Statistical properties of distance estimators

Dechang Chen; Michael Fries; Xiuzhen Cheng

doi:10.1007/s00362-006-0309-8

Statistical properties of distance estimators

Dechang Chen^*, Michael Fries, Xiuzhen Cheng

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Estimating the distance between two points is of fundamental concern. This paper investigates some statistical properties of three estimators of the distance between two points on a plane. The results of several theoretical comparisons of the performance of the estimators assuming a large sample size are given. Also given is the comparison of the performance of the estimators using simulation when the sample size is small. These comparisons suggest that the estimator of choice is not the most "natural" estimator in this situation. Although the discussion is given in the framework of the plane, the results are readily extended to high dimensional spaces.

Original language	English
Pages (from-to)	631-641
Number of pages	11
Journal	Statistical Papers
Volume	47
Issue number	4
DOIs	https://doi.org/10.1007/s00362-006-0309-8
State	Published - Oct 2006
Externally published	Yes

Keywords

MLE
Metric
UMVUE

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10.1007/s00362-006-0309-8

Cite this

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title = "Statistical properties of distance estimators",

abstract = "Estimating the distance between two points is of fundamental concern. This paper investigates some statistical properties of three estimators of the distance between two points on a plane. The results of several theoretical comparisons of the performance of the estimators assuming a large sample size are given. Also given is the comparison of the performance of the estimators using simulation when the sample size is small. These comparisons suggest that the estimator of choice is not the most {"}natural{"} estimator in this situation. Although the discussion is given in the framework of the plane, the results are readily extended to high dimensional spaces.",

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author = "Dechang Chen and Michael Fries and Xiuzhen Cheng",

year = "2006",

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AU - Fries, Michael

AU - Cheng, Xiuzhen

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AB - Estimating the distance between two points is of fundamental concern. This paper investigates some statistical properties of three estimators of the distance between two points on a plane. The results of several theoretical comparisons of the performance of the estimators assuming a large sample size are given. Also given is the comparison of the performance of the estimators using simulation when the sample size is small. These comparisons suggest that the estimator of choice is not the most "natural" estimator in this situation. Although the discussion is given in the framework of the plane, the results are readily extended to high dimensional spaces.

KW - MLE

KW - Metric

KW - UMVUE

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JO - Statistical Papers

JF - Statistical Papers

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ER -

Statistical properties of distance estimators

Abstract

Keywords

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