On Statistical Properties of a Veracity Scoring Method for Spatial Data

Measuring the veracity or reliability of observations is of utmost importance, especially in scenarios where a portion of the observations can be noisy, for example, when the information is gathered in a non-laboratory environment or through an automated system. Assessing the veracity of observations is difficult when no “good” quality replication or reference data is present, which is often the case in real-world applications. In this article, we define a veracity scoring method for geostatistical data based on “local” summaries of the observations and develop an estimation methodology for parameters of a spatial regression model incorporating the veracity scores (VS) to guard against undesirable effects of corrupted data. Under a nonstationary 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 advantages of the VS-based estimators as compared to the ordinary least squares (OLS) estimator by analyzing their asymptotic mean squared errors, both theoretically and empirically. In addition, we illustrate the merits of the VS-based technique in real-life applications by comparing the results against the existing robust geostatistical approaches on a real dataset and a simulated dataset in the real-data domain.