Nonparametric estimation of multivariate convex-transformed densities

We study estimation of multivariate densities $p$ of the form $p(x)=h(g(x))$ for $x\in \mathbb {R}^d$ and for a fixed monotone function $h$ and an unknown convex function $g$. The canonical example is $h(y)=e^{-y}$ for $y\in \mathbb {R}$; in this case, the resulting class of densities [\mathcal {P}(e^{-y})={p=\exp(-g):g is convex}] is well known as the class of log-concave densities. Other functions $h$ allow for classes of densities with heavier tails than the log-concave class. We first investigate when the maximum likelihood estimator $\hat{p}$ exists for the class $\mathcal {P}(h)$ for various choices of monotone transformations $h$, including decreasing and increasing functions $h$. The resulting models for increasing transformations $h$ extend the classes of log-convex densities studied previously in the econometrics literature, corresponding to $h(y)=\exp(y)$. We then establish consistency of the maximum likelihood estimator for fairly general functions $h$, including the log-concave class $\mathcal {P}(e^{-y})$ and many others. In a final section, we provide asymptotic minimax lower bounds for the estimation of $p$ and its vector of derivatives at a fixed point $x_0$ under natural smoothness hypotheses on $h$ and $g$. The proofs rely heavily on results from convex analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOS840 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Possibilities and features of zero-ischemia nephron-sparing surgery in localized kidney cancer

Kidney cancer (KCa) is one of the greatest challenges in oncological urology due to the increase in morbidity and mortality rates annually. In the treatment of KCa, preservation of renal function is an important objective, in addition to achieving oncological results. The article presents the experience of treatment of 175 KCa-patients of pT1a – T2aN0M0 stages, who underwent nephron-saving surgery (NSS) with preventive hemostatic sutures. Functional outcomes of NSS were studied in the groups without cross-linking (group 1; n = 150) and with cross-linking of the renal pedicle (group 2; n = 25). Kidney resection with prophylactic suturing has been shown to allow removal of a tumour of almost any localisation. By avoiding cross-linking of the renal pedicle during surgery, post-ischemic changes in the renal parenchyma are minimised. Thus, one month after surgery, the perfusion indexes in groups 1 & 2 were 45.2 ± 3.0% vs 35.5 ± 3.3%; renal indexes were 44.8 ± 2.4% vs 39.1 ± 1.4%; areas of the functioning parenchyma were 52.0 ± 10.0% vs 35.0 ± 9.0%, respectively

Bi-log-concave distribution functions

Nonparametric statistics for distribution functions F or densities f=F' under qualitative shape constraints provides an interesting alternative to classical parametric or entirely nonparametric approaches. We contribute to this area by considering a new shape constraint: F is said to be bi-log-concave, if both log(F) and log(1 - F) are concave. Many commonly considered distributions are compatible with this constraint. For instance, any c.d.f. F with log-concave density f = F' is bi-log-concave. But in contrast to the latter constraint, bi-log-concavity allows for multimodal densities. We provide various characterizations. It is shown that combining any nonparametric confidence band for F with the new shape-constraint leads to substantial improvements, particularly in the tails. To pinpoint this, we show that these confidence bands imply non-trivial confidence bounds for arbitrary moments and the moment generating function of F

Development of context training ideas for the organization of industrial training in college

Обоснована целесообразность применения технологии контекстного обучения для производственного обучения студентов колледжа с целью оптимизации формирования их компетенцийThe authors substantiate the advisability of using contextual learning technology for industrial training of college students in order to optimize the formation of their professional competence

Prognosis of recurrent myocardial infarction based on shortliffe fuzzy models using the electrical characteristics of biologically active points

This report discusses the employment of the electrical characteristics of biologically active points (BAP) in the meridian of the heart to solve the task of prognosticating recurrence of myocardial infarctions during the rehabilitation period using fuzzy decision rule

Определение полисорбата 80 в биофармацевтических препаратах с помощью оптимизированной колориметрической методики

Objectives. We hereby describe an improvement of a previously developed quantification technique for polysorbate 80 in biopharmaceutical formulations (darbepoetin alfa and eculizumab) and report the validation of the new approach.Methods. Polysorbate was isolated from analyte samples by protein precipitation using an organic solvent, followed by supernatant evaporation in vacuum. Polysorbate was derivatized using a ferric thiocyanate reagent and extracted into an organic phase; the relevant optical density measurements were performed.Results. We established the optimal conditions for each step of the analysis procedure. The accuracy was 97–102% in the tested analytical range, the relative standard deviation did not exceed 5%, and the limit of quantification was 0.01 mg/mL.Conclusions. The reported approach is highly sensitive; polysorbate isolation and quantification do not depend on the matrix or, most importantly, the protein.Цели. В данной работе была усовершенствована ранее разработанная методика определения полисорбата 80 в биотехнологических препаратах (дарбэпоэтин альфа, экулизумаб), а также проведена ее валидация.Методы. Полисорбат извлекали из пробы осаждением белка органическим растворителем, затем выпаривали супернатант в вакууме. Полисорбат дериватизировали оптимизированным железо–тиоцианатным реагентом; дериват экстрагировали в слой органического растворителя и измеряли оптическую плотность.Результаты. Были установлены оптимальные условия для каждой стадии методики. Правильность находится в диапазоне степени извлечения 97–102%, относительное стандартное отклонение составляет не более 5%, предел количественного определения методики 0.01 мг/мл.Выводы. Представленная методика имеет высокую чувствительность. Извлечение и определение полисорбата не зависят от матрикса пробы – прежде всего, от присутствующего белка

A STUDY OF EXTREMISM AS A COMPLEX INTER-BRANCH CONCEPT

Purpose: The aim of the study is to investigate extremism as a complex inter-branch concept which complicates law enforcement practice. Methodology: This is an analytic-dialectical research whose data are obtained through the analysis of historical, legal and sociological texts and data. Main Findings: When defining extremism in the basic law of anti-extremist legislation, it is necessary to proceed from the fact that the phenomenon, the concept of which should be formulated, is manifested in different spheres of social and political life. In conclusion, extremism creates an ideological basis for terrorism, but the acts of terrorism go beyond the concept of extremism. Applications: This article can be used by regional schools, cultural organizations and universities. Novelty/Originality: In this study, correlation between the phenomena of terrorism and extremism has been studied on the basis of definition for terrorist act given in part 1 of article 205 of the criminal code of the Russian Federation