Statistical Shape Analysis of The Sand Hills in Ardestan in Presence of Measurement Error

According to multiple sources of errors, shape data are often prone to measurement error. Ignoring such error, if does exists, causes many problems including the biasedness of the estimators. The estimators coming from variables without including the measurement errors are called naive estimators. These for rotation and scale parameters are biased, while using the Procrustes matching for two dimensional shape data. To correct this and to improve the naive estimators, regression calibration methods that can be obtained through the complex regression models and invoking the complex normal distribution, as well as the conditional score are proposed in this paper. Moreover, their performance are studied in simulation studies. Also, the statistical shape analysis of the sand hills in Ardestan in Iran is undertaken in presence of measurement errors.