{ "metadata": { "name": "", "signature": "sha256:11958373380860ee5e5aa61e7c2cd5677c7ca0a969d0c07986d02154f8452801" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from IPython.html.widgets import interact\n", "from scipy import stats\n", "import seaborn as sns\n", "import pandas as pd" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Previously, we talk about maximum likelihood estimation and maximum a-posteriori estimation and in each case we started out with a probability density function of some kind and we further assumed that the samples were identically distributed and independent. The idea behind robust statistics is to construct estimators that can survive the weakening of either or both of these assumptions.\n", "\n", "The first idea to consider is the notion of *location*, which is a generalization of the idea of \"central value\". Typically, we just use an estimate of the mean for this, but we will see shortly why that is a bad idea. The general idea of Location satisfies the following requirements\n", "\n", "Let $X$ be a random variable with distribution $F$, and let $\\theta(X)$ be some descriptive\n", "measure of $F$. Then $\\theta(X)$ is said to be a measure of *location* if for any constants *a* and *b*, we have the following:\n", "\n", "$$\\theta(X+b) = \\theta(X) +b$$\n", "\n", "$$\\theta(-X) = -\\theta(X)$$\n", "\n", "$$X \\ge 0 \\Rightarrow \\theta(X) \\ge 0$$\n", "\n", "$$\\theta(a X) = a\\theta(X)$$\n", "\n", "The first condition is called *location equivariance* (or *shift-invariance* in signal processing lingo). The fourth condition is called *scale equivariance*, which means that the units that $X$ is measured in should not effect the value of the location estimator. These Requirements capture the idea of what we intuitively mean by *centrality* of a distribution, or where most of the probability mass is located.\n", "\n", "For example, the mean estimator is $\\hat{\\mu}=\\frac{1}{n}\\sum X_i$. The first requirement is obviously satisfied as $\\hat{\\mu}=\\frac{1}{n}\\sum (X_i+b) = b + \\frac{1}{n}\\sum X_i =b+\\hat{\\mu}$. Let us consider the second requirement:$\\hat{\\mu}=\\frac{1}{n}\\sum -X_i = -\\hat{\\mu}$. Finally, the last requirement is satisfied with $\\hat{\\mu}=\\frac{1}{n}\\sum a X_i =a \\hat{\\mu}$." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "What do we mean by robust estimators?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have the generalized location of centrality embodied in the *location* parameter, what can we do with it? The next idea is to nail down is the concept of * robust* estimators. Previously, we assumed that our samples were all identically distributed. The key idea is that the samples might be actually coming from a distribution that is contaminated by another nearby distribution, as in the following:\n", "\n", "$$F(X) = \\epsilon G(X) + (1-\\epsilon)H(X)$$\n", "\n", "where $\\epsilon$ is between zero and one. This means that our data samples $\\lbrace X_i \\rbrace$ actually derived from two separate distributions, $G(X)$ and $H(X)$. We just don't know how they are mixed together. What we really want is an estimator that captures