{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 正态总体的假设检验\n", "如果$x_i\\sim N\\left( \\mu, \\sigma^2 \\right)$,那么$\\bar{x}\\sim N\\left(\\mu,\\frac{\\sigma^2}{N}\\right)$,或者,如果我们用样本方差替代总体方差,那么有:$$\\frac{\\bar{x}-\\mu}{\\sqrt{\\frac{s^2}{N}}}\\sim t(N-1)$$\n", "如果在原假设:$H_0:\\mu=\\mu_0$的条件下,我们的假设检验统计量:$$\\frac{\\bar{x}-\\mu_0}{\\sqrt{\\frac{s^2}{N}}}\\sim t(N-1)$$\n", "因而为了检验总体期望$\\mu=\\mu_0$,我们可以首先计算检验统计量,并确定拒绝域,进而做出决策。\n", "我们知道,假设检验有两类错误,第I类错误即原假设为真,错误地拒绝原假设的概率;而第II类错误即备择假设为真,错误的接受原假设的概率。这两类错误可以使用势函数(power function)来表示。\n", "在下面的程序中,我们将在原假设$H_0:\\mu_0=0$的条件下,对不同的真实总体参数$\\mu_0$重复进行1000次假设检验,并以此计算出拒绝原假设的概率,即势函数。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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Xuo4CBJyvv/5aa9asOfRYGiAUUNCAADBs2DBFRESwzAkcwcHzailoCCUUNCAA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\nZwJykwCA+ikyMlIXX3yxMjIyVFFR4To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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "from scipy import special as func\n", "\n", "def sampling(mu, sigma2, N):\n", " x=nprd.normal(mu,np.sqrt(sigma2),N)\n", " return x\n", "\n", "def t_testing(x,mu0,alpha=0.05):\n", " \"\"\" t-Test under the H0: E(x)=mu0 \"\"\"\n", " critical_value=func.stdtrit(len(x)-1,1-alpha/2)\n", " ## test statistic\n", " t=(np.mean(x)-mu0)/np.sqrt(np.std(x)/len(x))\n", " ## decision\n", " if t<-1*critical_value or t>critical_value:\n", " rejected=1\n", " else:\n", " rejected=0\n", " return rejected\n", "\n", "## true value\n", "mu=np.linspace(-2,2,51)\n", "sigma2=1\n", "N=10 # sample size\n", "## iteration times\n", "M=1000\n", "## significance level and critical value\n", "alpha=0.05\n", "\n", "rejection=np.zeros(len(mu))\n", "for j in range(len(mu)):\n", " m=mu[j]\n", " ## results\n", " rejected=np.zeros(M)\n", " for i in range(M):\n", " ## sampling\n", " x=sampling(m, sigma2, N)\n", " rejected[i]=t_testing(x,0,alpha)\n", " rejection[j]=np.mean(rejected)\n", "\n", "## plot\n", "## 导入matplotlib\n", "import matplotlib.pyplot as plt \n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n", "\n", "plt.plot(mu,rejection,label=r'Power',color='black') ## power function\n", "plt.xlabel(r'$\\mu_0$')\n", "plt.ylabel(r'$P(rejection)$')\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 非正态总体的大样本检验\n", "如果$x_i\\sim \\left( \\mu, \\sigma^2 \\right)$,那么在大样本条件下,$\\bar{x}\\sim N\\left(\\mu,\\frac{\\sigma^2}{N}\\right)$,或者,如果我们用样本方差替代总体方差,那么有:$$\\frac{\\bar{x}-\\mu}{\\sqrt{\\frac{s^2}{N}}}\\sim N\\left(0,1\\right)$$\n", "如果在原假设:$H_0:\\mu=\\mu_0$的条件下,我们的假设检验统计量:$$\\frac{\\bar{x}-\\mu_0}{\\sqrt{\\frac{s^2}{N}}}\\sim N\\left(0,1\\right)$$\n", "因而为了检验总体期望$\\mu=\\mu_0$,我们可以首先计算检验统计量,并确定拒绝域,进而做出决策。\n", "特别的,当$x_i\\sim Ber(p)$,即服从概率为$p$的伯努利分布时,在大样本条件下,我们可以用样本比例$\\hat{p}=\\bar{x}$对总体概率$p$进行检验,在$H_0:p=p_0$的原假设下,我们有如下两个检验统计量:\n", "* 方法一: $$\\frac{\\hat{p}-p_0}{\\sqrt{\\frac{p_0(1-p_0)}{N}}}\\sim N\\left(0,1\\right)$$\n", "* 方法二: $$\\frac{\\hat{p}-p_0}{\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{N}}}\\sim N\\left(0,1\\right)$$\n", "根据大数定律,$\\hat{p}\\rightarrow^p p_0$,因而以上两种方法在大样本条件下应该是等价的,而小样本情况下可能存在差异。