GOODNESS-OF-FIT TESTS BASED ON KERNEL DENSITY ESTIMATORS WITH FIXED SMOOTHING PARAMETERS
研究了Fan(1994)提出的偏差校正拟合优度检验，通过固定平滑参数得到非正态渐近分布，并提出了参数自助法来近似临界值，适用于检验密度函数是否属于某参数族。
In this paper, we study the bias-corrected test developed in Fan (1994). It is based on the integrated squared difference between a kernel estimator of the unknown density function of a random vector and a kernel smoothed estimator of the parametric density function to be tested under the null hypothesis. We provide an alternative asymptotic approximation of the finite-sample distribution of this test by fixing the smoothing parameter. In contrast to the normal approximation obtained in Fan (1994) in which the smoothing parameter shrinks to zero as the sample size grows to infinity, we obtain a non-normal asymptotic distribution for the bias-corrected test. A parametric bootstrap procedure is proposed to approximate the critical values of this test. We show both analytically and by simulation that the proposed bootstrap procedure works. Consistency and local power properties of the bias-corrected test with a fixed smoothing parameter are also discussed.