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

Erratum: “Searches for Gravitational Waves from Known Pulsars at Two Harmonics in 2015–2017 LIGO Data” (2019, ApJ, 879, 10)

Due to an error at the publisher, in the published article the number of pulsars presented in the paper is incorrect in multiple places throughout the text. Specifically, "222" pulsars should be "221." Additionally, the number of pulsars for which we have EM observations that fully overlap with O1 and O2 changes from "168" to "167." Elsewhere, in the machine-readable table of Table 1 and in Table 2, the row corresponding to pulsar J0952-0607 should be excised as well. Finally, in the caption for Table 2 the number of pulsars changes from "188" to "187.

Sex- and age-related differences in the management and outcomes of chronic heart failure: an analysis of patients from the ESC HFA EORP Heart Failure Long-Term Registry

Aims: This study aimed to assess age- and sex-related differences in management and 1-year risk for all-cause mortality and hospitalization in chronic heart failure (HF) patients. Methods and results: Of 16 354 patients included in the European Society of Cardiology Heart Failure Long-Term Registry, 9428 chronic HF patients were analysed [median age: 66 years; 28.5% women; mean left ventricular ejection fraction (LVEF) 37%]. Rates of use of guideline-directed medical therapy (GDMT) were high (angiotensin-converting enzyme inhibitors/angiotensin receptor blockers, beta-blockers and mineralocorticoid receptor antagonists: 85.7%, 88.7% and 58.8%, respectively). Crude GDMT utilization rates were lower in women than in men (all differences: P\ua0 64 0.001), and GDMT use became lower with ageing in both sexes, at baseline and at 1-year follow-up. Sex was not an independent predictor of GDMT prescription; however, age >75 years was a significant predictor of GDMT underutilization. Rates of all-cause mortality were lower in women than in men (7.1% vs. 8.7%; P\ua0=\ua00.015), as were rates of all-cause hospitalization (21.9% vs. 27.3%; P\ua075 years. Conclusions: There was a decline in GDMT use with advanced age in both sexes. Sex was not an independent predictor of GDMT or adverse outcomes. However, age >75 years independently predicted lower GDMT use and higher all-cause mortality in patients with LVEF 6445%

ICAR: endoscopic skull‐base surgery

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Pancreatic Exocrine Insufficiency: A Rare Cause of Nonalcoholic Steatohepatitis

This is an electronic version of an Article published in the American Journal of Gastroenterology 2008; 103(1): 245-246.ArticleAmerican journal of gastroenterology. 103(1): 245-246 (2008)journal articl