計量經(jīng)濟第四章ppt課件(已修改)
2025-05-15 07:37 本頁面
【正文】 Multiple Regression Analysis: Inference 多元回歸分析：推斷 (1) y = b0 + b1x1 + b2x2 + . . . bkxk + u Lecture Outline 本課提綱 ? CLM assumptions and Sampling Distributions of the OLS Estimators 經(jīng)典假設與 OLS估計量的樣本分布 ? Background review of hypothesis testing 假設檢驗的背景知識 ? Onesided and twosided t tests 單邊與雙邊 t檢驗 ? Calculating the p values 計算 p值 Assumption (Normality) 假設 （正態(tài)） ? So far, we know that given the GaussMarkov assumptions, OLS is BLUE, 我們已經(jīng)知道當 Gauss－ Markov假設成立時， OLS是最優(yōu)線性無偏估計。 ? In order to do classical hypothesis testing, we need to add another assumption (beyond the GaussMarkov assumptions) 為了進行經(jīng)典的假設檢驗，我們要在 Gauss－ Markov假設之外增加另一假設。 ? Assumption (Normality): Assume that u is independent of x1, x2,…, xk and u is normally distributed with zero mean and variance s2: u ~ Normal(0,s2) 假設 （正態(tài)）：假設 u與 x1, x2,…, xk獨立，且 u服從均值為 0，方差為 s2的正態(tài)分布。 CLM Assumptions 經(jīng)典線性模型假設 ? Assumptions – are called the classical linear model (CLM) assumptions. 假設 ? We refer to the model under these six assumptions as the classical linear model. 我們將滿足這六個假設的模型稱為經(jīng)典線性模型 ? Under CLM, OLS is not only BLUE, but also the minimum variance unbiased estimator, that is, among linear and nonlinear estimators, OLS estimator gives the smallest variance. ? 在經(jīng)典線性模型假設下， OLS不僅是 BLUE，而且是 最小方差無偏估計量 ，即在所有線性和非線性的估計量中， OLS估計量具有最小的方差。 CLM Assumptions 經(jīng)典線性模型假設 ? We can summarize the population assumptions of CLM as follows 我們對總體的經(jīng)典線性模型假設做個總結 ? y|x ~ Normal(b0 + b1x1 +…+ bkxk, ,s2) ? While for now we just assume normality, sometimes this is not the case 盡管現(xiàn)在我們假設了正態(tài)，但有時候并不是這種情況 CLM Assumptions 經(jīng)典線性模型假設 ? What should we do when the normality assumption fails? 如果正態(tài)假設不成立怎么辦？ ? Using a transformation, especially taking the log, often yields a distribution that is closer to normal. 通過變換，特別是通過取自然對數(shù)，往往可以得到接近于正態(tài)的分布。 Theorem Normal Sampling Distributions 定理 正態(tài)樣本分布 ? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?是誤差的線性組合服從正態(tài)分布，因為它故量的樣本值有假設下，條件于解釋變在jj?0 , 1N o r m a l ~ ??,?,N o r m a l ~?C L Me r r o r s t h eofn c o m b i n a t i ol i n e ar a isi t b e c a u s en o r m a l l y dd i s t r i b u t e is ?0 , 1N o r m a l ~ ?? t h atso ,?,N o r m a l ~? st v ar i a b l ei n d e p e n d e n t h e of v a l u ess am p l e o n t h e lc o n d i t i o n a s,a s s u m p t i o n C L M U n d er t h ebbbbbbbbbbbbbbjjjjjjjjjjjjsdV a rsdV a r?? Testing Hypotheses about a Single Population Parameter: the ttest 對單個總體參數(shù)的假設檢驗： t檢驗 ? Consider a population model () which satisfies the CLM assumptions. We now study how to test hypotheses about
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