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| 核密度估计与分布检验 (KDE)× | Lilliefors 正态性检验× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1956 | 1967 |
| 提出者≠ | Rosenblatt (1956); Parzen (1962); textbook treatment by Silverman | Hubert W. Lilliefors |
| 类型≠ | Nonparametric density estimation | Goodness-of-fit / normality test |
| 开创性文献≠ | Rosenblatt, M. (1956). Remarks on Some Nonparametric Estimates of a Density Function. Annals of Mathematical Statistics, 27(3), 832-837. DOI ↗ | 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. DOI ↗ |
| 别名≠ | kernel density estimate, KDE, Parzen window estimation, nonparametric density estimation | Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi |
| 相关≠ | 4 | 5 |
| 摘要≠ | 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. |
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