在经典的统计推断中，一方面，数据假定来自同一个总体；另一方面，数据要求服从对称分布。在真实世界中，数据严格来自同一个总体且对称的情况非常少有。此时若忽略数据的混合、偏斜特征，仍用同质、对称分布进行统计推断可能导致不合理甚至是错误的统计推断结论。为了更好地拟合数据，充分提取数据的信息，偏态回归模型是一类非常重要的模型。因此，本项目针对来自不同总体的偏态(SN,StN)数据，根据偏态数据的三个重要特征：均值、中位数和众数分别是总体“平均水平”、“中等水平”和“多数水平”的标志值，分别建立混合均值、中位数和众数回归模型，并进行系统深入的统计推断与算法研究。具体来说，为了更好地拟合实际中遇到的高维、混合型复杂（缺失、测量误差、删失和纵向）偏态数据，建立复杂(参数、非参数和半参数)混合均值、中位数和众数回归模型，重点研究上述复杂模型的估计理论、Bayesian推断、统计诊断、变量选择和算法研究。

In classical statistical inference, on the one hand, the data is assumed to come from the same population, on the other hand, the data is required to follow symmetric distribution. In the real world, the data strictly comes from the same population and symmetric distribution is very rare. If we ignore the mixture and/or skewness characteristics of the data, we still use the homogeneous and/or symmetric distribution to infer the statistical data, which may lead to unreasonable or even misleading results when the practical data reveal skewness feature. In order to better fit the data and comprehensively, accurately extract the information of the data, the skewed regression model is a kind of very important model. Therefore, this project is for skewed data (SN, StN) from the different populations, according to the three important features of the skewed data: the mean, median and mode are respectively the sign values of "average level", "medium level" and "most level", establish the mixture of mean, median and mode regression models, respectively, and systematically and deeply research statistical inference and algorithm. Especially, in order to better fit the actual high dimensional, mixture complex (missing, measurement error, censored, longitudinal data) skewed data, establish the complex (parameter, nonparametric and semiparametric) mixture of mean, median and mode regression models. The key research is focused the estimation theory, Bayesian inference，statistical diagnostics, variable selection and algorithm research of the above complex mixture regression models based on the complex mixture skewed data.