B ¤ŠãZ‡ ã@sˆdZddlmZmZddlZddlmZddl m Z ddl m Z e  d¡dejfd d „ZGd d „d eƒZeƒZGd d„deƒZeƒZdS)zò 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. é)ÚcallableÚrangeN)Únormé)Únorms)Útoolsgè?cCs<t |¡}t|ƒr t |||¡}tjt ||¡||dS)a¤ 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` )Úaxis)ÚnpÚasarrayrZapply_over_axesÚmedianÚfabs)ÚaÚcrÚcenter©rú7lib/python3.7/site-packages/statsmodels/robust/scale.pyÚmads rc@s,eZdZdZd dd„Zdd d „Zd d „ZdS)ÚHubera. 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)) çø?ç:Œ0âŽyE>éNcCsV||_||_||_||_dt |¡d}||dd|d|t |¡|_dS)Nér)rÚmaxiterÚtolrÚGaussianÚcdfZpdfÚgamma)ÚselfrrrrZtmprrrÚ__init__Ns zHuber.__init__rcCs”t |¡}|dkr4|jdd}tj||d}d}n|jd}|}d}|dkr\t||d}n|}t |||j¡}t |||j¡}| ||||||¡S)a0 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) Nrr)rTF)r r Úshaper rrÚ unsqueezeÚ_estimate_both)rr ÚmuZ initscalerÚnÚest_muÚscalerrrÚ__call__Vs  zHuber.__call__c Cs‚xlt|jƒD]\}|rt|jdkrVt |||j|||j|¡ |¡|j|}q|t  |||j|||j|j ¡}n|  ¡}t   |||j¡}t t |||¡|j¡} |  |¡} t t | ||d|¡||j|j|| |jd¡} t   | ||j¡} t t t || ¡| |j ¡¡} t t t ||¡| |j ¡¡} | rR| s\|}| }q|  ¡|   ¡fSqWtd|jƒ‚dS)ad 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 NrzJjoint estimation of location and scale failed to converge in %d iterations)rrrr ZcliprÚsumrrZestimate_locationrZsqueezerr Z less_equalr ÚsqrtrZalltrueÚ ValueError)rr r%r"rr$r#Ú_ZnmuÚsubsetZcardÚnscaleZtest1Ztest2rrrr!ƒs,  " &" zHuber._estimate_both)rrrN)NNr)Ú__name__Ú __module__Ú __qualname__Ú__doc__rr&r!rrrrr/s  -rc@s"eZdZdZd dd„Zdd„Zd S) Ú HuberScalea¤ 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) ç@ç:Œ0âŽyE>rcCs||_||_||_dS)N)Údrr)rr4rrrrrrÔszHuberScale.__init__c s||ˆjddˆjdt ˆj¡dˆjt dtj¡t dˆjd¡}tˆƒ}‡‡fdd„‰‡‡‡fdd„}tj|g}d}xpt  ||d||¡ˆj krþ|ˆj krþt d||t  ||dƒ¡|dd¡} |  | ¡|d7}qW|dS) Nrrgà?gà¿cst t ˆ|¡ˆj¡S)N)r Zlessr r4)Úx)ÚresidrrrÚÞsz%HuberScale.__call__..cs2ˆ|ƒˆ|dddˆ|ƒˆjddS)Nrr)r4)Ús)r6rr+rrr7ßséÿÿÿÿ)r4rrr r(ZpiZexprÚinfÚabsrrr'Úappend) rZdf_residZnobsr6Úhr8ZchiZ scalehistZniterr,r)r6rr+rr&Ùs: "    zHuberScale.__call__N)r2r3r)r-r.r/r0rr&rrrrr1±s" r1)r0Zstatsmodels.compat.pythonrrZnumpyr Z scipy.statsrrÚrZstatsmodels.toolsrZppfr rÚobjectrZhuberr1Z hubers_scalerrrrÚ s   ;