Partial Unimodal Bayesian Regression Using Bernstein Polynomial

• Main Authors: Li-Hsueh Cheng, 鄭麗雪
• Other Authors: Yuh-Jenn Wu
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/35386600473955400866

碩士 === 中原大學 === 應用數學研究所 === 98 === The estimated regression function is an important statistical problem, and partially linear models have many applications. Such as Hardle et al (2000) example, Engle, Granger, Rice and Weiss (1986) were among the first to consider the partially linear model. They analyzed the relationship between temperature and electricity usage. We rst mention several examples from the existing literature. Most of the examples are concerned with practical problems involving partially linear models. They used data based on the monthly electricity sales yi for four cities, the monthly price of electricity x1, income x2, and average daily temperature t. They modeled the electricity demand y as the sum of a smooth function g of monthly temperature t, and a linear function of x1 and x2, as well as with 11 monthly dummy variables x3, . . . , x13. In this paper, mainly used in agriculture, the first application for the amount of fertilizer and crops harvest relationship. Suppose the amount of fertilizer as the x-axis and the crops harvest as the y-axis, the graph is unimodal, if there are two or more kind of the fertilizer and crops harvest relationship. The second application is the crops harvest and two or more kind of the fertilizer and the relationship between seasons. We use partially linear regression model for analysis and comparison, the unimodal model using Bernstein polynomials to describe, using Bayesian methods to estimate, algorithm with Markov Chain Monte Carlo method to calculate.