the location of $G(X)$ in the face of random intermittent contamination by $H(X)$. It can get even worse than that because we don't know that there is only one contaminating $H(X)$ distribution out there. There may be a whole family of distributions that are contaminating $G(X)$ that we don't know of. This means that whatever estimators we construct have to be derived from families of distributions instead of a distribution, which is what we have been assuming for maximum-likelihood estimators. This is what makes robust estimation so difficult --- the extended theory has to deal with spaces of function distributions instead of particular parameters of a particular probability distribution.\n", "\n", "* Influence function\n", "* Outlier Detection\n", "* Estimates of location\n", " - definition of location\n", "* Trimmed means\n", "* Windsorized means\n", "* Hodges Lehmann statistics\n", "* Asymptotic efficiency\n", "* Fisher Consistent\n", "\n", "* Robust Regression \n", " \n", "\n", " - least median\n", " - outliers" ] }, { "cell_type": "code", "collapsed": false, "input": [ "n0=stats.norm(0,1)\n", "n1=stats.norm(0,10)\n", "xi = linspace(-5,5,100)\n", "\n", "fig,ax=subplots()\n", "ax.plot(xi,n0.pdf(xi))\n", "ax.plot(xi,n1.pdf(xi))\n", "\n", "def bias_coin(phead = .5):\n", " while True:\n", " yield int( np.random.rand() < phead ) \n", "\n", "pct_mixed = 0.1\n", "bias_coin_gen = bias_coin(pct_mixed) \n", "dual_set = [n0,n1]\n", "samples = [ dual_set[bias_coin_gen.next()].rvs() for i in range(500) ]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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20zIV2rY62ztKPJFiU6xyTetey+0Uq44AcLjjIje1Fd559kJ7T3lF22l5lrMTky+gnwQe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\nmF0u4KSnOU6AgBMg6ARwcAg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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "hist(samples,bins=20)\n", "title('average = %3.3f, median=%3.3f pct_mixed=%3.3f'%(mean(samples),np.median(samples),pct_mixed))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "import sympy.stats\n", "from sympy.abc import x\n", "eps = sympy.symbols('epsilon')\n", "\n", "mixed_cdf = sympy.stats.cdf(sympy.stats.Normal('x',0,1),'x')(x)*(1-eps) + eps*sympy.stats.cdf(sympy.stats.Normal('x',1,2),'x')(x)\n", "mixed_pdf = sympy.diff(mixed_cdf,x)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_mixed_dist(epsilon=.1):\n", " n1 = stats.norm(1,2)\n", " xi = linspace(-5,5,100)\n", " fig,ax = subplots()\n", " ax.plot(xi,[sympy.lambdify(x,mixed_pdf.subs(eps,epsilon))(i) for i in xi],label='mixed',lw=2)\n", " ax.plot(xi,n0.pdf(xi),label='g(x)',linestyle='--')\n", " ax.plot(xi,n1.pdf(xi),label='h(x)',linestyle='--')\n", " ax.legend(loc=0)\n", " ax.set_title('epsilon = %2.2f'%(epsilon))\n", " ax.vlines(0,0,.4,linestyle='-',color='g')\n", " ax.vlines(epsilon,0,.4,linestyle='-',color='b')\n", "\n", "interact(plot_mixed_dist,epsilon=(0,1,.05))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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z2kwhrCaDt4QIIT39IzS1DRAbY2NhYZrV4QTM8hLPzcbOmlYqu2voGen1UUII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\nX4TZYGbdkX8RCAcAuP6yQuwWA/uOtPLONplkPit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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "M-estimators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "M-estimators