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Yasutaka Shimizu

Publications and source records attributed to Yasutaka Shimizu.

At least 19 recordsLinked to original sources
arXiv2026

Local increment inference for time-inhomogeneous drift in Gaussian processes

We study statistical inference for deterministic drifts in Gaussian process models under high-frequency observations over an expanding time horizon. Using a least squares-type contrast based on first-order increments, we establish consistency and asymptotic normality under conditions on drift accumulation and increment dependence.A key feature is that the convergence rate is determined jointly by the deterministic signal and the full covariance structure of the weighted Gaussian increments, rather than by local noise roughness alone.For power and fixed-frequency periodic drifts under Gaussian and Ornstein-Uhlenbeck covariance kernels, we derive explicit convergence rates and limiting variances, revealing distinct regimes depending on the drift structure and, for periodic drifts, the noise spectrum. These results clarify the respective roles of sampling frequency and observation horizon.

math.ST↗
arXiv2026

M-estimation for Gaussian processes with time-inhomogeneous drifts from high-frequency data

We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian component with a parametric kernel. Our method constructs a local contrast function from adjacent increments, which avoids inversion of large covariance matrices and allows for efficient computation. We prove consistency and asymptotic normality of the resulting estimators under general ergodicity conditions. A distinctive feature of our approach is that the drift estimator attains a nonstandard convergence rate, stemming from the direct Riemann integrability of the drift density. This highlights a fundamental difference from standard estimation regimes. Furthermore, when the local contrast fails to identify all parameters in the covariance kernel, moment-based corrections can be incorporated to recover identifiability. The proposed framework is simple, flexible, and particularly well suited for high-frequency inference with time-inhomogeneous structure.

math.ST↗
arXiv2026

Real-time Win Probability and Latent Player Ability via STATS X in Team Sports

This study proposes a statistically grounded framework for real-time win probability evaluation and player assessment in score-based team sports, based on minute-by-minute cumulative box-score data. We introduce a continuous dominance indicator (T-score) that maps final scores to real values consistent with win/lose outcomes, and formulate it as a time-evolving stochastic representation (T-process) driven by standardized cumulative statistics. This structure captures temporal game dynamics and enables sequential, analytically tractable updates of in-game win probability. Through this stochastic formulation, competitive advantage is decomposed into interpretable statistical components. Furthermore, we define a latent contribution index, STATS X, which quantifies a player's involvement in favorable dominance intervals identified by the T-process. This allows us to separate a team's baseline strength from game-specific performance fluctuations and provides a coherent, structural evaluation framework for both teams and players. While we do not implement AI methods in this paper, our framework is positioned as a foundational step toward hybrid integration with AI. By providing a structured time-series representation of dominance with an explicit probabilistic interpretation, the framework enables flexible learning mechanisms and incorporation of high-dimensional data, while preserving statistical coherence and interpretability. This work provides a basis for advancing AI-driven sports analytics.

stat.AP↗
arXiv2025

From CKLS Process to CIR-type and OU-type Processes: Using a Twice-differentiable Mapping and Generalized Girsanov's Theorem

We study a twice-differentiable transformation applied to a CKLS-type short-rate model with linear drift and power-type diffusion. The transformation yields a new process whose diffusion component has a square-root structure and whose drift becomes nonlinear. A critical reassessment of earlier studies using similar transformations reveals fundamental errors in model specification and derivations. To address this, we introduce a generalized Girsanov change of measure that adjusts the drift of the transformed process. Under the resulting equivalent measure, the dynamics reduce to the classical Cox-Ingersoll-Ross (CIR) model. Using the Yamada-Watanabe-Engelbert theorem, we establish existence, uniqueness, and positivity of solutions, and show that the combined transformation and measure change is valid only under specific parameter restrictions, including those most relevant for financial applications. The CIR representation allows us to exploit known results on stationary distributions, moments, and boundary behavior. Under an additional coefficient relationship, the process can be further linked to an Ornstein-Uhlenbeck framework, yielding explicit distributional properties under the equivalent measure. Finally, since standard martingale conditions are not applicable, we prove directly that the associated Radon-Nikodym derivative is a true martingale by invoking a recent criterion based on Feller's explosion test and boundary classification.

