手法を比較

	カーネル密度推定と分布検定 (KDE)	正規性リリフォース検定
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1956	1967
提唱者	Rosenblatt (1956); Parzen (1962); textbook treatment by Silverman	Hubert W. Lilliefors
種類	Nonparametric density estimation	Goodness-of-fit / normality test
原典	Rosenblatt, M. (1956). Remarks on Some Nonparametric Estimates of a Density Function. Annals of Mathematical Statistics, 27(3), 832-837.	Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. Journal of the American Statistical Association, 62(318), 399-402.
別名	kernel density estimate, KDE, Parzen window estimation, nonparametric density estimation	Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi
関連	4	5
概要	Kernel Density Estimation is a nonparametric method that estimates a continuous probability density by placing a smooth kernel function over each observation, without assuming any parametric distribution. It traces back to Rosenblatt (1956) and the textbook treatment by Silverman (1986), and it also supports distribution-comparison tests built on the estimated densities.	The Lilliefors test is a goodness-of-fit test that checks whether a continuous sample comes from a normal (or exponential) distribution when the mean and variance are unknown and estimated from the data. Introduced by Hubert W. Lilliefors in 1967, it adjusts the critical values of the Kolmogorov-Smirnov test so that they remain valid once the distribution's parameters are estimated rather than known in advance.