are generalized maximum likelihood estimators. Recall that for maximum likelihood, we want to maximize the likelihood function as in the following:\n", "\n", "$$L_{\\mu}(x_i) = \\prod f_0(x_i-\\mu)$$\n", "\n", "and then to find the estimator $\\hat{\\mu}$ so that\n", "\n", "$$\\hat{\\mu} = \\arg \\max_{\\mu} L_{\\mu}(x_i)$$\n", "\n", "So far, everything is the same as our usual maximum-likelihood derivation except for the fact that we don't know $f_0$, the distribution of the $\\lbrace X_i\\rbrace$. Making the convenient definition of\n", "\n", "$$\\rho = -\\log f_0$$\n", "\n", "we obtain the more convenient form of the likelihood product and the optimal $\\hat{\\mu}$ as\n", "\n", "$$\\hat{\\mu} = \\arg \\min_{\\mu} \\sum \\rho(x_i-\\mu)$$\n", "\n", "If $\\rho$ is differentiable, then differentiating this with respect to $\\mu$ gives\n", "\n", "$$\\sum \\psi(x_i-\\hat{\\mu}) = 0$$\n", "\n", "with $\\psi = \\rho'$ and for technical reasons we will assume that $\\psi$ is increasing. The key idea here is we want to consider general $\\rho$ functions that my not be MLE for *any* distribution.\n" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "The distribution of M-estimates " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a given distribution $F$, we define $\\mu_0=\\mu(F)$ as the solution to the following \n", "\n", "$$\\mathbb{E}_F(\\psi(x-\\mu_0))= 0$$\n", "\n", "It is technical to show, but it turns out that $\\hat{\\mu} \\sim \\mathcal{N}(\\mu_0,\\frac{v}{n})$ with\n", "\n", "$$v = \\frac{\\mathbb{E}_F(\\psi(x-\\mu_0)^2)}{(\\mathbb{E}_F(\\psi^\\prime(x-\\mu_0)))^2}$$\n", "\n", "Thus, we can say that $\\hat{\\mu}$ is asymptotically normal with asymptotic value $\\mu_0$ and asymptotic variance $v$. This leads to the efficiency ratio which is defined as the following:\n", "\n", "$$\\texttt{Eff}(\\hat{\\mu})= \\frac{v_0}{v}$$\n", "\n", "where $v_0$ is the asymptotic variance of the MLE and measures how near $\\hat{\\mu}$ is to the optimum. for example, if for two estimates with asymptotic variances $v_1$ and $v_2$, we have $v_1=3v_2$, then first estimate requires three times as many observations to obtain the same variance as the second.\n", "\n", "For example, for the sample mean (i.e. $\\hat{\\mu}=\\frac{1}{n} \\sum X_i$) with $F=\\mathcal{N}$, we have $\\rho=x^2/2$ and $\\psi=x$ and also $\\psi'=1$. Thus, we have $v=\\mathbb{V}(x)$. Alternatively, using the sample median as the estimator for the location, we have $v=\\frac{1}{4 f(\\mu_0)^2}$. Thus, if we have $F=\\mathcal{N}(0,1)$, for the sample median, we obtain $v=\\frac{2\\pi}{4} \\approx 1.571$. This means that the sample median takes approximately 1.6 times as many samples to obtain the same variance for the location as the sample mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way to think about M-estimates is a weighted means. Most of the time, we have $\\psi(0)=0$ and $\\psi'(0)$ exists so that $\\psi$ is approximately linear at the