Nonparametric regression for locally stationary random fields under stochastic sampling design

In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in $R_{n} =[0,A_{n}]^{d} \subset \mathbb{R}^{d}$. We first derive the uniform convergence rate of general kernel estimators, followed by the asymptotic normality of an estimator for the mean function of the model. Moreover, we consider additive models to avoid the curse of dimensionality arising from the dependence of the convergence rate of estimators on the number of covariates. Subsequently, we derive the uniform convergence rate and joint asymptotic normality of the estimators for additive functions. We also introduce approximately $m_{n}$-dependent RFs to provide examples of LSRFs. We find that these RFs include a wide class of L\'evy-driven moving average RFs.Comment: 50 page

On the estimation of locally stationary functional time series

This paper develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series. We introduce a kernel-based method to estimate the time-varying covariance operator and the time-varying mean function of a locally stationary functional time series. Subsequently, we derive the convergence rate of the kernel estimator of the covariance operator and associated eigenvalue and eigenfunctions. We also establish a central limit theorem for the kernel-based locally weighted sample mean. As applications of our results, we discuss the prediction of locally stationary functional time series and methods for testing the equality of time-varying mean functions in two functional samples.Comment: 37 page

Local polynomial regression for spatial data on Rd\mathbb{R}^d

This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can generate irregularly spaced sampling sites in a flexible manner including both pure increasing and mixed increasing domain frameworks. We first introduce a nonparametric regression model for spatial data defined on $\mathbb{R}^d$ and then establish the asymptotic normality of LP estimators with general order $p \geq 1$. We also propose methods for constructing confidence intervals and establish uniform convergence rates of LP estimators. Our dependence structure conditions on the underlying processes cover a wide class of random fields such as L\'evy-driven continuous autoregressive moving average random fields. As an application of our main results, we discuss a two-sample testing problem for mean functions and their partial derivatives.Comment: 45 page

Tako-tsubo cardiomyopathy: Clinical presentation and underlying mechanism

AbstractSince Dr Sato at Hiroshima City Hospital first recognized and reported the concept of tako-tsubo cardiomyopathy in 1990, this disorder has become accepted worldwide as a distinct clinical entity. Tako-tsubo cardiomyopathy is an important disorder as a differential diagnosis of acute myocardial infarction. This disorder usually occurs in postmenopausal women of an advanced age, and is characterized by transient left ventricular apical wall motion abnormalities associated with emotional or physical stress. Typically, left ventricular apical wall motion abnormalities are transient and resolve during a period of days to weeks. The prognosis is generally favorable. However, several acute complications have been reported such as congestive heart failure, cardiac rupture, hypotension, left ventricular apical thrombosis, or Torsade de Pointes. Several possible mechanisms such as multivessel coronary artery spasm, coronary microvascular dysfunction, myocarditis, or catecholamine toxicity have been proposed to explain tako-tsubo cardiomyopathy, but its pathophysiology is not well understood

On the uniform convergence of deconvolution estimators from repeated measurements

This paper studies the uniform convergence rates of Li and Vuong's (1998, Journal of Multivariate Analysis 65, 139-165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31-46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491-533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions