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利用特征值选择局部多项式回归的带宽AI 解读

Summary Local polynomial regression is commonly used for estimating regression functions. In practice, however, with rough functions or sparse data, a poor choice of bandwidth can lead to unstable estimates of the function or its derivatives. We derive a new expression for the leading term of the bias by using the eigenvalues of the weighted design matrix where the bias depends on the arrangement of the X-values in the bandwidth window. We then use this result to determine a…

谱密度峰值位置的弱收敛与自适应估计AI 解读

Adaptive nonparametric kernel estimators for the location of a peak of the spectral density of a stationary time series are proposed and investigated. They are based on direct smoothing of the periodogram where the amount of smoothing is determined automatically in an asymptotically optimal fashion. These adaptive estimators minimize the asymptotic mean squared error. Adaptivity is derived from the weak convergence of a two-parameter stochastic process in a deviation and a…