论文检索

小噪声下维度发散的网络随机微分方程推断AI 解读

We consider inference for network stochastic differential equations in a small-noise, high-dimensional regime, where the diffusion coefficient vanishes with $\ep\to0$ while the network size and parameter dimension may diverge. We develop a minimum-distance estimation framework based on a deterministic measurement model that may omit nuisance terms in the drift, and derive a non-asymptotic error bound decomposing the estimation error into stochastic fluctuation, nuisance…

风险比较定理及其在扩散系数深度学习中的应用AI 解读

We investigate the nonparametric estimation of the diffusion matrix in stochastic differential equations featuring multidimensional, strong mixing covariate processes. We propose a flexible statistical framework based on general function classes that does not require a linear basis representation, rendering our results directly applicable to deep neural network estimators. Our approach employs a two-step estimation procedure: constructing a preliminary nonparametric…

批次式多臂老虎机的渐近展开AI 解读

In bandit algorithms, the randomly time-varying adaptive experimental design makes it difficult to apply traditional limit theorems to off-policy evaluation of the treatment effect. Moreover, the normal approximation by the central limit theorem becomes unsatisfactory for lack of information due to the small sample size of the inferior arm. To resolve this issue, we introduce a backwards asymptotic expansion method and prove the validity of this scheme based on the partial…

全局跳跃过滤与已实现波动率AI 解读

For a semimartingale with jumps, we propose a new estimation method for integrated volatility, i.e., the quadratic variation of the continuous martingale part, based on the global jump filter proposed by Inatsugu and Yoshida [8]. To decide whether each increment of the process has jumps, the global jump filter adopts the upper $α$-quantile of the absolute increments as the threshold. This jump filter is called global since it uses all the observations to classify one…