\n", "此外,我们还可以使用对数似然比检验(log likelihood ratio test)。我们知道,对于伯努利分布,其似然函数为:$$L\\left(p|x\\right)=\\sum_{i=1}^{N}\\left[ x_i\\ln{p}+(1-x_i)\\ln{1-p}\\right]=N_1\\ln{p}+(N-N_1)\\ln{1-p}$$其中$N_1=\\sum_{i=1}^N x_i$。在$H_0:p=p_0$的原假设下,即在$p=p_0$的约束下,似然函数为$$L\\left(p_0|x\\right)=N_1\\ln{p_0}+(N-N_1)\\ln{1-p_0}$$因而我们可以构建检验统计量:$$2\\left[L\\left(\\hat{p}|x\\right)-L\\left(p_0|x\\right)\\right]\\sim \\chi^2(1)$$其中$\\hat{p}$为$p$的极大似然估计。因而我们有:\n", "* 方法三:$$2\\left[L\\left(\\frac{N_1}{N}|x\\right)-L\\left(p_0|x\\right)\\right]\\sim \\chi^2(1)$$\n", "接下来,我们将在原假设$H_0:p=0.5$的条件下,针对不同的真值$p_0$,重复1000次假设检验,比较以上三个检验统计量的势函数。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Library/Frameworks/Python.framework/Versions/3.5/lib/python3.5/site-packages/ipykernel_launcher.py:29: RuntimeWarning: divide by zero encountered in double_scalars\n", "/Library/Frameworks/Python.framework/Versions/3.5/lib/python3.5/site-packages/ipykernel_launcher.py:44: RuntimeWarning: divide by zero encountered in log\n", "/Library/Frameworks/Python.framework/Versions/3.5/lib/python3.5/site-packages/ipykernel_launcher.py:44: RuntimeWarning: invalid value encountered in multiply\n" ] }, { "data": { "image/png": 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CaQVkpbu+lT5UU1PDvHnzvrkc0N7uVs8OOQTOOMPreHtNBVqwTJ4M8fHbraKN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\n/s3hzz4jEAiQ5TXcnjMLtEig5P9YqcX3nUEpNVw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HA37dar7sl1Gkncgz3Zu1Izxux4BT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\nOxz8fOONnDx50uq34B68vKBZfdMS9cceOHzM2jyn98D0K/0emIEBZtX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IBg4IIUrFLySE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KReNcp0iI0ECTkLZ8j73ouGQxaxYtdp0iIn6s27x51PXpS3xGhusUCREaaBLS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\nRIcOHQDo27cvxcXFREZGnrH9pk2bSE1NJSys9v7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random as nprd\n", "from scipy import special as func\n", "\n", "def sampling(p,N):\n", " ## 产生Bernouli样本\n", " x=nprd.rand(N)critical_value:\n", " rejected=1\n", " else:\n", " rejected=0\n", " return rejected\n", "\n", "## second method\n", "def z_testing2(x,p0,alpha=0.05):\n", " \"\"\" z-Test under the H0: p=p0 \"\"\"\n", " critical_value=func.ndtri(1-alpha/2)\n", " ## test statistic\n", " phat=np.mean(x)\n", " z=np.sqrt(len(x))*(phat-p0)/np.sqrt(phat*(1-phat))\n", " ## decision\n", " if z<-1*critical_value or z>critical_value:\n", " rejected=1\n", " else:\n", " rejected=0\n", " return rejected\n", "\n", "## third method\n", "def z_testing3(x,p0,alpha=0.05):\n", " \"\"\" likelihood ratio test under the H0: p=p0 \"\"\"\n", " ## test statistic\n", " N=len(x)\n", " N1=np.sum(x)\n", " phat=np.mean(x)\n", " L=N1*np.log(phat)+(N-N1)*np.log(1-phat)\n", " L0=N1*np.log(p0)+(N-N1)*np.log(1-p0)\n", " chi=2*(L-L0)\n", " # p-value\n", " pvalue=1-func.chdtr(1,chi)\n", " ## decision\n", " if pvalue