Development of regional regression relationships with censored data

When no discharge record is available for a site, a regional regression rel ationship can be used to estimate low-flow quantiles. Problems arise in the derivation of such models when some at-site quantile estimates are reporte d as zero. One concern is that quantile estimates reported as zero may be i n the range from zero to the measurement threshold. A second concern is tha t a logarithmic transformation cannot be used with zero quantile estimates, so traditional log linear least squares estimators cannot be computed. Thi s paper uses visual examples and Monte Carlo simulation to compare the perf ormance of techniques for estimating the parameters of a regional regressio n model when some at-site quantile estimates are zero. Ordinary least squar es (OLS) techniques employed in practice include adding a small constant to all at-site quantile estimates (denoted OLSC), or neglecting all observati on reported as zero (denoted OLSD). OLSC and OLSD performed poorly compared to the use of a Tobit model, which is a maximum likelihood estimator (MLE) procedure that represents the below threshold estimates as a range from ze ro to the threshold level. For a small amount of censoring, the OLSD method can be acceptable. A weighted Tobit model that accounts for the heterosced asticity of the residuals in the regression model provided relatively littl e gain over the ordinary Tobit model.