The paper compares linear, quadratic, and cubical regression together with several weighted and robust approaches in the context of lipophilicity determination. The comparison is done on 35 model compounds on data from different modifiers used on RP18, CN, and silica plates. It can be concluded that the use of weighted and moderately robust regression technique increases correlation between extrapolated retention and real lipophilicity, whereas polynomial and very robust techniques give visibly worse results due to their excessive flexibility and higher extrapolation uncertainty. Additionally, we have compared averaging retention from different modifiers by RF, k, and RM values. The results are similar; however, surprisingly, RF averaging performs slightly better to the other approaches.
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In this apper, a robust structural approach to detection, object segmentation and calculation of object features in medical images of different modalities is proposed. The goal of the presented approach is the detection and feature-based objective description of objects of interest in medical images for diagnosis of lesions in a natural way and in accordance with the physician diagnostic feature used in the clinical practice. A set of local structural features was divided in two classes: propetrties of planar object shape and intensity distribution prperties. Experimental results of the extraction of diagnostic properties of lessions on lung images confirmed the advantage of the proposed method over the conventional approach of histogram-based segmentation.
Activities of radioisotopes were measured in samples of forest soil. The samples were collected in forests situated along the roads from Złoty Stok (Poland) to Hradec Králové (Czech Republic). Each soil profile was separated into individual horizons and subhorizons. Activities of radioisotopes were measured in the sample of each soil horizon. Activities of the following radioisotopes were determined by gamma-ray spectrometry: 214Pb, 214Bi, 231Th, 235U, 212Pb, 212Bi and 228Ac. Distributions of the data concerning radioactivities were positively skewed. The lowest activity was found for 235U (median value was 2.25 Bg/kg) and the highest one for 228Ac (16.26 Bg/kg in median). In organic horizons activities of radionuclides were lower than in organic ones. Interrelation between activities was examined using ordinary and robust regression methods. It was found that activities of the radioisotopes were well correlated.
There are many sample surveys of populations that contain outliers (extreme values). This is especially true in business, agricultural, household and medicine surveys. Outliers can have a large distorting influence on classical statistical methods that are optimal under the assumption of normality or linearity. As a result, the presence of extreme observations may adversely affect estimation, especially when it is carried out at a low level of aggregation. To deal with this problem, several alternative techniques of estimation, less sensitive to outliers, have been proposed in the statistical literature. In this paper we attempt to apply and assess some robust regression methods (LTS, M-estimation, S-estimation, MM-estimation) in the business survey conducted within the framework of official statistics.
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Robust statistical regression is a regression which is insensitive to so called excess observations, due to measurement errors or non-typical observations. Various coefficients selection criteria - such as minimization of the weighted sum of squared deviations, minimization of the sum of residuals absolute values, minimization of the median of squared residuals - are used to determine the robust regression equation for discrete data. Similarly, in the case of regression with interval data various methods are used to determine the robust regression equation, e.g. the multi criteria programming. In the paper a method of constructing a robust linear regression for interval data is proposed, which makes use of the multi criteria programming, in which the median criterion is proposed as the robustness criterion. We propose a procedure for arriving at the final interval regression (using various models) and apply this procedure to constructing an interval regression model for electricity load in a Polish city.
Odporne procedury estymacji umożliwiają zredukowanie wpływu błędów nadmiernych na wyniki pomiarów. Zastosowanie metody najmniejszej mediany kwadratów (MNMK) do wyznaczania charakterystyk aparatury pomiarowej wiąże się z koniecznością oceny otrzymanych wyników. W pracy zaproponowano metodę szacowania wariancji przewidywanej średniej wartości obserwacji dla MNMK. Przeprowadzono również badania symulacyjne w celu porównania vvyników oszacowania z otrzymanymi w trakcie symulowanego eksperymentu. Uzyskane rezultaty potwierdzają poprawność proponowanych koncepcji.
EN
Robust regression is commonly used to reduce effects caused by outliers in measurement data sets. Evaluation of calibration lines of measuring instruments determined with a use of a least median of squares (LMS) method is essential. Standard error of mean response might be used to estimate the quality of the calibration lines. An idea of estimation of the standard error of mean response in case of the LMS method is proposed in this paper. A priori procedure enables to perform the estimation before the measurements. A posteriori procedure is used after the measurements, when there are available its results. The procedures a priori and a posteriori have been verified in simulation research. The estimated and calculated on simulation values of LMS standard errors of mean response have been compared to proof correctness of the estimation method. Relatively small errors of estimation confirm that the procedure is correct.
W wielu badaniach z zakresu statystyki gospodarczej liczebność próby jest na tyle duża, że obserwacje odstające mają stosunkowo niewielki wpływ na wartości szacowanych parametrów. W badaniach prowadzonych na niskim poziomie agregacji w ramach statystyki krótkookresowej obecność obserwacji odstających może być jednak znacząca. Z tego powodu w przypadku populacji takich jak populacja przedsiębiorstw obok podejścia klasycznego w badaniach powinien być uwzględniany nurt metod odpornych na występowanie jednostek nietypowych. W literaturze przedmiotu zaproponowano wiele alternatywnych metod estymacji mniej wrażliwych na wartości odstające. W opracowaniu weryfikacji empirycznej poddano jedną z nich – M-estymację. Celem analizy była ocena jej użyteczności w odniesieniu do badania małych przedsiębiorstw.
EN
In many business surveys, sample sizes are large enough to compensate for the presence of outliers, which have a relatively small impact on estimates. However, at low levels of aggregation, the impact of outliers might be significant. Therefore, in the case of a population such as the population of enterprises, the classical approach should be accompanied by methods that resist the occurrence of outliers. To deal with this problem, several alternative technique of estimation, less sensitive to outliers, have been proposed in the statistics literature. In this paper we look at one of them – M-estimation, and compare its usefulness in the small businesses survey.
The main aim of this study is the prediction and quantity evaluation of important yarn properties (tensile, unevenness, hairiness and imperfections of yarn) from fibre properties by the robust regression and extra sum squares methods. We used cotton fibre and yarn properties measured by means of an HVI system and Uster tester. Properties of 87 Controlled samples of ring-spun cotton yarn with linear densities ranging from 19.2 to 37.4 tex with twist multiple: atex = 3927.8 (from from 19.2 to 37.4 tex) were used. In this way we selected the effective variables by considering all possible regressions and through the criteria of the mean square error (MSE) and adjusted R2. Optimum equations with appropriate variables and relative importance of various variables were also investigated. After the fit, desirable MSE statistics and large adjusted R2 values were observed.
PL
Głównym celem badań było przewidzenie i określenie podstawowych właściwości przędz (wytrzymałość na rozciąganie, nierównomierność, włochatość i błędy przędzy) na podstawie właściwości włókien stosując regresję odpornościową i metodą opartą na sumie kwadratów. Do badań przędz i włókien bawełnianych stosowano system HVI i przyrząd Uster. Badano właściwości 87 próbek przędz obrączkowych o masie liniowej od 19.2 do 37.4 tex i współczynniku skrętu atex = 3927.8. Czynniki mające największy wpływ na jakość przędzy wytypowano stosując kryteria błędu średniokwadratowego (MSE) oraz skorygowany współczynnik determinacji R2. Opracowano rownież optymalne rownania i poddano je analizie. Określono współczynniki R2 oraz błąd średniokwadratowy.
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