The paper presents an empirical comparison of performance of three well known M – estimators (i.e. Huber, Tukey and Hampel’s M – estimators) and also some new ones. The new M – estimators were motivated by weighting functions applied in orthogonal polynomials theory, kernel density estimation as well as one derived from Wigner semicircle probability distribution. M – estimators were used to detect outlying observations in contaminated datasets. Calculations were performed using iteratively reweighted least-squares (IRLS). Since the residual variance (used in covariance matrices construction) is not a robust measure of scale the tests employed also robust measures i.e. interquartile range and normalized median absolute deviation. The methods were tested on a simple leveling network in a large number of variants showing bad and good sides of M – estimation. The new M – estimators have been equipped with theoretical tuning constants to obtain 95% efficiency with respect to the standard normal distribution. The need for data – dependent tuning constants rather than those established theoretically is also pointed out.
Objective: The goal of this contribution is to present and familiarize the medical community with the method for the assessment of trace and essentials elements in prostate tissue sections. Materials and methods: X-ray fl uorescence based technique (namely Synchrotron Induced X-ray Emission (SRIXE)) is described in terms of methodology, sample preparation and the evaluation of the recorded results (spectral data sets). Materials for the samples were collected from the patients underwent radical prostatectomy due to Adenocarcinoma prostatae. Specimens were freeze-dried, cut by microtome (to the thickness of 15 μm), one slice was placed on Mylar foil (for SRIXE measurements) and adjacent one on microscopic glass (for histopathological assessment). Results: Results presented here show the usability of SRIXE method for the evaluation of concentration of trace and essential elements in prostate tissue sections with the spatial resolution better than 15 microns. Discussion: Histopathological analysis of samples, which is only focused on morphological features, is unable to reveal information about changes in biochemical signature of tissues aff ected by the illness. SRIXE is a powerful and promising technique to analyse even very low concentrations of selected elements at the cellular level without any labelling or separating procedures. Obtained results may be correlated with classic histopathological assessment allowing for drawing conclusions on the changes in certain elements concentrations with the progression of disease. Moreover, mentioned in this work analysis, can be performed for any type of biological tissues.