The behavior of the NPMLE of a decreasing density near the boundaries of the support

We investigate the behavior of the nonparametric maximum likelihood estimator $\hat{f}_n$ for a decreasing density $f$ near the boundaries of the support of $f$. We establish the limiting distribution of $\hat{f}_n(n^{-\alpha})$, where we need to distinguish between different values of $0<\alpha<1$. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of $f$ at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.Comment: Published at http://dx.doi.org/10.1214/009053606000000100 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic normality of the LkL_k-error of the Grenander estimator

We investigate the limit behavior of the $L_k$-distance between a decreasing density $f$ and its nonparametric maximum likelihood estimator $\hat{f}_n$ for $k\geq1$. Due to the inconsistency of $\hat{f}_n$ at zero, the case $k=2.5$ turns out to be a kind of transition point. We extend asymptotic normality of the $L_1$-distance to the $L_k$-distance for $1\leq k<2.5$, and obtain the analogous limiting result for a modification of the $L_k$-distance for $k\geq2.5$. Since the $L_1$-distance is the area between $f$ and $\hat{f}_n$, which is also the area between the inverse $g$ of $f$ and the more tractable inverse $U_n$ of $\hat{f}_n$, the problem can be reduced immediately to deriving asymptotic normality of the $L_1$-distance between $U_n$ and $g$. Although we lose this easy correspondence for $k>1$, we show that the $L_k$-distance between $f$ and $\hat{f}_n$ is asymptotically equivalent to the $L_k$-distance between $U_n$ and $g$.Comment: Published at http://dx.doi.org/10.1214/009053605000000462 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The limit distribution of the L∞L_{\infty}-error of Grenander-type estimators

Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of $[0,1]$. The rate of convergence is found to be of order $(n/\log n)^{-1/3}$ and the limiting distribution to be Gumbel.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1015 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessment of the possibility for large-scale 238Pu production in a VVER-1000 power reactor

The paper presents the estimates for the possibility for large-scale production of 238Pu in the core of a VVER-1000 power reactor. The Np-fraction of minor actinides extracted from transuranic radioactive waste is proposed to be used as the starting material. The irradiation device with NpO2 fuel elements is installed at the reactor core center. The NpO2 fuel lattice pitch is varied and the irradiation device is surrounded by a heavy moderator layer to create the best possible spectral conditions for large-scale production (~ 3 kg/year) of conditioned plutonium with the required isotopic composition (not less than 85% of 238Pu and not more than 2 ppm of 236Pu). Plutonium with such isotopic composition can be used as the thermal source in thermoelectric radioisotope generators and in cardiac pacemakers. It has been demonstrated that the estimated scale of the 238Pu production in a VVER-type power reactor exceeds considerably the existing scale of its production in research reactors

Search and evaluation of pharmacodynamic and pharmacokinetic parameters of selective blocker of TRPA₁ ion channels from the group of substituted pyrazinopyrimidinones

Search considerations evaluation of pharmacodynamic and pharmacokinetic parameters of selective blocker of TRPA₁ ion channels from the group of substituted pyrazinopyrimidinone

Ocean-bottom seismographs based on broadband MET sensors: architecture and deployment case study in the Arctic

The Arctic seas are now of particular interest due to their prospects in terms of hydrocarbon extraction, development of marine transport routes, etc. Thus, various geohazards, including those related to seismicity, require detailed studies, especially by instrumental methods. This paper is devoted to the ocean-bottom seismographs (OBS) based on broadband molecular–electronic transfer (MET) sensors and a deployment case study in the Laptev Sea. The purpose of the study is to introduce the architecture of several modifications of OBS and to demonstrate their applicability in solving different tasks in the framework of seismic hazard assessment for the Arctic seas. To do this, we used the first results of several pilot deployments of the OBS developed by Shirshov Institute of Oceanology of the Russian Academy of Sciences (IO RAS) and IP Ilyinskiy A.D. in the Laptev Sea that took place in 2018–2020. We highlighted various seismological applications of OBS based on broadband MET sensors CME-4311 (60 s) and CME-4111 (120 s), including the analysis of ambient seismic noise, registering the signals of large remote earthquakes and weak local microearthquakes, and the instrumental approach of the site response assessment. The main characteristics of the broadband MET sensors and OBS architectures turned out to be suitable for obtaining high-quality OBS records under the Arctic conditions to solve seismological problems. In addition, the obtained case study results showed the prospects in a broader context, such as the possible influence of the seismotectonic factor on the bottom-up thawing of subsea permafrost and massive methane release, probably from decaying hydrates and deep geological sources. The described OBS will be actively used in further Arctic expeditions

Growth of few-wall carbon nanotubes with narrow diameter distribution over Fe-Mo-MgO catalyst by methane/acetylene catalytic decomposition

Few-wall carbon nanotubes were synthesized by methane/acetylene decomposition over bimetallic Fe-Mo catalyst with MgO (1:8:40) support at the temperature of 900°C. No calcinations and reduction pretreatments were applied to the catalytic powder. The transmission electron microscopy investigation showed that the synthesized carbon nanotubes [CNTs] have high purity and narrow diameter distribution. Raman spectrum showed that the ratio of G to D band line intensities of IG/ID is approximately 10, and the peaks in the low frequency range were attributed to the radial breathing mode corresponding to the nanotubes of small diameters. Thermogravimetric analysis data indicated no amorphous carbon phases. Experiments conducted at higher gas pressures showed the increase of CNT yield up to 83%. Mössbauer spectroscopy, magnetization measurements, X-ray diffraction, high-resolution transmission electron microscopy, and electron diffraction were employed to evaluate the nature of catalyst particles

The limit process of the difference between the empirical distribution function and its concave majorant

We consider the process -Fn, being the difference between the empirical distribution function Fn and its least concave majorant , corresponding to a sample from a decreasing density. We extend Wang's result on pointwise convergence of -Fn and prove that this difference converges as a process in distribution to the corresponding process for two-sided Brownian motion with parabolic drift.Least concave majorant Empirical distribution function Brownian motion with parabolic drift Isotonic estimation Monotone density