计量经济第四章4-1.ppt

Multiple Regression Analysis: Inference 多元回归分析：推断 (1),y = b0 + b1x1 + b2x2 + . . . bkxk + u,Lecture Outline 本课提纲,CLM assumptions and Sampling Distributions of the OLS Estimators 经典假设与OLS估计量的样本分布 Background review of hypothesis testing 假设检验的背景知识 One-sided and two-sided t tests 单边与双边t检验 Calculating the p values 计算p值,Assumption MLR.6 (Normality) 假设MLR.6 （正态）,So far, we know that given the Gauss-Markov assumptions, OLS is BLUE, 我们已经知道当GaussMarkov假设成立时，OLS是最优线性无偏估计。 In order to do classical hypothesis testing, we need to add another assumption (beyond the Gauss-Markov assumptions) 为了进行经典的假设检验，我们要在GaussMarkov假设之外增加另一假设。 Assumption MLR.6 (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) 假设MLR.6 （正态）：假设u与x1, x2, xk独立，且u服从均值为0，方差为s2的正态分布。,CLM Assumptions 经典线性模型假设,Assumptions MLR.1 MLR.6 are called the classical linear model (CLM) assumptions. 假设MLR.1-MLR.6被称为经典线性模型假设 We refer to the model under these six assumptions as the classical linear model. 我们将满足这六个假设的模型称为经典线性模型 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. 在经典线性模型假设下，OLS不仅是BLUE，而且是最小方差无偏估计量，即在所有线性和非线性的估计量中，OLS估计量具有最小的方差。,CLM Assumptions 经典线性模型假设,We can summarize the population assumptions of CLM as follows 我们对总体的经典线性模型假设做个总结 y|x Normal(b0 + b1x1 + bkxk, ,s2) While for now we just assume normality, sometimes this is not the case 尽管现在我们假设了正态，但有时候并不是这种情况,CLM Assumptions 经典线性模型假设,What should we do when the normality assumption fails? 如果正态假设不成立怎么办？ Using a transformation, especially taking the log, often yields a distribution that is closer to normal. 通过变换，特别是通过取自然对数，往往可以得到接近于正态的分布。,Theorem 4.1 Normal Sampling Distributions 定理4.1 正态样本分布,4.2 Testing Hypotheses about a Single Population Parameter: the t-test 对单个总体参数的假设检验：t检验,Consider a population model (4.2) which satisfies the CLM assumptions. We now study how to test hypotheses about a particular 考虑总体中满足CLM的模型 我们现在研究如何对一个特定的 进行假设检验,Background Review 背景知识回顾,The hypothesis to be tested is called the null hypothesis. 被检验的假设称为零假设 Hypothesis testing entails using data to compare the null hypothesis with a second hypothesis, i.e., the alternative hypothesis. 假设检验利用数据将零假设和另一个假设（替代假设）进行比较,Background Review 背景知识回顾,The alternative hypothesis specifies what is true if the null hypothesis is not. 替代假设给出在零假设不成立时的真实情况。 Our goal: use the evidence in a randomly selected sample of data to decide whether to accept the null hypothesis. 我们的目的：利用一个随机选取的样本提供给我们的证据来决定是否应当接受零假设。,Background Review 背景知识回顾,Two kinds of mistakes are possible in hypothesis testing. 在假设检验中存在两种可能的错误。 Type I error: reject the null hypothesis when it is in fact true. 第一类错误：当零假设为真时拒绝零假设（弃真） Type II error: fail to reject the null when it is actually false. 第二类错误：当零假设为假时未拒绝零假设（取伪）,Background Review 背景知识回顾,Hypothesis testing rules are constructed to make the probability of committing type I error fairly small. 我们建立一些假设检验的规则使发生第一类错误的概率非常小。 The significance level (level) of a test is the probability of a Type I error. 一个检验的显著性水平是发生第一类错误的概率。 Commonly specified significance levels: 0.1,0.05, 0.01. If it equals 0.05, it means the researcher is willing to falsely reject the null at 5% of the time. 通常设定的限制性水平为：0.1,0.05,0.01。如果为0.05意味着研究者愿意在5的检验中错误地拒绝零假设。,Background Review 背景知识回顾,The critical value of the test statistic is the value of the statistic for which the test just reject the null hypothesis at the given significance level. 检验统计量的临界值是使得零假设刚好在给定显著性水平上被拒绝的统计量的值。 The set of values of the test statistic for which the test rejects the null is the rejection region, and the values of the test statistic for which it does not reject the null is the acceptance region. 假设检验中，使得零假设被拒绝的检验统计量的取值范围称为拒绝域，使得零假设不能被拒绝的检验统计量的取值范围成为接受域。,Background Review 背景知识回顾,A test statistic (T) is some function of the random sample. When we compute the statistic for