math.PR↗
arXiv2025

Estimation of the elasticity for CKLS model from high-frequency observations

We investigate parametric estimation of the elasticity parameter in the CKLS diffusion based on high-frequency data. First, we transform the CKLS diffusion to a CIR-type one via a smooth state-space mapping and the general Girsanov change of measure. This transformation enables the applications of existing inference tools for CIR processes while ensuring possibilities of transferring the resulting limit theorems back to the original probability space. However, because Feller's condition fails, many existing high-frequency likelihood-based procedures cannot be applied directly, since their discretization schemes approximate likelihood terms involving the reciprocal of the process by Riemann sums that are no longer well-defined once the paths are allowed to hit zero. Instead, we estimate the drift coefficient of the transformed CIR-type model via a procedure based on its positive Harris recurrence, which is valid in the high-frequency regime. Exploiting the drift-elasticity relationship implied by the CKLS--CIR transformation, with the help of an initial estimation, we obtain an estimator of the CKLS elasticity from the CIR drift estimator in the transformed model. This yields a closed-form estimator of the elasticity parameter with an explicit asymptotic variance. We establish its $p$-consistency, stable convergence in law, and asymptotic normality. Finally, we show that stable convergence in law is invariant under equivalent changes of measure, thereby guaranteeing that the Gaussian limit remains invariant under the original measure.

math.ST↗
arXiv2025

M-Estimation based on quasi-processes from discrete samples of Levy processes

We propose a novel estimation framework for path-dependent functionals of Levy processes from discretely observed data. Traditional approaches rely on Monte Carlo simulation of full paths, which requires complete model specification and heavy computation. In contrast, our quasi-process method constructs pseudo-paths directly from observed increments by random permutation, preserving the increment distribution while enabling repeated evaluation of functionals. Under a high-frequency, long-term sampling regime, we establish weak convergence of the quasi-process to the true Levy process and prove consistency and asymptotic normality of the resulting $M$-estimator. This bootstrap-like approach provides a practical and computationally efficient tool for inference from a single trajectory and offers promising extensions to multivariate modeling, machine learning integration, and risk management.

stat.ME↗
arXiv2025

Maximum likelihood estimation of mean functions for Gaussian processes under small noise asymptotics

Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be written explicitly. When it is subjected to a small noise asymptotic condition leading to the vanishing of the primary Gaussian noise, we attain local asymptotic normality results, accompanied by insights into the asymptotic efficiency of these estimators. In addition, we introduce M-estimators based on discrete samples, which also leads us to the asymptotic efficiency. Furthermore, we provide quasi-information criteria for model selection analogous to Akaike Information Criteria in discretely observed cases.

math.ST↗
arXiv2024

Adaptive Bayes estimator for stochastic differential equations with jumps under small noise asymptotics

In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term, and jump term, as well as the Poisson intensity and the probability density function of the underlying jump. We propose estimators based on adaptive Bayesian estimation from discrete observations. We demonstrate the consistency and asymptotic normality of the estimators within the framework of small noise asymptotics.

math.ST↗
arXiv2024

Approximation and estimation of scale functions for spectrally negative Levy processes

The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit representations in general. This paper introduces a novel series representation for this scale function, employing Laguerre polynomials to construct a uniformly convergent approximate sequence. Additionally, we derive statistical inference based on specific discrete observations, presenting estimators of scale functions that are asymptotically normal.

math.ST↗
arXiv2024

Mortality Prediction using Survival Energy Models with Functional Data Analysis

The Survival Energy Model (SEM), as originally introduced by Shimizu et al. (2020), is designed to characterize human bioenergetics by employing diffusion processes or inverse Gaussian processes. While parametric models have been employed to articulate the SEM, they exhibit inherent sensitivity in their parameters and hyperparameters, which in turn introduces issues of instability in estimation and prediction. In this paper, we demonstrate that the utilization of functional data analysis techniques for nonparametric estimation and prediction of critical functions within the SEM leads to a substantial enhancement in prediction performance.

