arXiv subjects

Masayuki Uchida

Publications and source records attributed to Masayuki Uchida.

33 records · Page 2Linked to original sources

arXiv2022

Adaptive inference for small diffusion processes based on sampled data

We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to estimate the drift parameter and the diffusion parameter. In this paper, we propose two types of adaptive estimators for both parameters and show their asymptotic properties under $\varepsilon\to0$, $n\to\infty$ and the balance condition that $(\varepsilon n^ρ)^{-1} =O(1)$ for some $ρ>0$. Using these adaptive estimators, we also introduce consistent adaptive testing methods and prove that test statistics for adaptive tests have asymptotic distributions under null hypothesis. In simulation studies, we examine and compare asymptotic behaviors of the two kinds of adaptive estimators and test statistics. Moreover, we treat the SIR model which describes a simple epidemic spread for a biological application.

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arXiv2021

Change point inference in ergodic diffusion processes based on high frequency data

We deal with the change point problem in ergodic diffusion processes based on high frequency data. Tonaki et al. (2020, 2021) studied the change point problem for the ergodic diffusion process model. However, the change point problem for the drift parameter when the diffusion parameter changes is still open. Therefore, we consider the change detection and the change point estimation for the drift parameter taking into account that there is a change point in the diffusion parameter. Moreover, we examine the performance of the tests and the estimation with numerical simulations.

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arXiv2021

Estimation for change point of discretely observed ergodic diffusion processes

We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any changes are detected by this method, the next question to be considered is where the change point is. Therefore, we propose the method to estimate the change point of the parameter for two cases: the case where there is a change in the diffusion parameter, and the case where there is no change in the diffusion parameter but a change in the drift parameter. Furthermore, we present rates of convergence and distributional results of the change point estimators. Some examples and simulation results are also given.

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arXiv2020

Adaptive testing method for ergodic diffusion processes based on high frequency data

We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the adaptive estimator and provide three types of test statistics: likelihood ratio type test, Wald type test and Rao's score type test. It is proved that these test statistics converge in distribution to the chi-squared distribution under null hypothesis and have consistency of the tests against alternatives. Moreover, these test statistics converge in distribution to the non-central chi-squared distribution under local alternatives. We also give some simulation studies of the behavior of the three types of test statistics.

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arXiv2020

Adaptive estimator for a parabolic linear SPDE with a small noise

We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned data with respect to space obtained from the high frequency data, the minimum contrast estimators of two coefficient parameters of the SPDE are proposed. With these estimators and the thinned data with respect to time obtained from the high frequency data, we construct an approximation of the coordinate process of the SPDE. Using the approximate coordinate process, we obtain the adaptive estimator of a coefficient parameter of the SPDE. Moreover, we give simulation results of the proposed estimators of the SPDE.

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arXiv2020

Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations

We consider the adaptive test for the parameter change in discretely observed ergodic diffusion processes based on the cusum test. Using two test statistics based on the two quasi-log likelihood functions of the diffusion parameter and the drift parameter, we perform the change point tests for both diffusion and drift parameters of the diffusion process. It is shown that the test statistics have the limiting distribution of the sup of the norm of a Brownian bridge. Simulation results are illustrated for the 1-dimensional Ornstein-Uhlenbeck process.

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arXiv2019

Parametric estimation for a parabolic linear SPDE model based on sampled data

We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned data obtained from the high frequency data, adaptive estimators of the coefficient parameters including the volatility parameter of a parabolic linear SPDE model are proposed. Moreover, we give some examples and simulation results of the adaptive estimators of the SPDE model based on the high frequency data.

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arXiv2019

Parametric estimation for convolutionally observed diffusion processes

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion processes and some kernel functions with respect to time parameter. We discuss the estimation and test theories for the parameter determining the smoothness of the observation, as well as the least-square-type estimation for the parameters in the diffusion coefficient and the drift one of the latent diffusion process. In addition to the theoretical discussion, we also examine the performance of the estimation and the test with computational simulation, and show an example of real data analysis for one EEG data whose observation can be regarded as smoother one than ordinary diffusion processes with statistical significance.

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arXiv2019

Quasi-likelihood analysis of an ergodic diffusion plus noise

We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and drift parameters are introduced and the polynomial-type large deviation inequalities for those quasi-likelihoods are shown to see the convergence of moments for those estimators.

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arXiv2018

Hybrid estimation for ergodic diffusion processes based on noisy discrete observations

We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial values for optimisation of the quasi likelihood function of ergodic diffusion processes with noisy observations, we construct the initial Bayes type estimator based on the local means of the noisy observations. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators with the initial Bayes type estimators are shown, and a concrete example and the simulation results are given.

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arXiv2018

Inference for ergodic diffusions plus noise

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation noise, the diffusion parameter and the drift one of the latent diffusion process. Moreover, it can lessen the computational burden compared to simultaneous maximum likelihood-type estimation. In addition to adaptive estimation, we propose a test to see if noise exists or not, and analyse real data as the example such that data contains observation noise with statistical significance.

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arXiv2018

Adaptive test for ergodic diffusions plus noise

We propose some parametric tests for ergodic diffusion-plus-noise model, which is a version of state-space modelling in statistics for stochastic diffusion equations. The test statistics are classified into three types: likelihood-ratio-type test statistic; Wald-type one; and Rao-type one. All the test statistics are constructed with quasi-likelihood-functions for local mean sequence of noised observation. We also simulate the behaviour of them for several practical hypothesis tests and check the convergence in law of test statistics under null hypotheses and consistency of the test under alternative ones. We apply the method for real data analysis of wind data, and examine some sets of the hypotheses mainly with respect to the structure of diffusion coefficient.

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arXiv2017

Adaptive estimation and noise detection for an ergodic diffusion with observation noises

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arXiv2012

Nondegeneracy of Random Field and Estimation of Diffusion

We construct a quasi likelihood analysis for diffusions under the high-frequency sampling over a finite time interval. For this, we prove a polynomial type large deviation inequality for the quasi likelihood random field. Then it becomes crucial to prove nondegeneracy of a key index chi_0. By nature of the sampling setting, chi_0 is random. This makes it difficult to apply a naive sufficient condition, and requires a new machinery. In order to establish a quasi likelihood analysis, we need quantitative estimate of the nondegeneracy of chi_0. The existence of a nondegenerate local section of a certain tensor bundle associated with the statistical random field solves this problem.

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arXiv2007

Parametric estimation for partially hidden diffusion processes sampled at discrete times

For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $τ$, but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is to estimate finite dimensional parameter in both drift and diffusion coefficients under a partially hidden diffusion process obtained by a discrete sampling scheme. It is assumed that the sampling occurs at regularly spaced time intervals of length $h_n$ such that $n h_n=T$. The asymptotic is when $h_n\to0$, $T\to\infty$ and $n h_n^2\to 0$ as $n\to\infty$. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved.

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