Nonparametric estimation of a convex bathtub-shaped hazard function

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ202 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Estimation of a discrete monotone distribution

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood estimator strictly dominates both the rearrangement and empirical estimators in cases when the distribution has intervals of constancy. For example, when the distribution is uniform on $\{0, ..., y \}$, the asymptotic risk of the method of rearrangements estimator (in squared $\ell_2$ norm) is $y/(y+1)$, while the asymptotic risk of the MLE is of order $(\log y)/(y+1)$. For strictly decreasing distributions, the estimators are asymptotically equivalent.Comment: 39 pages. See also http://www.stat.washington.edu/www/research/reports/2009/ http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.htm

Convergence of linear functionals of the Grenander estimator under misspecification

Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate $n^{1/3}$ if the true density is curved [Sankhy\={a} Ser. A 31 (1969) 23-36] and at rate $n^{1/2}$ if the density is flat [Ann. Probab. 11 (1983) 328-345; Canad. J. Statist. 27 (1999) 557-566]. In the case that the true density is misspecified, the results of Patilea [Ann. Statist. 29 (2001) 94-123] tell us that the global convergence rate is of order $n^{1/3}$ in Hellinger distance. Here, we show that the local convergence rate is $n^{1/2}$ at a point where the density is misspecified. This is not in contradiction with the results of Patilea [Ann. Statist. 29 (2001) 94-123]: the global convergence rate simply comes from locally curved well-specified regions. Furthermore, we study global convergence under misspecification by considering linear functionals. The rate of convergence is $n^{1/2}$ and we show that the limit is made up of two independent terms: a mean-zero Gaussian term and a second term (with nonzero mean) which is present only if the density has well-specified locally flat regions.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1196 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this problem. We use this formula and the mark specific cumulative hazard function of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This result leads to necessary and sufficient conditions for consistency of the MLE which imply that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks. Our theoretical results are supported by simulations.Comment: 27 pages, 4 figure

HL-1 cells express an inwardly rectifying K+ current activated via muscarinic receptors comparable to that in mouse atrial myocytes

An inwardly rectifying K^+ current is present in atrial cardiac myocytes that is activated by acetylcholine (I_{KACh}). Physiologically, activation of the current in the SA node is important in slowing the heart rate with increased parasympathetic tone. It is a paradigm for the direct regulation of signaling effectors by the Gβγ G-protein subunit. Many questions have been addressed in heterologous expression systems with less focus on the behaviour in native myocytes partly because of the technical difficulties in undertaking comparable studies in native cells. In this study, we characterise a potassium current in the atrial-derived cell line HL-1. Using an electrophysiological approach, we compare the characteristics of the potassium current with those in native atrial cells and in a HEK cell line expressing the cloned Kir3.1/3.4 channel. The potassium current recorded in HL-1 is inwardly rectifying and activated by the muscarinic agonist carbachol. Carbachol-activated currents were inhibited by pertussis toxin and tertiapin-Q. The basal current was time-dependently increased when GTP was substituted in the patch-clamp pipette by the non-hydrolysable analogue GTPγS. We compared the kinetics of current modulation in HL-1 with those of freshly isolated atrial mouse cardiomyocytes. The current activation and deactivation kinetics in HL-1 cells are comparable to those measured in atrial cardiomyocytes. Using immunofluorescence, we found GIRK4 at the membrane in HL-1 cells. Real-time RT-PCR confirms the presence of mRNA for the main G-protein subunits, as well as for M2 muscarinic and A1 adenosine receptors. The data suggest HL-1 cells are a good model to study IKAch

Wheat straw hemicellulose films as affected by citric acid.

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A specific case in the classification of woods by FTIR and chemometric: discrimination of Fagales from Malpighiales

Fourier transform infrared (FTIR) spectroscopic data was used to classify wood samples from nine species within the Fagales and Malpighiales using a range of multivariate statistical methods. Taxonomic classification of the family Fagaceae and Betulaceae from Angiosperm Phylogenetic System Classification (APG II System) was successfully performed using supervised pattern recognition techniques. A methodology for wood sample discrimination was developed using both sapwood and heartwood samples. Ten and eight biomarkers emerged from the dataset to discriminate order and family, respectively. In the species studied FTIR in combination with multivariate analysis highlighted significant chemical differences in hemicelluloses, cellulose and guaiacyl (lignin) and shows promise as a suitable approach for wood sample classification

Закономерности изменения физико-механических свойств сплава Zr-1%Nb при комплексном ионно-плазменном модифицировании поверхности и наводороживании

В работе были изучены особенности изменения морфологии, структуры и физико-механических свойств циркониевого сплава Zr-1%Nb, подвергнутого комплексному ионно-плазменному модифицированию поверхности методами плазменно-иммерсионной ионной имплантации титана и осаждения покрытий нитрида титана. Показана высокая эффективность защиты сформированных структур от проникновения водорода в циркониевый сплав. Изучены механизмы сорбции и захвата водорода в титансодержащем модифицированном слое.In the present work, the features of the change in the morphology, structure, and physico-mechanical properties of zirconium alloy Zr-1%Nb subjected to complex ion-plasma surface modification by the methods of plasma-immersion titanium ion implantation and deposition of titanium nitride coatings were studied. The high protective properties of the formed structures against hydrogen permeation into the zirconium alloy is shown. Mechanisms of sorption and capture of hydrogen in a titanium-doped modified layer are studied

Pathways and modification of warm water flowing beneath Thwaites Ice Shelf, West Antarctica

Thwaites Glacier is the most rapidly changing outlet of the West Antarctic Ice Sheet and adds large uncertainty to 21st century sea-level rise predictions. Here, we present the first direct observations of ocean temperature, salinity, and oxygen beneath Thwaites Ice Shelf front, collected by an autonomous underwater vehicle. On the basis of these data, pathways and modification of water flowing into the cavity are identified. Deep water underneath the central ice shelf derives from a previously underestimated eastern branch of warm water entering the cavity from Pine Island Bay. Inflow of warm and outflow of melt-enriched waters are identified in two seafloor troughs to the north. Spatial property gradients highlight a previously unknown convergence zone in one trough, where different water masses meet and mix. Our observations show warm water impinging from all sides on pinning points critical to ice-shelf stability, a scenario that may lead to unpinning and retreat