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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…

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…