# On Statistical Properties of A Veracity Scoring Method for Spatial Data

## TL;DR

This paper develops a veracity scoring method for spatial data without reference data, providing consistent parameter estimation and demonstrating advantages over traditional methods through simulations and real data application.

## Contribution

It introduces a novel veracity scoring approach based on local summaries for spatial data lacking reference data, along with a consistent estimation method and theoretical analysis.

## Key findings

- VS-based estimators are consistent under non-stationary noise.
- VS estimators outperform OLS in asymptotic mean squared error.
- Method successfully applied to real coal seam data.

## Abstract

Measuring veracity or reliability of noisy data is of utmost importance, especially in the scenarios where the information are gathered through automated systems. In a recent paper, Chakraborty et. al. (2019) have introduced a veracity scoring technique for geostatistical data. The authors have used a high-quality `reference' data to measure the veracity of the varying-quality observations and incorporated the veracity scores in their analysis of mobile-sensor generated noisy weather data to generate efficient predictions of the ambient temperature process. In this paper, we consider the scenario when no reference data is available and hence, the veracity scores (referred as VS) are defined based on `local' summaries of the observations. We develop a VS-based estimation method for parameters of a spatial regression model. Under a non-stationary noise structure and fairly general assumptions on the underlying spatial process, we show that the VS-based estimators of the regression parameters are consistent. Moreover, we establish the advantage of the VS-based estimators as compared to the ordinary least squares (OLS) estimator by analyzing their asymptotic mean squared errors. We illustrate the merits of the VS-based technique through simulations and apply the methodology to a real data set on mass percentages of ash in coal seams in Pennsylvania.