Estimation And Application Of Non-parametric And Semi-parametric Model

Non-parametric regression method is an important direction for the development of statistics in recent years. It is widely used in the natural sciences and social sciences fields. Because of specific forms for regression function and error distribution in practical applications do not need to pre-select, so the non-parametric regression model can accurately reflect the actual application of real information. And it gets people’s more attentions. Semiparametric model not only has parametric components,but also has nonparametric components. So compared with the parametric regression model is more flexible, and compared with the non-parametric model has better extension. And it can explain the prediction effect of some variables.Firstly, this thesis describes two kinds of unitary non-parametric regression, smoothing spline regression and local polynomial regression. The methods are used to analyze the effect of the South China tiger inbreeding coefficient and mean litter size on juvenile mortality. The results show that the bigger mean litter size and inbreeding coefficient will reduce the survival rate of tiger cubs. Secondly, two kinds of multivariate nonparametric estimation models are introduced, namely generalized additive model and nonparametric multivariate regression model, meanwhile the methods are used to analyze the South China tiger inbreeding coefficient and mean litter size with nest interaction influence on juvenile mortality. So far,as far as the authors know,there is no related research whether the inbreeding coefficient and the mean litter size have significant effect on juvenile mortality.The results showed that the negative impact of mean litter size on the South China tiger cub mortality is not significant, and the impact of the inbreeding coefficient on the South China tiger cub mortality is significant. The paper also explain the problems caused by inbreeding depression, then as to the genetic rescue methods, put forward related suggestions, for better protection of the South China tiger and retaining its reproduction to offer help.The paper in the last chapter we launch the study of variable coefficient local polynomial model. Inspired by Sun and Lin’s research on variable coefficient linear model, the variable coefficient section polynomial model local rank estimations are given, and multi-stage method to achieve loacl rank estimation are proposed. Subject to different error distributions, especially heavy-tailed distribution, the numerical simulation analysis is concerned. The results show that the local rank estimation (LR) is an effective estimation method.