Nonparametric hyperrectangular tolerance and prediction regions for setting multivariate reference regions in laboratory medicine

Reference regions are widely used in clinical chemistry and laboratory medicine to interpret the results of biochemical or physiological tests of patients. There are well-established methods in the literature for reference limits for univariate measurements; however, limited methods are available for the construction of multivariate reference regions, since traditional multivariate statistical regions (e.g. confidence, prediction, and tolerance regions) are not constructed based on a hyperrectangular geometry. The present work addresses this problem by developing multivariate hyperrectangular nonparametric tolerance regions for setting the reference regions. The approach utilizes statistical data depth to determine which points to trim and then the extremes of the trimmed dataset are used as the faces of the hyperrectangular region. Also presented is a strategy for determining the number of points to trim based on previously established asymptotic results. An extensive coverage study shows the favorable performance of the proposed procedure for moderate to large sample sizes. The procedure is applied to obtain reference regions for addressing two important clinical problems: (1) assessing kidney function in adolescents and (2) characterizing insulin-like growth factor concentrations in the serum of adults.

EVALUATION OF LINES OF BARE OATS FOR SEVERAL ECONOMIC AND BIOLOGICAL TRAITS IN THE CONDITIONS OF CENTRAL BLACK EARTH

Проведена оценка биологических и хозяйственных свойств линий голозерного овса, полученных от скрещивания как с голозерными формами, так и с пленчатыми сортами местной селекции. В поисках исходного материала в 2004 г. оценено более 140 номеров голозерного овса коллекции ВИР различного происхождения. Установлено, что подавляющая часть изучаемых генотипов существенно уступает по комплексу хозяйственно-биологических признаков сортам пленчатого овса. Лучшие результаты показали скрещивания голозерных форм Крестьянский местный (Россия), Ac Lotta (Канада), Bullion (Великобритания) и др. с сортами местной селекции – Лев, Яков, Буланый, ЗАЛП, при участии которых создан ряд перспективных линий голозерного овса. Главным итогом селекции данной культуры стало внесение в Госреестр селекционных достижений сорта Немчиновский 61 с регионами допуска 2, 3, 5 и передача в 2020 г. на Государственное сортоиспытание сорта Азиль (линия 57h2396). Изучены посевные качества семян сортообразцов голозерного и пленчатого овса, их фитосанитарное состояние и адаптивные свойства на фонах искусственно создаваемых стрессов (обезвоживание сахарозой, засоление хлоридом натрия и закисление сульфатом алюминия), определены различия между показателями голозерного и посевного овса. Представлен анализ всхожести и зараженности семян фузариозом за период 2011-2019 гг. Выявлен комплекс возбудителей болезней семян овса с наиболее частой встречаемостью родов Fusarium, Pyrenophora, Alternaria, Penicillium и Bacterium. Установлено, что голозерные формы уступают пленчатым по всем показателям. На фоне искусственно создаваемых стрессов лучшие результаты по адаптивности показали пленчатый сорт Яков и голозерный Азиль. The biological and economic properties of the bare oats lines, obtained from crosses both with bare forms and with filmy varieties of local selection were evaluated. Since 2004, more than 140 samples of various origins from VIR collection have been evaluated in search of source material. It was found that the vast majority of the studied genotypes contains a complex of negative characteristics, which were unsuitable for selection. The best results were shown by the crosses of the hulless forms Krestyanskyy Mestny (Russia), Abel (Germany), Ac Batton (and others) with locally created varieties - Lev, Yakov, Bulany, ZALP, with the participation of which a significant material was created for promising lines of bare oats. The main result of this culture selection was the introduction of the Nemchinovsky 61 variety with tolerance regions 2, 3, 5, into the State Register of breeding achievements, and the transfer in 2020 to the State variety test of the Azil variety (line 57h2396). The sowing qualities of seeds of bare and filmy oats varieties, their phytosanitary condition and adaptive properties against the background of artificially created stresses (dehydration with sucrose, salinity with sodium chloride and acidification with aluminum sulfate) were studied, and the differences between the types of oats parameters were determined. The analysis of germination and infection of seeds with Fusarium infection for the period 2011-2019 is thereby presented. A complex of oat seed pathogens with the most frequent occurrence of the genera Fusarium, Pyrenophora, Alternaria, Penicillium and Bacterium was revealed. It has been established, that bare forms are inferior to filmy in all those respects. Against the background of artificially created stresses, the best results in adaptability were shown by the filmy variety Yakov and bare variety Azil

Adopting Tolerance Regions in Environmental Economics

Uncertainty often lies when there is limited knowledge about the process one has to follow regarding the investigation of a real-world problem. In practice, uncertainty is related with the assumed estimation model of the physical problem, and mainly concerns the involved parameters. A typical examplecan be an Environmental Economics system. There are many model specifications that estimate the so-called Benefit Area of such system. For the evaluation of the optimal level of pollution, we can adopt the corresponding tolerance region, and hence we can refer to this optimal level via future observations rather than some parameters estimation. Tolerance regions can be either classical or expected tolerance regions. The associated (four) Benefit Areas can be evaluated through a proposed tolerance region procedure, and not through the usual confidence interval/region approach. Therefore, four possible optimal levels of pollution can be obtained, as well as the corresponding tolerance region for the reduction pollution point.