arXiv subjects

Yoshihiko Nishiyama

Publications and source records attributed to Yoshihiko Nishiyama.

3 recordsLinked to original sources

arXiv2026

A New Approach to Goodness of Fit for Ergodic Markov Processes

We introduce a new density-based goodness of fit test for ergodic Markov processes. Our test compares the data against the class of models specified in the null hypothesis, and rejects if no model in the class yields a stationary density that matches with the data. No alternative needs to be specified in order to implement the test. Although our test compares densities, estimation of smoothing parameters is not required, and the test has nontrivial power against $1/\sqrt{n}$ local alternatives. The test provides new perspectives on some existing problems in econometric and financial modeling.

stat.ME↗

arXiv2024

Fully Data-driven Normalized and Exponentiated Kernel Density Estimator with Hyvärinen Score

We introduce a new deal of kernel density estimation using an exponentiated form of kernel density estimators. The density estimator has two hyperparameters flexibly controlling the smoothness of the resulting density. We tune them in a data-driven manner by minimizing an objective function based on the Hyvärinen score to avoid the optimization involving the intractable normalizing constant due to the exponentiation. We show the asymptotic properties of the proposed estimator and emphasize the importance of including the two hyperparameters for flexible density estimation. Our simulation studies and application to income data show that the proposed density estimator is appealing when the underlying density is multi-modal or observations contain outliers.

stat.ME↗

arXiv2022

Higher-Order Asymptotic Properties of Kernel Density Estimator with Global Plug-In and Its Accompanying Pilot Bandwidth

This study investigates the effect of bandwidth selection via a plug-in method on the asymptotic structure of the nonparametric kernel density estimator. We generalise the result of Hall and Kang (2001) and find that the plug-in method has no effect on the asymptotic structure of the estimator up to the order of $O\{(nh_0)^{-1/2}+h_0^L\}=O(n^{-L/(2L+1)})$ for a bandwidth $h_0$ and any kernel order $L$ when the kernel order for pilot estimation $L_p$ is high enough. We also provide the valid Edgeworth expansion up to the order of $O\{(nh_0)^{-1}+h_0^{2L}\}$ and find that, as long as the $L_p$ is high enough , the plug-in method has an effect from on the term whose convergence rate is $O\{(nh_0)^{-1/2}h_0+h_0^{L+1}\}=O(n^{-(L+1)/(2L+1)})$. In other words, we derive the exact achievable convergence rate of the deviation between the distribution functions of the estimator with a deterministic bandwidth and with the plug-in bandwidth. In addition, we weaken the conditions on kernel order $L_p$ for pilot estimation by considering the effect of pilot bandwidth associated with the plug-in bandwidth. We also show that the bandwidth selection via the global plug-in method possibly has an effect on the asymptotic structure even up to the order of $O\{(nh_0)^{-1/2}+h_0^L\}$. Finally, Monte Carlo experiments are conducted to see whether our approximation improves previous results.

math.ST↗