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This paper considers the asymptotic properties of the error density estimator in the nonlinear autoregressive models with α -mixing errors. The asymptotic distribution and uniform convergence rate for the kernel density estimator of error density function are obtained. Last, some simulations of histograms, confidence intervals and mean integrated square errors are illustrated, which agree with our theoretical results. [ABSTRACT FROM AUTHOR]

Introduction: The objective of the present study was to evaluate the efficacy and safety of MP-AzeFlu nasal spray in comparison to commercially available azelastine hydrochloride and fluticasone propionate sprays in Chinese patients with moderate-to-severe allergic rhinitis (AR). Methods: We conducted a 14-day multicenter, randomized, double-blind, active controlled prospective clinical study in adult and adolescent patients with AR, who had moderate-to-severe symptoms. The primary efficacy endpoint was the change from baseline in combined 12-h reflective total nasal symptom score (rTNSS) (morning [AM] + afternoon [PM]). The safety profile of the study medications was assessed through the recording, reporting, and analysis of baseline medical conditions, adverse events (AEs), vital signs, and focused nasal examination. Three hundred patients per treatment group were randomized, which led to a total sample size estimation of 900 patients. Results: MP-AzeFlu group showed significantly higher symptom reduction for the entire 2-week treatment period in rTNSS when compared with the AZE group (LS mean difference: − 1.96; 95% CI: − 2.53, − 1.39; p < 0.0001), or the FLU group (LS mean difference: − 0.98; 95% CI: − 1.55, − 0.41; p = 0.0007). The results of adult RQLQ showed improvement in QoL in all treatment groups. Except for dysgeusia (bitter taste) that was reported by more patients (13 [4.3%]) in the MP-AzeFlu group, the incidence of all other TEAEs in the MP-AzeFlu group was comparable or even lower than in other treatment groups. Conclusions: MP-AzeFlu, when administered as one spray per nostril twice daily for 14 days, alleviated AR symptoms in Chinese patients with moderate-to-severe AR. Trial Registration: Clinicaltrials.gov; NCT03599791, Registered June 29, 2018, retrospectively registered, https://clinicaltrials.gov/ct2/show/NCT03599791. [ABSTRACT FROM AUTHOR]

This correction notice addresses an error in the original article titled "A Clinical Study to Assess the Efficacy and Safety of MP-AzeFlu Nasal Spray in Comparison to Commercially Available Azelastine Hydrochloride and Fluticasone Propionate Nasal Sprays in Chinese Volunteers with Allergic Rhinitis." The correction pertains to the affiliation of one of the authors, Jing Pan, which was incorrectly stated as "Department of Otolaryngology Head and Neck Surgery, Tianjing Renmin Hospital, Nankai University, Tianjing, China." The correct affiliation for Jing Pan is "Department of Otolaryngology Head and Neck Surgery, Tianjin Union Medicine Centre, Tianjin 300121, China." The correction notice is authored by Bing Zhou, Lei Cheng, Jing Pan, Huizhong Wang, Yongde Jin, Changqing Zhao, Peng Lin, Guolin Tan, Hongyan Fang, Hua Zhang, Huifang Zhou, Yaowu Dong, Hans Christian Kuhl, Rajesh Kumar Ramalingam, and Duc Tung Nguyen. [Extracted from the article]

In order to realize the rapid start-up of upflow anaerobic sludge blanket (UASB) reactor, the iron ion in different valence state was added to UASB. The results indicated that the start-up time of R3 (FeCl) was 48 h faster than that of R2 (zero-valent iron (ZVI)). It was because the FeCl could rapidly promote granulation of sludge as a flocculant. However, ZVI released Fe through corrosion slowly, and then the Fe increased start-up speed by enhancing enzyme activity and enriching methanogens. In addition, the ZVI and FeCl could promote hydrolysis acidification and strengthen the decomposition of long-chain fatty acids. The detection of iron ions showed that iron ions mainly existed in the sludge. Because the high concentration of Fe could inhibit anaerobic bacteria activity, excess Fe could be changed into iron hydroxide precipitation to hinder the mass transfer process of anaerobic bacteria under the alkaline condition. The FeCl was suitable to be added at the initial stage of UASB start-up, and the ZVI was more fitted to be used in the middle stage of reactor start-up to improve the redox ability. [ABSTRACT FROM AUTHOR]

Differential genotype error in case-control association studies occurs when cases and controls are genotyped under different conditions. Existence of differential errors can considerably bias the association test, resulting in inflation of type I error and spurious significance. With the availability of high-throughput genotyping technologies such as the SNPchip, null markers that are unlinked with the disease can be used to correct for the bias caused by differential errors. A similar method, known as the genomic control, had been used to correct for population stratification in association studies. In this paper, we show that the same idea can be used to correct for the bias caused by differential errors, under the assumption that the null markers and the candidate marker are subject to the same or similar genotyping error model. The variance inflation is shown to be minor and the bias in the association test is the major source of type I error inflation in the presence of differential errors. Our method centralizes the test statistic by deducting the bias estimated from null markers through a quadratic regression method, which adjusts for the variability of null marker allele frequencies. Simulation results show that the proposed method performs very well in correcting for the type I error inflations. [ABSTRACT FROM AUTHOR]