ó áp7]c@s¶dZddlmZddlZddlmZddlm Z ddl m Z ej dd ƒd ej d „Zd efd „ƒYZeƒZdefd„ƒYZeƒZdS(sò Support and standalone functions for Robust Linear Models References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York, 1981. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. iÿÿÿÿ(trangeN(tnormi(tnorms(ttoolsig@icCsWtj|ƒ}t|ƒr3tj|||ƒ}ntjtj||ƒ|d|ƒS(s¤ The Median Absolute Deviation along given axis of an array Parameters ---------- a : array-like Input array. c : float, optional The normalization constant. Defined as scipy.stats.norm.ppf(3/4.), which is approximately .6745. axis : int, optional The defaul is 0. Can also be None. center : callable or float If a callable is provided, such as the default `np.median` then it is expected to be called center(a). The axis argument will be applied via np.apply_over_axes. Otherwise, provide a float. Returns ------- mad : float `mad` = median(abs(`a` - center))/`c` taxis(tnptasarraytcallabletapply_over_axestmediantfabs(tatcRtcenter((s7lib/python2.7/site-packages/statsmodels/robust/scale.pytmads tHubercBs>eZdZddddd„Zdddd„Zd„ZRS( s. Huber's proposal 2 for estimating location and scale jointly. Parameters ---------- c : float, optional Threshold used in threshold for chi=psi**2. Default value is 1.5. tol : float, optional Tolerance for convergence. Default value is 1e-08. maxiter : int, optional0 Maximum number of iterations. Default value is 30. norm : statsmodels.robust.norms.RobustNorm, optional A robust norm used in M estimator of location. If None, the location estimator defaults to a one-step fixed point version of the M-estimator using Huber's T. call Return joint estimates of Huber's scale and location. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> chem_data = np.array([2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9, 3.03, ... 3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5, 3.6, 3.7, 3.7, 3.7, 3.7, ... 3.77, 5.28, 28.95]) >>> sm.robust.scale.huber(chem_data) (array(3.2054980819923693), array(0.67365260010478967)) gø?g:Œ0âŽyE>icCsm||_||_||_||_dtj|ƒd}||dd|d|tj|ƒ|_dS(Nii(R tmaxiterttolRtGaussiantcdftpdftgamma(tselfR RRRttmp((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyt__init__Os     icCsÖtj|ƒ}|dkrJ|jdd}tj|d|ƒ}t}n|jd}|}t}|dkr„t|d|ƒ}n|}tj |||jƒ}tj |||jƒ}|j ||||||ƒS(s0 Compute Huber's proposal 2 estimate of scale, using an optional initial value of scale and an optional estimate of mu. If mu is supplied, it is not reestimated. Parameters ---------- a : array 1d array mu : float or None, optional If the location mu is supplied then it is not reestimated. Default is None, which means that it is estimated. initscale : float or None, optional A first guess on scale. If initscale is None then the standardized median absolute deviation of a is used. Notes ----- `Huber` minimizes the function sum(psi((a[i]-mu)/scale)**2) as a function of (mu, scale), where psi(x) = np.clip(x, -self.c, self.c) iiRN( RRtNonetshapeR tTruetFalseRRt unsqueezet_estimate_both(RR tmut initscaleRtntest_mutscale((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyt__call__Ws    c Csxçt|jƒD]Ö}|rš|jdkrmtj|||j|||j|ƒj|ƒ|j|}q¦t j |||j|||j|j ƒ}n |j ƒ}t j|||jƒ}tjtj|||ƒ|jƒ} | j|ƒ} tjtj| ||d|ƒ||j|j|| |jdƒ} t j| ||jƒ} tjtjtj|| ƒ| |j ƒƒ} tjtjtj||ƒ| |j ƒƒ} | o¾| sÐ|}| }q|j ƒ| j ƒfSqWtd|jƒ‚dS(sd Estimate scale and location simultaneously with the following pseudo_loop: while not_converged: mu, scale = estimate_location(a, scale, mu), estimate_scale(a, scale, mu) where estimate_location is an M-estimator and estimate_scale implements the check used in Section 5.5 of Venables & Ripley isJjoint estimation of location and scale failed to converge in %d iterationsN(RRRRRtclipR tsumRRtestimate_locationRtsqueezeRRt less_equalR tsqrtRtalltruet ValueError(RR R#RRR"R!t_tnmutsubsettcardtnscalettest1ttest2((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyR„s, + &!+/  N(t__name__t __module__t__doc__RRR$R(((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyR0s-t HuberScalecBs)eZdZdddd„Zd„ZRS(s¦ Huber's scaling for fitting robust linear models. Huber's scale is intended to be used as the scale estimate in the IRLS algorithm and is slightly different than the `Huber` class. Parameters ---------- d : float, optional d is the tuning constant for Huber's scale. Default is 2.5 tol : float, optional The convergence tolerance maxiter : int, optiona The maximum number of iterations. The default is 30. Methods ------- call Return's Huber's scale computed as below Notes -------- Huber's scale is the iterative solution to scale_(i+1)**2 = 1/(n*h)*sum(chi(r/sigma_i)*sigma_i**2 where the Huber function is chi(x) = (x**2)/2 for \|x\| < d chi(x) = (d**2)/2 for \|x\| >= d and the Huber constant h = (n-p)/n*(d**2 + (1-d**2)*\ scipy.stats.norm.cdf(d) - .5 - d*sqrt(2*pi)*exp(-0.5*d**2) g@g:Œ0âŽyE>icCs||_||_||_dS(N(tdRR(RR8RR((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyRØs  c sJ||ˆjddˆjdtjˆjƒdˆjtjdtjƒtjdˆjdƒ}tˆƒ}‡‡fd†‰‡‡‡fd†}tj|g}d}xŒtj ||d||ƒˆj krA|ˆj krAtjd||tj ||dƒƒ|ddƒ} |j | ƒ|d7}q¶W|dS(Niigà?gà¿cs tjtjˆ|ƒˆjƒS(N(RtlessR R8(tx(tresidR(s7lib/python2.7/site-packages/statsmodels/robust/scale.pytâtcs7ˆ|ƒˆ|dddˆ|ƒˆjddS(Nii(R8(ts(R;RR/(s7lib/python2.7/site-packages/statsmodels/robust/scale.pyR<ãR=iÿÿÿÿ(R8RRRR*tpitexpRtinftabsRRR&tappend( Rtdf_residtnobsR;thR>tchit scalehisttniterR1((R;RR/s7lib/python2.7/site-packages/statsmodels/robust/scale.pyR$ÝsG +( (R4R5R6RR$(((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyR7µs"(R6tstatsmodels.compat.pythonRtnumpyRt scipy.statsRRR=Rtstatsmodels.toolsRtppfR RtobjectRthuberR7t hubers_scale(((s7lib/python2.7/site-packages/statsmodels/robust/scale.pyt s "‚ <