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利用特殊回归变量识别第一类与第二类错误概率：司法误判应用AI 解读

We nonparametrically identify Type I and Type II error rates when mistakes are unobserved. Our strategy reframes the setting as a misclassified binary choice model, using a special regressor to identify the misclassification probabilities. Identification requires an exclusion restriction and a large support condition. When the exclusion restriction is in doubt, we show how our estimands can be interpreted as bounds under a weaker monotonicity condition. Bounds are also…

α 混合三角阵列和的收敛速率及连续时间漂移函数估计应用AI 解读

The convergence rates of the sums of α -mixing (or strongly mixing) triangular arrays of heterogeneous random variables are derived. We pay particular attention to the case where central limit theorems may fail to hold, due to relatively strong time-series dependence and/or the nonexistence of higher-order moments. Several previous studies have presented various versions of laws of large numbers for sequences/triangular arrays, but their convergence rates were not fully…

连续时间扩散过程核非参数估计的一致收敛速率：阻尼函数方法AI 解读

In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya–Watson type, introducing a new technical device called a damping function . This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant…

通过非参数滤波估计随机波动率模型AI 解读

A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle…

零常返时间序列中非参数估计量的一致收敛AI 解读

This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series.