Distributional theory for the DIA method

Journal article (2017)

Authors

P.J.G. Teunissen Mathematical Geodesy and Positioning - CEG , Curtin University
Research Group
Mathematical Geodesy and Positioning (CEG) (TU Delft)
Copyright: © 2017 P.J.G. Teunissen
DOI: https://doi.org/10.1007/s00190-017-1045-7
Bias Best linear unbiased prediction (BLUP) Best linear unbiased estimation (BLUE) Correct detection (CD) Correct identification (CI) Missed detection (MD) Baarda test statistic Detection, Identification and Adaptation (DIA) DIA estimator Hazardous probability Misclosure partitioning Tienstra transformation Voronoi-partitioning unit sphere
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Published Date

06-07-2017

Language

English

Faculty

Civil Engineering & Geosciences

Department

Geoscience and Remote Sensing

Research Group

Mathematical Geodesy and Positioning

Abstract

The DIA method for the detection, identification and adaptation of model misspecifications combines estimation with testing. The aim of the present contribution is to introduce a unifying framework for the rigorous capture of this combination. By using a canonical model formulation and a partitioning of misclosure space, we show that the whole estimation–testing scheme can be captured in one single DIA estimator. We study the characteristics of this estimator and discuss some of its distributional properties. With the distribution of the DIA estimator provided, one can then study all the characteristics of the combined estimation and testing scheme, as well as analyse how they propagate into final outcomes. Examples are given, as well as a discussion on how the distributional properties compare with their usage in practice.