Adaptive test for ergodic diffusions plus noise

Nakakita, Shogo H.; Uchida, Masayuki

doi:10.1016/j.jspi.2019.03.006

Cited by 11 publications

(8 citation statements)

References 21 publications

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“…Let us consider the case where it holds

n h_{n}^{γ} \to 0

for some γ ∈ (1,3/2]; then,

k_{n} {normalΔ}_{n}^{2} = n h_{n}^{2 - 1 false/ τ} \to 0

if γ > 2 − 1/ τ , which is the condition that can be eased with a larger τ . On the other hand, there does not exist any C > 0 such that

I^{false(2, 2 false), τ} = C J^{false(2, 2 false), τ}

if τ = 2, which makes it difficult to compose test statistics like the likelihood ratio ones (see Nakakita & Uchida, ). Hence, in practice, a τ value sufficiently close to 2 can be optimal, but it would be hard to discuss goodness‐of‐fit of models when τ = 2 exactly.…”

Section: Resultsmentioning

confidence: 99%

Inference for ergodic diffusions plus noise

Nakakita

Uchida

2018

Scandinavian J Statistics

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We research an 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 analyze real data as the example such that the data contain observation noise with statistical significance.

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“…Let us consider the case where it holds

n h_{n}^{γ} \to 0

for some γ ∈ (1,3/2]; then,

k_{n} {normalΔ}_{n}^{2} = n h_{n}^{2 - 1 false/ τ} \to 0

if γ > 2 − 1/ τ , which is the condition that can be eased with a larger τ . On the other hand, there does not exist any C > 0 such that

I^{false(2, 2 false), τ} = C J^{false(2, 2 false), τ}

Section: Resultsmentioning

confidence: 99%

Inference for ergodic diffusions plus noise

Nakakita

Uchida

2018

Scandinavian J Statistics

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“…These contributions, especially the third one, will cultivate the motivation to study statistical approaches for convolutionally observed diffusion processes furthermore, such as estimation of kernel function V appearing in the convoluted diffusion

, test theory for parameters

and

as likelihood-ratio-type test statistics, for example, see [ 29 , 30 ], large deviation inequalities for quasi-likelihood functions and associated discussion of Bayes-type estimators, e.g., [ 6 , 31 , 32 , 33 ]. By these future works, it is expected that the applicability of stochastic differential equations in real data analysis and contributions to the areas with high frequency observation of phenomena such as EEG will be enhanced.…”

Section: Discussionmentioning

confidence: 99%

Inference for Convolutionally Observed Diffusion Processes

Nakakita

Uchida

2020

Entropy

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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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“…For adaptive parametric estimation for ergodic diffusion processes, many researchers studied and obtained the asymptotic results, see Prakasa Rao [16,17], Yoshida [26], Kessler [10], and Uchida and Yoshida [23]. Nakakita and Uchida [14] investigated the adaptive test for noisy ergodic diffusion processes. They derived the asymptotic null distribution of the adaptive test statistics based on the local means and consistency of the tests under alternatives.…”

Section: Introductionmentioning

confidence: 99%

Adaptive inference for small diffusion processes based on sampled data

Kawai¹,

Uchida²

2021

Preprint

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We consider parametric estimation for multi-dimensional diffusion processes with a small dispersion parameter ε from discrete observations. For parametric estimation of diffusion processes, the main targets are the drift parameter α and the diffusion parameter β. In this paper, we propose two types of adaptive estimators for (α, β) and show their asymptotic properties under ε → 0, n → ∞ and the balance condition that (εn ρ ) −1 = O(1) for some ρ ≥ 1/2. In simulation studies, we examine and compare asymptotic behaviors of the two kinds of adaptive estimators. Moreover, we treat the SIR model which describes a simple epidemic spread for a biological application.

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Adaptive test for ergodic diffusions plus noise

Cited by 11 publications

References 21 publications

Inference for ergodic diffusions plus noise

Inference for ergodic diffusions plus noise

Inference for Convolutionally Observed Diffusion Processes

Adaptive inference for small diffusion processes based on sampled data

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