origin. Using the following definition:\n", "\n", "\n", "$$W(x) = \\begin{cases}\n", " \\psi(x)/x & \\text{if} \\: x \\neq 0 \\\\\n", " \\psi'(x) & \\text{if} \\: x =0 \n", " \\end{cases}\n", "$$\n", "\n", "We can write our earlier equation as follows:\n", "\n", "$$\\sum W(x_i-\\hat{\\mu})(x_i-\\hat{\\mu}) = 0$$\n", "\n", "Solving this for $\\hat{\\mu}$ yields the following,\n", "\n", "$$\\hat{\\mu} = \\frac{\\sum w_{i} x_i}{\\sum w_{i}}$$\n", "\n", "where $w_{i}=W(x_i-\\hat{\\mu})$. The question that remains is how to pick the $\\psi$ functions." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Huber functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The family of Huber function is defined by the following:\n", "\n", "$$\\rho_k(x ) = \\begin{cases}\n", " x^2 & \\text{if} \\: |x|\\le k \\\\\n", " 2 k |x|-k^2 & \\text{if} \\: |x| \\gt k\n", " \\end{cases}\n", "$$\n", "\n", "with corresponding derivatives $2\\psi_k(x)$ with\n", "\n", "$$\\psi_k(x ) = \\begin{cases}\n", " x & \\text{if} \\: |x|\\le k \\\\\n", " \\text{sgn}(x)k & \\text{if} \\: |x| \\gt k\n", " \\end{cases}\n", "$$\n", "where the limiting cases $k \\rightarrow \\infty$ and $k \\rightarrow 0$ correspond to the mean and median, respectively. To see this, take $\\psi_{\\infty} = x$ and therefore $W(x) = 1$ and thus the defining equation results in\n", "\n", "$$\\sum_{i=1}^{n} (x_i-\\hat{\\mu}) = 0$$\n", "\n", "and then solving this leads to $\\hat{\\mu} = \\frac{1}{n}\\sum x_i$. Note that choosing $k=0$ leads to the sample median, but that is not so straightforward to solve for." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "colors=['b','r']\n", "for k in [1,2]:\n", " ax.plot(xi,np.ma.masked_array(xi,abs(xi)>k),color=colors[k-1])\n", " ax.plot(xi,np.ma.masked_array(np.sign(xi)*k,abs(xi)" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $W$ function corresponding to Huber's $\\psi$ is the following:\n", "\n", "$$W_k(x) = \\min\\Big{\\lbrace} 1, \\frac{k}{|x|} \\Big{\\rbrace}$$\n", "\n", "which is plotted in the following cell for a few values of $k$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "ax.plot(xi,np.vstack([np.ones(xi.shape),2/abs(xi)]).min(axis=0),label='k=2')\n", "ax.plot(xi,np.vstack([np.ones(xi.shape),1/abs(xi)]).min(axis=0),label='k=1')\n", "ax.axis(ymax=1.1)\n", "ax.legend(loc=0)\n", "ax.set_title(\"Huber's weight function\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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MTiLMRIqxCCqP18cH+xqIdjlYNjvd6DgTIntSm0ugZWzVnbgCFs5KJSEmgo/2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\nXHuhrCEOpgNthznUpqEmzWRh2jyj4wg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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another alternative intuitive way to interpret the M-estimate is to rewrite the following:\n", "\n", "$$\\hat{\\mu} = \\hat{\\mu} +\\frac{1}{n}\\sum_i \\psi(x_i-\\hat{\\mu}) = \\frac{1}{n} \\sum_i \\zeta(x_i,\\hat{\\mu})$$\n", "\n", "which for the Huber family of functions takes on the form :\n", "\n", "$$\\zeta(x,\\mu) = \\begin{cases}\n", " \\mu - k & \\text{if} \\: x \\lt \\mu-k \\\\\n", " x & \\text{if} \\: \\mu-k \\le x \\le \\mu+k \\\\\n", " \\mu+k & \\text{if} \\: x \\gt \\mu \\\\\n", " \\end{cases}\n", "$$\n", "\n", "Thus, the interpretation here is that $\\hat{\\mu}$ is the average of the truncated pseudo-observations $\\zeta_i$ where the observations beyond a certain point are clipped at the $k$-offset of the $\\hat{\\mu}$. