arXiv subjects

Daisuke Kurisu

Publications and source records attributed to Daisuke Kurisu.

26 records · Page 2Linked to original sources

arXiv2022

Adaptively Robust Small Area Estimation: Balancing Robustness and Efficiency of Empirical Bayes Confidence Intervals

Empirical Bayes small area estimation based on the well-known Fay-Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when the assumed distribution is plausible. This paper proposes a simple modification of the standard empirical Bayes methods with adaptively balancing robustness and efficiency. The proposed method employs gamma-divergence instead of the marginal log-likelihood and optimizes a tuning parameter controlling robustness by pursuing the efficiency of empirical Bayes confidence intervals for areal parameters. We provide an asymptotic theory of the proposed method under both the correct specification of the assumed distribution and the existence of outlying areas. We investigate the numerical performance of the proposed method through simulations and an application to small area estimation of average crime numbers.

stat.ME↗

arXiv2021

Gaussian approximation and spatially dependent wild bootstrap for high-dimensional spatial data

In this paper, we establish a high-dimensional CLT for the sample mean of $p$-dimensional spatial data observed over irregularly spaced sampling sites in $\mathbb{R}^d$, allowing the dimension $p$ to be much larger than the sample size $n$. We adopt a stochastic sampling scheme that can generate irregularly spaced sampling sites in a flexible manner and include both pure increasing domain and mixed increasing domain frameworks. To facilitate statistical inference, we develop the spatially dependent wild bootstrap (SDWB) and justify its asymptotic validity in high dimensions by deriving error bounds that hold almost surely conditionally on the stochastic sampling sites. Our dependence conditions on the underlying random field cover a wide class of random fields such as Gaussian random fields and continuous autoregressive moving average random fields. Through numerical simulations and a real data analysis, we demonstrate the usefulness of our bootstrap-based inference in several applications, including joint confidence interval construction for high-dimensional spatial data and change-point detection for spatio-temporal data.

math.ST↗

arXiv2019

Particulate Air Pollution, Birth Outcomes, and Infant Mortality: Evidence from Japan's Automobile Emission Control Law of 1992

This study investigates the impacts of the Automobile NOx Law of 1992 on ambient air pollutants and fetal and infant health outcomes in Japan. Using panel data taken from more than 1,500 monitoring stations between 1987 and 1997, we find that NOx and SO2 levels reduced by 87% and 52%, respectively in regulated areas following the 1992 regulation. In addition, using a municipal-level Vital Statistics panel dataset and adopting the regression differences-in-differences method, we find that the enactment of the regulation explained most of the improvements in the fetal death rate between 1991 and 1993. This study is the first to provide evidence on the positive impacts of this large-scale automobile regulation policy on fetal health.

econ.GN↗

arXiv2019

Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations

This study examines a nonparametric inference on a stationary Lévy-driven Ornstein-Uhlenbeck (OU) process $X = (X_{t})_{t \geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the Lévy measure of the Lévy-driven OU process $X$ under macroscopic observations. We also derive, for the estimator, multivariate central limit theorems over a finite number of design points, and high-dimensional central limit theorems in the case wherein the number of design points increases with an increase in the sample size. Built on these asymptotic results, we develop methods to construct confidence bands for the Lévy measure and propose a practical method for bandwidth selection.

stat.ME↗

arXiv2019

On nonparametric inference for spatial regression models under domain expanding and infill asymptotics

In this paper, we develop nonparametric inference on spatial regression models as an extension of Lu and Tj\ostheim(2014), which develops nonparametric inference on density functions of stationary spatial processes under domain expanding and infill (DEI) asymptotics. In particular, we derive multivariate central limit theorems of mean and variance functions of nonparametric spatial regression models. Built upon those results, we propose a method to construct confidence bands for mean and variance functions.

math.ST↗

arXiv2017

Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations

This paper develops bootstrap methods to construct uniform confidence bands for nonparametric spectral estimation of Lévy densities under high-frequency observations. We assume that we observe $n$ discrete observations at frequency $1/Δ> 0$, and work with the high-frequency setup where $Δ= Δ_{n} \to 0$ and $nΔ\to \infty$ as $n \to \infty$. We employ a spectral (or Fourier-based) estimator of the Lévy density, and develop novel implementations of Gaussian multiplier (or wild) and empirical (or Efron's) bootstraps to construct confidence bands for the spectral estimator on a compact set that does not intersect the origin. We provide conditions under which the proposed confidence bands are asymptotically valid. Our confidence bands are shown to be asymptotically valid for a wide class of Lévy processes. We also develop a practical method for bandwidth selection, and conduct simulation studies to investigate the finite sample performance of the proposed confidence bands.

math.ST↗

arXiv2017

Discretization of Self-Exciting Peaks Over Threshold Models

In this paper, a framework on a discrete observation of (marked) point processes under the high-frequency observation is developed. Based on this framework, we first clarify the relation between random coefficient integer-valued autoregressive process with infinite order (RCINAR($\infty$)) and i.i.d.-marked self-exciting process, known as marked Hawkes process. For this purpose, we show that the point process constructed of the sum of a RCINAR($\infty$) converge weakly to a marked Hawkes process. This limit theorem establish that RCINAR($\infty$) processes can be seen as a discretely observed marked Hawkes processes when the observation frequency increases and thus build a bridge between discrete-time series analysis and the analysis of continuous-time stochastic process and give a new perspective in the point process approach in extreme value theory. Second, we give a necessary and sufficient condition of the stationarity of RCINAR($\infty$) process and give its random coefficient autoregressive (RCAR) representation. Finally, as an application of our results, we establish a rigorous theoretical justification of self-exciting peaks over threshold (SEPOT) model, which is a well-known as a (marked) Hawkes process model for the empirical analysis of extremal events in financial econometrics and of which, however, the theoretical validity have rarely discussed. Simulation results of the asymptotic properties of RCINAR($\infty$) shows some interesting implications for statistical applications.

math.ST↗

arXiv2016

Power variations and testing for co-jumps: the small noise approach

In this paper we study the effects of noise on the bipower variation (BPV), realized volatility (RV) and testing for co-jumps in high-frequency data under the small noise framework. We first establish asymptotic properties of the BPV in this framework. In the presence of the small noise, the RV is asymptotically biased and the additional asymptotic conditional variance term appears in its limit distribution. We also give feasible estimation methods of the asymptotic conditional variances of the RV. Second, we derive the asymptotic distribution of the test statistic proposed in Jacod and Todorov(2009) under the presence of small noise for testing the presence of co-jumps in two dimensional Itô semimartingale. In contrast to the setting in Jacod and Todorov(2009), we show that the additional conditional asymptotic variance terms appear, and give consistent estimation procedures for the asymptotic conditional variances in order to make the test feasible. Simulation experiments show that our asymptotic results give reasonable approximations in the finite sample cases.

math.ST↗