M/Ph0dZddlZddlmZddlmZddlm Z m Z ddl m Z ddl m Z ejd dejfd Zejd ejd z dfd Zdejd ejdzz dfdZdejd ejdzz fdZGddZeZGddZeZdS)a 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. C Croux, PJ Rousseeuw, 'Time-efficient algorithms for two highly robust estimators of scale' Computational statistics. Physica, Heidelberg, 1992. N)norm)tools) array_like float_like)norms)_qn?c t|dd}t|d}|jsd}nVt|r7|t j|||}n.||}nt|d}t j||z |z }|jsV| |jdkr tj St|j }| |t j |St j||S) 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 0.6745. axis : int, optional The default 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` aNndimcgcenterraxis)rrsizecallablenpapply_over_axesravelabsrnanlistshapepopemptymedian)r rrr center_valerrrs X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/robust/scale.pymadr"s. 1c%%%A1cA 62 &  2  +FAt<>> 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)) ?:0yE>Nc||_||_||_||_dt j|zdz }||dzd|z zzd|zt j|zz |_dSNr-r)rmaxitertolrGaussiancdfpdfgamma)selfrrMrLrtmps r!__init__zHuber.__init__sh  (,q//!A%16QW--A Q0GG r#rcntj|}|)|jddz }tj||}d}n|jd}|}d}|t ||}n|}t j|||j}t j|||j}|||||||S)a2 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 : ndarray 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) NrrrTF)rasarrayrrr"r unsqueeze_estimate_both)rRr mu initscalerr?est_muscales r!__call__zHuber.__call__s6 JqMM : QA14(((BFF ABF  %%%EEEtQW55 _Rqw / /""1eRvqAAAr#c t|jD]*}|r|jNtj|||j|zz ||j|zz||j|z }n>tj |||j|||j|j }n| }tj |||j}tjtj||z |z |j} | |} tj| ||z dzz|} ||jz|j|| z |jdzzz } tj| | z } tj | ||j} tjtjtj|| z | |j z}tjtjtj||z | |j z}|r|s|}| }| | fcSt'd|jz)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 Nr-zJjoint estimation of location and scale failed to converge in %d iterations)rangerLrrcliprsumrrestimate_locationrMr)rrW less_equalrrQsqrtallr')rRr r\rYrr[r?_nmusubsetcard scale_num scale_denomnscaletest1test2s r!rXzHuber._estimate_boths;t|$$( 7( 7A #9$ rDFUN2B%4G#d))'$-(C 15$)T2t|TXCC jjll/#tQW55C]261r6U*:#;#;TVDDF::d##DvSQ6==Idj.AGDMD,@DFaK+OOKWY455F_VT17;;FF bfUV^44ftx6GHHEF bfR#X..0ABBE 7e 7{{}}fnn&6&66666 +-1\ :   r#)rGrHrIN)NNr)__name__ __module__ __qualname____doc__rTr]rXr#r!rFrFs^<HHHH+B+B+B+BZ7 7 7 7 7 r#rFc eZdZdZddZdZdS) HuberScalea Huber's scaling for fitting robust linear models. Huber's scale is intended to be used as the scale estimate in the IRLS algorithm and is slightly different than the `Huber` class. Parameters ---------- d : float, optional d is the tuning constant for Huber's scale. Default is 2.5 tol : float, optional The convergence tolerance maxiter : int, optiona The maximum number of iterations. The default is 30. Methods ------- call Return's Huber's scale computed as below Notes ----- Huber's scale is the iterative solution to scale_(i+1)**2 = 1/(n*h)*sum(chi(r/sigma_i)*sigma_i**2 where the Huber function is chi(x) = (x**2)/2 for \|x\| < d chi(x) = (d**2)/2 for \|x\| >= d and the Huber constant h = (n-p)/n*(d**2 + (1-d**2)* scipy.stats.norm.cdf(d) - .5 - d*sqrt(2*pi)*exp(-0.5*d**2) @rHrIc0||_||_||_dSN)drMrL)rRryrMrLs r!rTzHuberScale.__init__ds r#c * ||z jdzdjdzz tjjzzdz jtjdtjzz tjdjdzzzz z}t}fd  fd}tj|g}d}tj ||dz ||z j kr|j krtjd||zz tj ||dz|ddzz} | | |dz }tj ||dz ||z j kr |j k|dS)Nr-rg?gcbtjtj|z jSrx)rlessrry)xresidrRs r!rhz#HuberScale.__call__..subsetvs%726%!),,df55 5r#cl||z dzzdz d|z jdzdz zzSrK)ry)sr~rRrhs r!chiz HuberScale.__call__..chiysK6!99 a//!3q66!99}! a7 r#)ryrNrOrrdpiexpr"infrrMrLraappend) rRdf_residnobsr~r@rr scalehistniterrlrhs ` ` @r!r]zHuberScale.__call__is  ! tv{?hl46&:&::;&BGAI../"&! 9K2L2LLM   JJ 6 6 6 6 6 6        VQK  F9UQY')E*:: ; ;dh F F $$W!8&Yr]++,,-B-1$%F   V $ $ $ QJE F9UQY')E*:: ; ;dh F F $$}r#N)rvrHrI)rorprqrrrTr]rsr#r!ruru@sB!!F $$$$$r#ru)rrnumpyr scipy.statsrrNstatsmodels.toolsrstatsmodels.tools.validationrrrr ppfrr"r,rdr8rDrFhuberru hubers_scalersr#r!rs  ((((((######????????X\' " "29*%*%*%*%ZX\% <8<#6#6 6Q::::@wrwqzzLHL$7$778q''''T \X\%%8%889@K K K K K K K K \ MMMMMMMM`z|| r#