### Abstract

We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate ofn
^{-2}can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.

Original language | English (US) |
---|---|

Pages (from-to) | 926-936 |

Number of pages | 11 |

Journal | Biometrics |

Volume | 67 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bias correction
- Spatial marked point process
- Spatial point process
- Subsampling

### ASJC Scopus subject areas

- Applied Mathematics
- Statistics and Probability
- Agricultural and Biological Sciences(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Medicine(all)

### Cite this

**Bias-Corrected Variance Estimation and Hypothesis Testing for Spatial Point and Marked Point Processes Using Subsampling.** / Guan, Yongtao.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Bias-Corrected Variance Estimation and Hypothesis Testing for Spatial Point and Marked Point Processes Using Subsampling

AU - Guan, Yongtao

PY - 2011/9

Y1 - 2011/9

N2 - We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate ofn -2can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.

AB - We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate ofn -2can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.

KW - Bias correction

KW - Spatial marked point process

KW - Spatial point process

KW - Subsampling

UR - http://www.scopus.com/inward/record.url?scp=80052814276&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052814276&partnerID=8YFLogxK

U2 - 10.1111/j.1541-0420.2010.01517.x

DO - 10.1111/j.1541-0420.2010.01517.x

M3 - Article

C2 - 21133879

AN - SCOPUS:80052814276

VL - 67

SP - 926

EP - 936

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 3

ER -