arXiv subjects

Hiroshi Shiraishi

Publications and source records attributed to Hiroshi Shiraishi.

5 recordsLinked to original sources

arXiv2026

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 unconditional weak convergence of the quasi-process and consistency of the uniformly randomized M-estimator under finite-horizon approximation and identification conditions. A separate normality theorem requires a central limit theorem for the conditional permutation score; this additional condition is verified directly for a quadratic endpoint contrast, but remains to be established for the default and dividend examples. Numerical experiments with the original, unsmoothed dividend criterion examine finite-sample concentration and dispersion beyond the verified scope of these sufficient conditions; they do not assert consistency or asymptotic normality for that criterion.

stat.ME↗

arXiv2025

Asymptotic Theory and Phase Transitions for Variable Importance in Quantile Regression Forests

Quantile Regression Forests (QRF) are widely used for non-parametric conditional quantile estimation, yet statistical inference for variable importance measures remains challenging due to the non-smoothness of the loss function and the complex bias-variance trade-off. In this paper, we develop a asymptotic theory for variable importance defined as the difference in pinball loss risks. We first establish the asymptotic normality of the QRF estimator by handling the non-differentiable pinball loss via Knight's identity. Second, we uncover a "phase transition" phenomenon governed by the subsampling rate $β$ (where $s \asymp n^β$). We prove that in the bias-dominated regime ($β\ge 1/2$), which corresponds to large subsample sizes typically favored in practice to maximize predictive accuracy, standard inference breaks down as the estimator converges to a deterministic bias constant rather than a zero-mean normal distribution. Finally, we derive the explicit analytic form of this asymptotic bias and discuss the theoretical feasibility of restoring valid inference via analytic bias correction. Our results highlight a fundamental trade-off between predictive performance and inferential validity, providing a theoretical foundation for understanding the intrinsic limitations of random forest inference in high-dimensional settings.

stat.ML↗

arXiv2025

Local Fr'echet Regression via RKHS embedding and Its Applications to Data Analysis on Manifolds

Local Fr'echet Regression (LFR) is a nonparametric regression method for settings in which the explanatory variable lies in a Euclidean space and the response variable lies in a metric space. It is used to estimate smooth trajectories in general metric spaces from noisy observations of random objects taking values in such spaces. Since metric spaces form a broad class of spaces that often lack algebraic structures such as addition or scalar multiplication characteristics typical of vector spaces the asymptotic theory for conventional random variables cannot be directly applied. As a result, deriving the asymptotic distribution of the LFR estimator is challenging. In this paper, we first extend nonparametric regression models for real-valued responses to Hilbert spaces and derive the asymptotic distribution of the LFR estimator in a Hilbert space setting. Furthermore, we propose a new estimator based on the LFR estimator in a reproducing kernel Hilbert space (RKHS), by mapping data from a general metric space into an RKHS. Finally, we consider applications of the proposed method to data lying on manifolds and construct confidence regions in metric spaces based on the derived asymptotic distribution.

math.ST↗

arXiv2022

Time series quantile regression using random forests

We discuss an application of Generalized Random Forests (GRF) proposed by Athey et al.(2019) to quantile regression for time series data. We extracted the theoretical results of the GRF consistency for i.i.d. data to time series data. In particular, in the main theorem, based only on the general assumptions for time series data in Davis and Nielsen (2020), and trees in Athey et al.(2019), we show that the tsQRF (time series Quantile Regression Forests) estimator is consistent. Davis and Nielsen (2020) also discussed the estimation problem using Random Forests (RF) for time series data, but the construction procedure of the RF treated by the GRF is essentially different, and different ideas are used throughout the theoretical proof. In addition, a simulation and real data analysis were conducted.In the simulation, the accuracy of the conditional quantile estimation was evaluated under time series models. In the real data using the Nikkei Stock Average, our estimator is demonstrated to be more sensitive than the others in terms of volatility, thus preventing underestimation of risk.

math.ST↗

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↗