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投影近似及其与核方法的对偶关系AI 解读

Projection pursuit regression and kernel regression are methods for estimating a smooth function of several variables from noisy data obtained at scattered sites. Methods based on local averaging can perform poorly in high dimensions (curse of dimensionality). Intuition and examples have suggested that projection based approaches can provide better fits. For what sorts of regression functions is this true? When and by how much do projection methods reduce the curse of…

抗异常值直线及相关回归方法AI 解读

In a bivariate (x, y) scatterplot the three-group resistant line is that line for which the median residual in each outer third of the data (ordered on x) is zero. It was proposed by Tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation. A dual plot representation of the procedure yields a fast, convergent algorithm, nonparametric confidence intervals for the slope, consistency, influence function, and asymptotic normality results.…

有效得分、方差分解与蒙特卡洛方差缩减AI 解读

Monte Carlo “swindles” or variance reduction techniques exploit the experimenter's knowledge of the stochastic structure governing the simulated data to construct more precise estimates of unknown parameters. Alternatively, one can reduce the number of replications (and thus the cost) needed to gain a desired level of precision. This article reviews the common case of swindles based on variance decompositions for estimating efficiencies and variances of location and…