Adaptive conditional bias-penalized kriging for improved spatial estimation of extremes

Accurate spatial estimation of extremes is an increasingly important topic in environmental research and risk assessment. Conditional bias (CB)-penalized kriging (CBPK) improves such estimation by minimizing linearly weighted sum of error variance and variance of Type-II error. However, CBPK requires skillful prescription of the weight for the CB penalty which is a significant challenge in practice. In this paper, we describe an extension of CBPK, referred to herein as adaptive conditional bias-penalized kriging (ACBPK), which objectively prescribes the weight for improved estimation of extremes without deteriorating performance in the unconditional mean squared error sense. For comparative evaluation in the real world, cross validation experiments were carried out for precipitation estimation using hourly rain gauge data in the Arkansas-Red River Basin (AB), central Texas (TX) and southeastern US (SE) areas. The results show that CB is detected for about 26, 24 and 25% of all data points in the AB, TX and SE cases, respectively, and that, given detection of CB, ACBPK reduces root mean square error of hourly precipitation exceeding 12.7 mm by 15, 21 and 9% and hourly precipitation exceeding 25.4 mm by 14, 26 and 10% relative to ordinary kriging (OK) for the AB, TX and SE cases, respectively. The overall findings indicate that, if accurate spatial estimation in the tails of the distribution is important or accurate modeling of spatiotemporally-varying correlation structure is a challenge, ACBPK should be favored over OK.