stat.AP↗
arXiv2023

A tail estimate for empirical processes of multivariate Gaussian under general dependence

In this paper, we discuss the convergence rate of empirical processes of Gaussian processes for a large class of function families. Our main goal is to show that the tail of the uniform norm of the empirical processes can be dominated by polynomials. We put forward the properties of Hermite polynomials which play a crucial role in the proof of main theorems. At the end of the paper, we show the expectation of the random quantity converging to zero at a more rapid rate n^{-1/2+ε} than ever shown rate n^{-1/3}.

math.PR↗
arXiv2023

Statistical inference for discretely sampled stochastic functional differential equations with small noise

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when the dispersion coefficient goes to zero and the sample size goes to infinity, simultaneously.

math.ST↗
arXiv2022

The Gerber-Shiu discounted penalty function: A review from practical perspectives

The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except for limited classes of penalty functions on rather simple risk models. In contrast to its great generality, the Gerber-Shiu function does not seem sufficiently prevalent in practice, largely due to a variety of difficulties in numerical approximation and statistical inference. To enhance research activities on such implementation aspects, we provide a comprehensive review of existing formulations and underlying surplus processes, as well as an extensive survey of analytical, semi-analytical and asymptotic methods for the Gerber-Shiu function, which altogether shed fresh light on its numerical methods and statistical inference for further developments. On the basis of an ambitious collection of 235 references, the present survey can serve as an insightful guidebook to model and method selection from practical perspectives as well.

q-fin.RM↗
arXiv2022

Semiparametric Estimation of Optimal Dividend Barrier for Spectrally Negative Lévy Process

We disucss a statistical estimation problem of an optimal dividend barrier when the surplus process follows a Lévy insurance risk process. The optimal dividend barrier is defined as the level of the barrier that maximizes the expectation of the present value of all dividend payments until ruin. In this paper, an estimatior of the expected present value of all dividend payments is defined based on ``quasi-process'' in which sample paths are generated by shuffling increments of a sample path of the Lévy insurance risk process. The consistency of the optimal dividend barrier estimator is shown. Moreover, our approach is examined numerically in the case of the compound Poisson risk model perturbed by diffusion.

math.ST↗
arXiv2022

Threshold estimation for jump-diffusions under small noise asymptotics

We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and asymptotic normality under new asymptotics. One of the novelties of the paper is that we give a new localization argument, which enables us to avoid truncation in the contrast function that has been used in earlier works and to deal with a wider class of jumps in threshold estimation than ever before.

math.ST↗
arXiv2022

Estimating the finite-time ruin probability of a surplus with a long memory via Malliavin calculus

We consider a surplus process of drifted fractional Brownian motion with the Hurst index $H>1/2$, which appears as a functional limit of drifted compound Poisson risk models with correlated claims, and this is a kind of representation of a surplus with a long memory. Our interest is to construct confidence intervals of the ruin probability of the surplus when the volatility parameter is unknown. We will obtain the derivative of the ruin probability w.r.t. the volatility parameter via Malliavin calculus, and apply the delta method to identify the asymptotic distribution of an estimated ruin probability.

math.ST↗
arXiv2022

Least squares estimators based on the Adams method for stochastic differential equations with small Lévy noise

We consider stochastic differential equations (SDEs) driven by small Lévy noise with some unknown parameters, and propose a new type of least squares estimators based on discrete samples from the SDEs. To approximate the increments of a process from the SDEs, we shall use not the usual Euler method, but the Adams method, that is, a well-known numerical approximation of the solution to the ordinary differential equation appearing in the limit of the SDE. We show the consistency of the proposed estimators as well as the asymptotic distribution in a suitable observation scheme. We also show that our estimators can be better than the usual LSE based on the Euler method in the finite sample performance.

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