Asymptotics for penalized spline estimators in quantile regression

Quantile regression predicts the $\tau$-quantile of the conditional distribution of a response variable given the explanatory variable for $\tau\in(0,1)$. The aim of this paper is to establish the asymptotic distribution of the quantile estimator obtained by penalized spline method. A simulation and an exploration of real data are performed to validate our results.Comment: 20 pages, 11 figure

Mixed effects models for large sized clustered extremes

Extreme value theory (EVT) provides an elegant mathematical tool for statistical analysis of rare events. Typically, when data are collected from multiple clusters, analysts want to preserve cluster information, such as region, period, and group. To consider large-sized cluster information in extreme value analysis, we incorporate the mixed effects model (MEM) into the regression technique in EVT. In the field of small area estimation, it is well known that the MEM is an important tool for providing reliable estimates of large-sized clusters with small sample sizes. In the context of EVT for rare event analysis, the sample size of extreme value data for each cluster is often small. Therefore, the MEM may contribute to improving the predictive accuracy of extreme value analysis. This motivates us to verify the effectiveness of the MEM in EVT through theoretical studies and numerical experiments, including its application to the risk assessment of heavy rainfall in Japan.Comment: 36 page

Bulk-edge correspondence for nonlinear eigenvalue problems

Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.Comment: 6 pages, 4 figure

Partially linear estimation using sufficient dimension reduction

In this paper, we study estimation for partial linear models. We assume radial basis functions for the nonparametric component of these models. To obtain the estimated curve with fitness and smoothness of the nonparametric component, we first apply the sufficient dimension reduction method to the radial basis functions. Then, the coefficients of the transformed radial basis functions are estimated. Finally, the coefficients in the parametric component can be estimated. The above procedure is iterated and hence the proposed method is based on an alternating estimation. The proposed method is highly versatile and is applicable not only to mean regression but also quantile regression and general robust regression. The \hbox{$\sqrt{n}$}-consistency and asymptotic normality of the estimator are derived. A simulation study is performed and an application to a real dataset is illustrated

Covariance Localization in Strongly Coupled Data Assimilation

The recent development of accurate coupled models of the Earth system and enhanced computation power have enabled numerical prediction with the coupled models in weather, sub-seasonal, seasonal, and interannual time scales as well as climate projection. In the shorter timescales, the initial condition, or the estimate of the present state of the system, is essential for accurate prediction. Coupled data assimilation (DA) based on an ensemble of forecasts seems to be a promising approach for this state estimate due to its inherent ability to estimate flow-dependent error covariance. Strongly coupled DA tries to incorporate more observations of the other subsystems into an analysis (e.g., ocean observations into the atmospheric analysis) using the coupled error covariances; the covariance is estimated with a finite ensemble, and spurious covariance must be eliminated by localization. Because the coupling strength between subsystems of the Earth is not a simple function of a distance, we develop a better localization strategy than the distance-dependent localization. Based on the estimated benefit of each observation into each analysis variable, we first propose the correlation-cutoff method, where localization of strongly coupled DA is guided by ensemble correlations of an offline DA cycle. The method achieves improved analysis accuracy when tested with a simple coupled model of the atmosphere and ocean. As a related topic, error growth and predictability of a coupled dynamical system with multiple timescales are explored using a simple chaotic model of the atmosphere and ocean. A discontinuous response of the attractor's characteristics to the coupling strength is reported. The characteristic of global atmosphere-ocean coupled error correlation is investigated using two sets of ensemble DA systems. This knowledge is essential for effectively implementing global strongly coupled atmosphere-ocean DA. We report and discuss common and uncommon features, and the importance of ocean model resolution is stressed. Finally, the correlation-cutoff method is realized for global atmosphere-ocean strongly coupled DA with neural networks. The combination of static information provided by the neural networks and flow-dependent error covariance estimated by the ensemble improves the atmospheric analysis in our proof-of-concept experiment. The neural networks' ability to reproduce the error statistics, computation cost in a DA system, as well as analysis quality are evaluated

An Enantioselective Synthesis of 2-Imidazolidinones through Bifunctional Thiourea-Catalyzed Tandem Mannich/Cyclization of Isocyanatomalonate Diester

A chiral bifunctional thiourea-catalyzed Mannich reaction of diethyl 2-isocyanatomalonate with N-sulfonylimines was described. The tandem cyclization proceeded smoothly after Mannch reaction, directly furnishing chiral 2-imidazolidinones in 72‒99% yields with 83‒98% ees. Sterically demanding sulfonyl group was crucial for aliphatic imines to afford the corresponding product in high enantioselectivity

Simultaneous Improvements in Performance and Durability of an Octahedral PtNix/C Electrocatalyst for Next-Generation Fuel Cells by Continuous, Compressive, and Concave Pt Skin Layers

Simultaneous improvements in oxygen reduction reaction (ORR) activity and long-term durability of Pt-based cathode catalysts are indispensable for the development of next-generation polymer electrolyte fuel cells but are still a major dilemma. We present a robust octahedral core–shell PtNix/C electrocatalyst with high ORR performance (mass activity and surface specific activity 6.8–16.9 and 20.3–24.0 times larger than those of Pt/C, respectively) and durability (negligible loss after 10000 accelerated durability test (ADT) cycles). The key factors of the robust octahedral nanostructure (core–shell Pt73Ni27/C) responsible for the remarkable activity and durability were found to be three continuous Pt skin layers with 2.0–3.6% compressive strain, concave facet arrangements (concave defects and high coordination), a symmetric Pt/Ni distribution, and a Pt67Ni33 intermetallic core, as found by STEM-EDS, in situ XAFS, XPS, etc. The robust core–shell Pt73Ni27/C was produced by the partial release of the stress, Pt/Ni rearrangement, and dimension reduction of an as-synthesized octahedral Pt50Ni50/C with 3.6–6.7% compressive Pt skin layers by Ni leaching during the activation process. The present results on the tailored synthesis of the PtNix structure and composition and the better control of the robust catalytic architecture renew the current knowledge and viewpoint for instability of octahedral PtNix/C samples to provide a new insight into the development of next-generation PEFC cathode catalysts