconom.2011.05.003

M3 - Article

AN - SCOPUS:80053306600

VL - 165

SP - 20

EP - 29

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -