ИСТИНА

Any eye tracker produces noisy recordings due to errors of a complex algorithm that calculates an instantaneous gaze direction. In most studies, this noise can be neglected, since the error is rather small. But in the studies of fixational eye movements the noise level of the equipment matches the amplitude of the useful signal. Data smoothing methods based on local polynomial regression with quadratic loss function (Savitzky, Golay, 1964) are commonly used to reduce the noise. Limitation of those methods is that the linear smoothers are very sensitive to outliers and leaps. To remove outliers a preliminary median smoothing is usually performed. It would be quite important to have one robust procedure as an alternative to this two-step smoothing process. We suggest a new implementation of a robust smoothing technique based on Huber M-smoother (Tsybakov, 1982a, 1982b, 1983). This method with a non-quadratic loss function is intermediate between median smoother and the ordinary Nadaraya-Watson kernel smoother (Härdle, 1990). An iterative algorithm is conventionally used to calculate the Huber estimate. Such smoothers are commonly not in use perhaps because eye movement data processing would take a lot of time for long records. However, A. Tsybakov and V. Doubrovski developed (unpublished report, 1990) a fast algorithm for calculating Huber's estimate in a finite number of steps for the statistical package XploRe (Härdle, 1990). The MATLAB/Octave implementation of this algorithm was tested on eye movements data containing microsaccades with amplitude up to 1°, and showed high efficiency. Supported by RFBR grant 19-013-00784