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非参数变量选择：EARTH算法AI 解读

We consider regression experiments involving a response variable Y and a large number of predictor variables X1, …, Xd, many of which may be irrelevant for the prediction of Y and thus must be removed before Y can be predicted from the X’s. We consider two procedures that select variables by using importance scores that measure the strength of the relationship between predictor variables and a response and keep those variables whose importance scores exceed a threshold. In…

局部多项式回归的可变带宽选择AI 解读

Summary The performances of data-driven bandwidth selection procedures in local polynomial regression are investigated by using asymptotic methods and simulation. The bandwidth selection procedures considered are based on minimizing ‘prelimit’ approximations to the (conditional) mean-squared error (MSE) when the MSE is considered as a function of the bandwidth h. We first consider approximations to the MSE that are based on Taylor expansions around h=0 of the bias part of…

平均导数分位数回归AI 解读

For fixed $\alpha \epsilon (0, 1)$, the quantile regression function gives the $\alpha$th quantile $\theta_{\alpha}(\mathbf{x})$ in the conditional distribution of a response variable Y given the value $\mathbf{X} = \mathbf{x}$ of a vector of covariates. It can be used to measure the effect of covariates not only in the center of a population, but also in the upper and lower tails. A functional that summarizes key features of the quantile specific relationship between X and…

全局泛函的非参数估计与回归协变量解释力度量AI 解读

In a nonparametric regression setting with multiple random predictor variables, we give the asymptotic distributions of estimators of global integral functionals of the regression surface. We apply the results to the problem of obtaining reliable estimators for the nonparametric coefficient of determination. This coefficient, which is also called Pearson's correlation ratio, gives the fraction of the total variability of a response that can be explained by a given set of…

相关曲线：回归局部解释方差的度量AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

作为回归局部方差解释度量的相关曲线AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

相关曲线：随协变量取值变化的关联度量AI 解读

For experiments where the strength of association between a response variable $Y$ and a covariate $X$ is different over different regions of values for the covariate $X$, we propose local nonparametric dependence functions which measure the strength of association between $Y$ and $X$ as a function of $X = x$. Our dependence functions are extensions of Galton's idea of strength of co-relation from the bivariate normal case to the nonparametric case. In particular, a…

两样本非线性模型的经验概率图与统计推断AI 解读

Let $X$ and $Y$ be two random variables with continuous distribution functions $F$ and $G$ and means $\mu$ and $\xi$. In a linear model, the crucial property of the contrast $\Delta = \xi - \mu$ is that $X + \Delta =_\mathscr{L} Y$, where $= _\mathscr{L}$ denotes equality in law. When the linear model does not hold, there is no real number $\Delta$ such that $X + \Delta = _\mathscr{L} Y$. However, it is shown that if parameters are allowed to be function valued, there is…