Efficiency of a Kernel Density Estimator Under an Autoregressive Dependence Model
研究了在自回归过程下，依赖结构如何影响核密度估计的效率，推导了傅里叶积分估计量的均方积分误差，发现即使轻微偏离独立也会导致效率显著下降，并探讨了最优平滑参数的选择。
Abstract The problem of estimating the probability density function of a strictly stationary process is considered. To study the effect of a dependence structure on the efficiency of a kernel density estimator, the mean integrated squared error (MISE) of the Fourier integral estimator (FIE) is derived on the assumption that the observed data are generated by a first-order autoregressive process. Numerical results for the normal and Cauchy densities show that even moderate departures from independence can lead to a considerable loss in efficiency of the FIE. In addition to efficiency considerations, the issue of determining an optimal smoothing parameter for the FIE under the autoregressive model is addressed.