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Asymptotic variance" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sympy import mpmath, symbols, diff, Piecewise, sign, lambdify\n", "from sympy.stats import density, cdf, Normal\n", "from sympy.abc import k,x" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "eps = symbols('epsilon')\n", "lpdf=diff(cdf(Normal('x',0,1))(x)*(1-eps)+ eps*cdf(Normal('x',0,10))(x),x)\n", "p = Piecewise((x,abs(x)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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8991KZsyYyXfffcP48ROorKxgzpxZLFnyOlFRUaxZs4qZM8/p0HkIIYTovnrUoim7y/fy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\nt/ef/buVXG9/5mfuiY8LOFJ4UfYvcKFkJY1BsBb86siw6uy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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Computable Example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "nsamples = 500\n", "ncols = 300\n", "xs = np.array([dual_set[bias_coin_gen.next()].rvs() for i in range(ncols)*nsamples ]).reshape(nsamples,-1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "ax.hist(np.mean(xs,0),20,alpha=0.8,label = 'mean')\n", "ax.hist(np.median(xs,0),20,alpha=0.3,label ='median')\n", "ax.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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hDl5wcU/6K6k9Q1naw0ZGL2Ts0PoQTZfmWRyqUx1svaVMVqKUJAwfPBvKC7NnetFNSR1y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\nXZIkqT91FcohhCG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7eG57V7XFjrWgH7aiAVicxfIhlKG0eIiYbwsJ3xaS0QAWq43x4ycy/fCZDB8+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\nhJEtfgLLGpk4aQq/uPCXMtErDcrK8vf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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "def huber_estim(x,k=1,tol=1e-6):\n", " if x.ndim==2: # loop over columns\n", " out = [] \n", " for i in range(x.shape[1]):\n", " out.append(huber_estim(x[:,i],k=k)) # recurse \n", " return np.array(out)\n", " else:\n", " mu = median(x)\n", " mad = median(abs(x-mu))*1.4826 # follow MADN convention\n", " while True:\n", " mu_i=mean(minimum(maximum(mu-k*mad,x),mu+k*mad))\n", " if abs(mu-mu_i) < tol*mad: break\n", " mu = mu_i\n", " return mu_i" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "huber_est={k:huber_estim(xs,k) for k in [1,1.5,2,3]}\n", "huber_est[0] = np.median(xs,axis=0)\n", "huber_est[4] = np.mean(xs,axis=0)\n", "fig,ax=subplots()\n", "sns.violinplot(pd.DataFrame(huber_est),ax=ax)\n", "ax.set_xticklabels(['median','1','1.5','2','3','mean']);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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08UdoaWrCdn46knz2e13WuWnIeh333v/XhL5gGejoURePP/owWXoDF1rO3v04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\nXckFF16Mt/EgnUfPrNE6sJrWRHwc8rt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Lc3PLAlXoLUePPkKRr4hToeCsn3M6FCTuODz6\n2PEFrMxbHnjgIYqLS7ja/+bMB09wrf8NaqprOXDg7gWqzBv27NnHQw89wqtv9nPm/Py3j/zW9y4x\n5o/wsY/9oqeWcM1oaGjgrnXr8Z9/Myc3+pho/NJZnESc7ixtu1owwQzQ1bWXnp67iQzaxEPz7z5x\nHIfQ1R/h88HHfvbjed39uGXLNtZ0dhJ6awRnDl1rwTeGKC4u4dFHCydw6urq2b1nH2ciYaLJmT+r\npOPwZjTM5g2baG2d/prHfFJdXcPevd0MjlwgkYjN6jnh6Dgj/mvcc+S+vP59y3j88Sdpa1vOt/71\nErHY3OctXL46xutnBjn60KOeHkY60HOQ6NgIoRtX3S7ljoyeeZ36xqVZW1u8oIIZ4IMffIrqmjrC\n13447y7t2Nhl4oE+nnzi/Z4as1kIlmXx/id/kkQ4Tujc6KyeExuJELka4OiDD3tqQ4rFcOTe+4k5\nDuei4RmPvRSNEEwkuOe+BxahMm85ePAwiWScodHLszp+YPgCQN63ljOKior40IeeZTwQ5eXTN+b0\nXMdx+O4PrlBfX8cjjzy+QBVmx549+ygtK6f329941/0X/+GrOfNzZGSQ4PUr3JvFdewLLpgrKir5\n8NMfIREeJTp0ds7PdxIxIjdeoa19JUeO3D/zE/JAZ+c6NmzaTOjsKMnYzF9mgm8OUVpexgMPzHwt\nX75Zs6aTpiWNnIlEZjz2TCRMVUUFW7ZsX4TKvKWzcx11tQ30pwN3JgPDF1i1aq0nu2QXyl13GTZt\n2sSPTl2f00Swy9f8XLsR4NFHT864yIXbysrK6ek5SCIcJB7O7sTcxTJivwrAwYPZ+9JYcMEMsGNH\nF+s3bCYy8DrJ+Mwtm4nCA2+QjIX5qY98NCcXNZiv48eeJBlNzDjWHB+LEu0L8uD976Wy0r39lN1i\nWRY9h+7hWiw67aVT0WSSS7Eoe/cdKIiu2cl8Ph/7ew4wOt5HbIbfwUBomGB4hJ6eg4tUnXc8+OCj\nBEMx3jo/+6G3H792g8rKCvbvz43P68g97wHeCTiAlUefeNcxXv05EY0wevZ1du/pzmrvYOEkywSW\nZfHUTz4NyQSR/tlPBEtEx4kNnaF7/0FWr167gBV6z9q1nazp7CR8fmzaiRqht0coKi7i3nsLozdh\nKnv2dANwPnr7VvOlaISE47Bnb/dileU5e/fux3GSDI5MP/t4YPgClmWxe/feRarMOzZu3Exj4xJO\n24OzOj4YjvH2pREOHDjs+dZyRltbOxs2bWXkzR+TjGfv+u3FMPLWKZKxKA8dfTirr1uQwQypFZvu\nuec+osPnSURmN+M4cuMURUVFnDzx/gWuzpsevP9hEsEY0etTzzpOxpJErgTYu3d/zu0alU3LlrXS\n2tzC+WnGmc9FI9RUVdHZuW4RK/OWFSs6aGpqYWDkwm2PcRyHwdGLGLOx4OYrQLoHpucwl66O4Q9E\nZzz+rXPDJJMOPT25NRb/8EOPEA8FGTv3htulzJqTSDDy+svctW4DK1euzuprF2wwAzz66HFKSksJ\nXz8147Hx0BCxsSscPfqw564HXCzbt++koqqS8EX/lI9HesdxEknuOfyeRa7Me3bv66EvFiOYvLU7\nO+44XIlF6crBtdSzybIs9u8/wNj4DSLRqb/sjQcHCUfG2b//wCJX5x2Z/ZHPnJu5O/utt4doaWn2\n/C5bk61fv5H2jpUMnXoJZxZXNHjB6NuvEwuO8/B7H836axfuWQGora3lkYcfIz5+lXhw4LbHOY5D\n5MarVFRW8eCD2e2yyCXFxcX07D9E7HqQZPTWwIlc9tPYtJQ1awqrm38qXV2pbtcLU0wCuxSNEHcc\ndnUVXtfsZJlu/8HRqbuzB0cu4vMVsXNn12KW5SmtrctpbV3GmQvTL8gSDMW40udnz56enFtXwbIs\nHn/sBFH/KGPn53Z9uxucZJKhUy/R3rGKzZu3Zv31CzqYAd7zngeprKohcuPUbcdO44EbxAP9PH7s\nRM5sLbdQevYfwkk6tyzTmQjEiA2GufvgkZw7KSyEtrZ2mpc0cm6KceZzkTBV5RUYk1970c5Ha+ty\nli1rY3Dk4i2PpbqxL7FhwybXdkHyiq6ubnr7/ATDt7/u+9ylERwHdu7cvYiVZc/27btYtrydoVd/\n4PlW89i5N4n6Rzl+7MSCnO8KPpjLyso5/vhJ4sEB4oHrtzzuOA6R/teorWvg7rvvdaFCb+noWMnS\nlmYil98dzOErqZ/3ZWnlm1xnWRZ7ew5xNRZ9V3d2zEnNxu7a2513O23N17593fgD/bd0Z48HB4lE\nA+zbt9+lyrxj+/ZdOA5cuHz7tQTOXRylvq6Wjo7c3K3JsiyOHztBZHSYsfPeXabTSSYZfPX7LG/v\nYNu2O9+wYioFH8wAhw7dQ01tPdGB129pNcfH+0iEhjj++ElK5rmlXz6xLItDPYeJDYVJBFLf3h3H\nIXplnNVrC+s605lkAuVs5J1JYBciqW7s7u7CHTOdLDPbemhSd3amG3vHjl1ulOUpK1euoqa6ivOX\npg7mRDLJxd4xtm7bldM9Vjt37mbZ8nYGX/m+Z1vNo2+/QXRshJPHn1iwz1rBTGrs9NhjjxMPDpKY\nNNYcHXyTmtqGnLkmcDFkWsWZ7uz4aJS4P8rBnsMuVuU9ra1trFjextkJ48xnI2Hqa2oLejb2ZK2t\nbbQ0t76rO9txHIZGL7N+vbqxIXXd9+bN27jY659yyO3a9QDRWCLnF6vx+XycPP4E0bFhRt/23gxt\nJ5Fg6JV/p71j5YK1lkHBfFNPz92UV1QRGXrr5n2J0DDx4ADvfejhglwE4naWLm2iY9UqIr2pPXUj\nveNYlkVX1x6XK/OenkP3MBCPMZKIE0omuRKL0t1zqKBnY09lX/d+xgL9RGOp7uxAaIhwdJy9e/e5\nXJl3bNy0lVA4Rv/QrStkXeodw7IsNmzY6EJl2bVjRxfL2zsYevX7OFNc1eCm0bOniY6PcfL4kwva\nM6GzQ1ppaSmH7z5C3H/t5mpg0ZFzFBWXcODAIZer857uvT3ERyOpSV99QTrXraO6usbtsjwnMzv7\nfCTCxWgEB9izV2Omk2U+p8H02tmDI5fwWT