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@arokem
Created December 14, 2012 17:37
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Calculation of the bias of the standard deviation (with the proof of it from http://stats.stackexchange.com/questions/11707/why-is-sample-standard-deviation-a-biased-estimator-of-sigma)
{
"metadata": {
"name": "std_bias"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": "s=np.random.normal(size=(50000,100))\nn = np.array(range(2,100))\n# Note that to estimate the population SD from a sample, use ddof=1 rather than the default ddof=0.\n# With ddof=0, the SD bias is 4x higher.\nsd_est = np.array([s[:, 0:ii].std(axis=1, ddof=1).mean() for ii in n])\nplot(n, sd_est)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 1,
"text": "[<matplotlib.lines.Line2D at 0x10ae3c390>]"
},
{
"output_type": "display_data",
"png": 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RokVKTk5WTk6OXnrppbDH3ijW9wHAHi5jjInai7tc6unL//730p49UlVVLw8KAGLc9WTn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\nADgMwQ8ADkPwA4DD/D9doV3juHggmwAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x10ae0ffd0>"
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Taken from http://stats.stackexchange.com/questions/11707/why-is-sample-standard-deviation-a-biased-estimator-of-sigma\n\nHere I will explicitly calculate the expectation of the sample standard deviation (the original poster's second question) from a normally distributed sample, at which point the bias is clear. \n\nThe unbiased sample variance of a set of points $x_1, ..., x_n$ is \n\n$$ s^{2} = \\frac{1}{n-1} \\sum_{i=1}^{n} (x_i - \\overline{x})^2 $$ \n\nIf the $x_i$'s are normally distributed, it is a fact that \n\n$$ \\frac{(n-1)s^2}{\\sigma^2} \\sim \\chi^{2}_{n-1} $$ \n\nwhere $\\sigma^2$ is the true variance. The $\\chi^2_{k}$ distribution has probability density \n\n$$ p(x) = \\frac{(1/2)^{k/2}}{\\Gamma(k/2)} x^{k/2 - 1}e^{-x/2} $$ \n\nusing this we can derive the expected value of $s$; \n\n$$ \\begin{align} E(s) &= \\sqrt{\\frac{\\sigma^2}{n-1}} E \\left( \\sqrt{\\frac{s^2(n-1)}{\\sigma^2}} \\right) \\\\\n&= \\sqrt{\\frac{\\sigma^2}{n-1}}\n\\int_{0}^{\\infty}\n\\sqrt{x} \\frac{(1/2)^{(n-1)/2}}{\\Gamma((n-1)/2)} x^{((n-1)/2) - 1}e^{-x/2} \\ dx \\end{align} $$ \n\nwhich follows from the definition of expected value and fact that $ \\sqrt{\\frac{s^2(n-1)}{\\sigma^2}}$ is the square root of a $\\chi^2$ distributed variable. The trick now is to rearrange terms so that the integrand becomes another $\\chi^2$ density: \n\n$$ \\begin{align} E(s) &= \\sqrt{\\frac{\\sigma^2}{n-1}}\n\\int_{0}^{\\infty}\n\\frac{(1/2)^{(n-1)/2}}{\\Gamma(\\frac{n-1}{2})} x^{(n/2) - 1}e^{-x/2} \\ dx \\\\\n&= \\sqrt{\\frac{\\sigma^2}{n-1}} \\cdot\n\\frac{ \\Gamma(n/2) }{ \\Gamma( \\frac{n-1}{2} ) }\n\\int_{0}^{\\infty}\n\\frac{(1/2)^{(n-1)/2}}{\\Gamma(n/2)} x^{(n/2) - 1}e^{-x/2} \\ dx \\\\\n&= \\sqrt{\\frac{\\sigma^2}{n-1}} \\cdot\n\\frac{ \\Gamma(n/2) }{ \\Gamma( \\frac{n-1}{2} ) } \\cdot\n\\frac{ (1/2)^{(n-1)/2} }{ (1/2)^{n/2} }\n\\underbrace{\n\\int_{0}^{\\infty}\n\\frac{(1/2)^{n/2}}{\\Gamma(n/2)} x^{(n/2) - 1}e^{-x/2} \\ dx}_{\\chi^2_n \\ {\\rm density} }\n\\end{align} \n$$\n\nnow we know the integrand the last line is equal to 1, since it is a $\\chi^2_{n}$ density. Simplifying constants a bit gives \n\n$$ E(s)\n= \\sigma \\cdot \\sqrt{ \\frac{2}{n-1} } \\cdot \\frac{ \\Gamma(n/2) }{ \\Gamma( \\frac{n-1}{2} ) } $$ \n\nTherefore the bias of $s$ is \n\n$$ \\sigma - E(s) = \\sigma \\bigg(1 - \\sqrt{ \\frac{2}{n-1} } \\cdot \\frac{ \\Gamma(n/2) }{ \\Gamma( \\frac{n-1}{2} ) } \\bigg) \\sim \\frac{\\sigma}{4 n} \\>$$ \nas $n \\to \\infty$.\n\nIt's not hard to see that this bias is not 0 for any finite $n$, thus proving the sample standard deviation is biased. Below the bias is plot as a function of $n$ for $\\sigma=1$ in red along with $1/4n$ in blue: \n"
},
{
"cell_type": "code",
"collapsed": false,
"input": "from scipy.special import gamma\n\nbias = sd_est * (1. - sqrt(2. / (n-1)) * (gamma(n / 2.) / gamma((n-1) / 2.)))\nplot(n,bias,'r-', n,sd_est/(4*n),'b-')\nxlabel('Sample size')\nylabel('Standard deviation estimate bias')\nlegend(('Full estimate','SD/4n approximation'))",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 7,
"text": "<matplotlib.legend.Legend at 0x110b36fd0>"
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P55dffmH58uX1EVvdSAO3EELYjNVk4ebmRlFREWvWrGHEiBG4uLhYtGHctqSB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\nIkqLyYKIiNJisiAiorSYLIiIKK0fKAXkcBZlFzsAAAAASUVORK5CYII=\n",
"text": "<matplotlib.figure.Figure at 0x110e60c50>"
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": "plot([0,100],[1,1],'k--', n,sd_est,'b-', n,(sd_est+sd_est/(4*n)),'c-', n,(sd_est+bias),'m-')\nxlabel('Sample size')\nylabel('Standard deviation estimate')\nlegend(('True population SD', 'Uncorrected estimate', 'Corrected (SD/4n approx.)', 'Corrected (full model)'),loc='lower right')",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 3,
"text": "<matplotlib.legend.Legend at 0x1082c37d0>"
},
{
"output_type": "display_data",
"png": 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yiyeuMfJVKnTp2FFvWVoa8PTTbZMexhh7HBgMFqtXrwYAfP/99yAivXXt+aG8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\nITJRsSCEECLT/wHoBUPegvNuYQAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x10ae1d350>"
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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