臺灣博碩士論文加值系統

迴歸曲線的估計是統計上的一個重要的問題, 而部份線性模型方面有很多的應用. 如Hardle等人(2000)所舉的例子: Engle, Granger, Rice和Weiss(1986)是最早考慮部份線性模型, 他們分析了溫度和電力使用的關係. 從現有的文獻,大多數的例子所關心的實際問題, 都涉及部份線性模型, 他們對於四個城市用它們的月售電量yi, 每個月用電價格x1, 收入x2, 和日均溫t, 來收集資料. 他們假設電力需求y 為平滑函數g 在每月溫度t 的函數值和x1, x2 以及11個月的虛擬變量x3, . . . , x13 的線性組合之總和, 因此它就是一個部份線性迴歸之問題.
在我們的這篇論文, 主要應用在農業上, 第一個應用為肥料的量和農作物的產量之間的關係. 假設把肥料的量當x 軸和農作物產量當y 軸, 其圖形為單峰,若有二種或二種以上的肥料和農作物產量之間的關係. 第二個應用就是農作物產量和二種或二種以上肥料以及季節之關係. 我們利用部份線性迴歸模型來做分析和比較, 單峰模型用伯氏多項式來描述, 用貝氏方法來估計, 演算法用馬可夫鏈蒙地卡羅方法來計算.

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.

目錄
摘要I
Abstract II
誌謝辭III
目錄IV
圖目錄V
表目錄VI
1 緒論1
2 模型架構3
2.1 貝氏迴歸. . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Bernstein多項式係數和圖形是單峰. . . . . . . . . . . . . . 4
2.3 事前分配的支集(Support of priors) . . . . . . . . . . . . . 5
3 貝氏推論6
3.1 事前分佈. . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2.1 獨立Metropolis-Hastings . . . . . . . . . . . . . . 7
3.2.2 Green-Metropolis-Hastings . . . . . . . . . . . . . 7
4 模擬計算10
5 討論15
參考文獻16

圖目錄
1 樣本數=101, σ = 0.1, β = 0.1 之圖形. . . . . . . . . . . 11
2 樣本數=401, σ = 0.1, β = 0.1 之圖形. . . . . . . . . . . 11
3 樣本數=101, σ = 0.1, β = 0.5 之圖形. . . . . . . . . . . 12
4 樣本數=401, σ = 0.1, β = 0.5 之圖形. . . . . . . . . . . 12
5 樣本數=101, σ = 0.5, β = 0.1 之圖形. . . . . . . . . . . 13
6 樣本數=401, σ = 0.5, β = 0.1 之圖形. . . . . . . . . . . 13
7 樣本數=101, σ = 0.5, β = 0.5 之圖形. . . . . . . . . . . 14
8 樣本數=401, σ = 0.5, β = 0.5 之圖形. . . . . . . . . . . 14

表目錄
1 模擬所得的平均數. . . . . . . . . . . . . . . . . . . . . . 10

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