527Cjc2diTbdiwCUhtUDHZ5Wt+VrS350XvgmVZPHHi\nfUT9o4yefd3tcm5KJuIMvvoDOlatWfCeCQXzBKkl/xxiY1dwnCRxfy87tu/Ki3/s2bZ16w4Awlf8\nxP1Rdu1Qa3kqS5Y00rG8nUvRCJeiERpqc3dyzkJavryNxsZmhkevADA0doXOTpO3+y7Px5IljTQ2\nNnDl2rvXEYjHk1y7EWD9hs0uVZZ9W7dup2PVmtRY8zRL2y6m0TOniQX8PHHifQs+jq9gnqCtrZ0l\njc3Ex6+RCA2RjEfYvVuBM5Vly1qprKm6uQrY+vW69Od2tuzYxfV4jKvxGJu37sjpyTkLxbIsdu3a\nxej4dQLhEULhUXZ1qbU8mTGb6O0bf9c4c19/gEQimVeX31mWxYnHnyAW8DN6dvbLJi+UZCLO0KmX\nWLWmk40bF/4LkIJ5ki2bt5AIDRIP9AOpFWnkVpZlsXZ1Jwl/jKLiYtrbO9wuybMyE72iySSdHt4b\n122bN2/FcZLcGHwbgI0bt7hckfcYs5FQOM7QyDsz/TMtaC/vuzwfmzdvZcXK1Qyeesn1VnOmtXzi\n8YWbiT2RgnmSNWvW4iRiJIID1NY1FPSazzPpWLEKJ5ZkaXOTJjNNY8WKjilvy7utXbsOy7IY9fdR\nUV7J8uVtbpfkOevWrQd4V3f2lT4/ra0teTfHI9VqPklsfIzRt90ba3YSCYZOvcTK1WsXpbUMCuZb\ntLYuByAZ89PW1u5yNd7W1NQMwJL6JS5X4m319Q03v2U3N7e4XI13VVRU0LikiUh0nI6OVeryn0Jz\ncwu1tTVcTgdzMulw9XqA9evzs3dhy5btqRnar/3IteuaR8+9SSzg5/HHFmaVr6komCdpbEwtkOHE\nwyxr0Ul0OpndfiorCm/f5bnw+XyUFhdjWZYmEs5geVsbiWSM9hW5tQnDYrEsC2M23hxnvj4QIBZL\nYEx+DrlZlsWxRx8nOjaM/+KZRX9/J5lk+LWXaG1bwZYt2xbtfRXMk9TWprqunWSC+vrC3EVqtior\nU4FcVKRrvGdSVFRMkVqAM2poSPW+LF261OVKvGv9+o2MB6KM+iP09qUW+Vm3Lr/GlyfauXM3jc0t\nDL32w2n3gl8I45fPERkd5rFHji1qD46CeZKioiJKS8sB8m7MJtsygazx5ZlZlgUK5hmVlZUBqGdh\nGp2dqRDu7Runt89P45KGvG5E+Hw+Hj76COHBG4Su9y7qew+d/hH1SxpvXme/WHRGnUJp+uRQVaVr\nKKeTyRmNBc6CBRb6nGZSVORL/6kNPm6nra2d0tISrt0IcO1GkM7O9W6XtOC6uw9QUVXF0OkfLdp7\nhvr7CN24ytEHHlr0xsec+yCNMRXAl4EmwA88bdv2wKRjPgG8L/3j/7Ft+9fvtNDFVFZWxrifgt/i\ncWYKmtmz9HHNwjtf8vRh3Y7P52Nlx0quXb9KIBhl9ZpOt0tacKWlpdx35H6+/vX/TdQ/QmlN/YK/\n5/AbL1NaVs6BA4cX/L0mm8/XgOeBV2zbPgR8CfjMxAeNMWuADwLdtm3vA+43xuTUlMGSklIAysvL\nXa7E29RQnr2y0lKttz4rqX9U+rc1vRUda25ey1wol+AdPnwvluVjxD614O8VDwXxXzjDgZ5DrjTQ\n5nOm6AF+J337ReCzkx6/BDxg23ZmlL4EuHXVdQ8rSZ9Ay8oUzNNZ5HkYOe0XP/krxOO33+ReUhTI\ns9Paupx4InX50LJly12uZnE0NCxh2/adnHr9NEu3d+NbwC+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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "huber_est={k:huber_estim(xs,k) for k in kvals}\n", "huber_est_df = pd.DataFrame(huber_est)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "sns.violinplot(huber_est_df,ax=ax)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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BIr4mTWFQMpkkuboGbuvSOgges+kwiEkiKDYrsaiVX4Z1gZbJY97oVbe+jHbb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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig2,ax=subplots()\n", "ax.plot(kvals,[case2(k,pct_mixed) for k in kvals],'-o',label='eps=0.1')\n", "(huber_est_df.var()*nsamples).plot(marker='o',label='est eps=0.1',ax=ax)\n", "ax.set_xlabel(\"k\")\n", "ax.set_ylabel(\"asymptotic variance\")\n", "ax.legend(loc=0)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 21, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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8HctruFPIrVrrZ5RSAcAeYBGwFvidqcmEEEIAvt2Vvi+3ildXH6Kh2U7mwBi+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\nmV2G02UQEWJj6lV9mTwqmbDgnjeDnOz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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Maronna, R. A., R. D. Martin, and V. J. Yohai. \"Robust Statistics: Theory and Methods\". 2006." ] } ], "metadata": {} } ] }