M/PhaddlZdZGddZGddeZGddeZGd d eZGd d eZGd deZGddeZ GddeZ GddeZ ddZ dS)Nc.|jdkdzdz }||zS)zabsolute value function that changes complex sign based on real sign This could be useful for complex step derivatives of functions that need abs. Not yet used. r)real)xsigns X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/robust/norms.py_cabsr s" FaK1 q D !8Oc0eZdZdZdZdZdZdZdZdS) RobustNormaZ The parent class for the norms used for robust regression. Lays out the methods expected of the robust norms to be used by statsmodels.RLM. See Also -------- statsmodels.rlm Notes ----- Currently only M-estimators are available. References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York, 1981. DC Montgomery, EA Peck. 'Introduction to Linear Regression Analysis', John Wiley and Sons, Inc., New York, 2001. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. ct)z| The robust criterion estimator function. Abstract method: -2 loglike used in M-estimator NotImplementedErrorselfzs r rhozRobustNorm.rho* "!r ct)z Derivative of rho. Sometimes referred to as the influence function. Abstract method: psi = rho' rrs r psizRobustNorm.psi4rr ct)z_ Returns the value of psi(z) / z Abstract method: psi(z) / z rrs r weightszRobustNorm.weights>rr ct)z Derivative of psi. Used to obtain robust covariance matrix. See statsmodels.rlm for more information. Abstract method: psi_derive = psi' rrs r psi_derivzRobustNorm.psi_derivHs "!r c,||SzH Returns the value of estimator rho applied to an input rrs r __call__zRobustNorm.__call__Txx{{r N) __name__ __module__ __qualname____doc__rrrrrr r r r si2""""""""" " " "r r c*eZdZdZdZdZdZdZdS) LeastSquaresz Least squares rho for M-estimation and its derived functions. See Also -------- statsmodels.robust.norms.RobustNorm c|dzdzS)z The least squares estimator rho function Parameters ---------- z : ndarray 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 r?r%rs r rzLeastSquares.rhods!tczr c*tj|S)a  The psi function for the least squares estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z )npasarrayrs r rzLeastSquares.psius"z!}}r crtj|}tj|jtjS)a@ The least squares estimator weighting function for the IRLS algorithm. The psi function scaled by the input z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = np.ones(z.shape) )r+r,onesshapefloat64rs r rzLeastSquares.weightss'" JqMMwqw +++r cJtj|jtjS)z The derivative of the least squares psi function. Returns ------- psi_deriv : ndarray ones(z.shape) Notes ----- Used to estimate the robust covariance matrix. )r+r.r/r0rs r rzLeastSquares.psi_derivswqw +++r N)r!r"r#r$rrrrr%r r r'r'[sZ"&,,,( , , , , ,r r'c8eZdZdZd dZdZdZdZdZdZ d S) HuberTz Huber's T for M estimation. Parameters ---------- t : float, optional The tuning constant for Huber's t function. The default value is 1.345. See Also -------- statsmodels.robust.norms.RobustNorm Q?c||_dSN)t)rr7s r __init__zHuberT.__init__ r ctj|}tjtj||jS)zE Huber's T is defined piecewise over the range for z )r+r, less_equalabsr7rs r _subsetzHuberT._subsets- JqMM}RVAYY///r ctj|}||}|dz|dzzd|z tj||jzd|jdzzz zzS)a8 The robust criterion function for Huber's t. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = .5*z**2 for \|z\| <= t rho(z) = \|z\|*t - .5*t**2 for \|z\| > t r)rr)r+r,r=r<r7rrtests r rz HuberT.rhosf JqMM||As QT!TbfQii$&03?BCD Er ctj|}||}||zd|z |jztj|zzS)aE The psi function for Huber's t estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= t psi(z) = sign(z)*t for \|z\| > t r)r+r,r=r7rr?s r rz HuberT.psisG$ JqMM||Aax1t8tv- :::r ctj|}tj|}||}tj|}d||<|d|z |jz|z z}|r|d}|S)aa Huber's t weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= t weights(z) = t/\|z\| for \|z\| > t ?rr)r+isscalar atleast_1dr=r<r7)rr z_isscalarr@abszvs r rzHuberT.weightssu$[^^ M!  ||AvayyT AH&- -  !Ar ctjtj||jt S)z The derivative of Huber's t psi function Notes ----- Used to estimate the robust covariance matrix. )r+r;r<r7astypefloatrs r rzHuberT.psi_derivs.}RVAYY//66u===r N)r4 r!r"r#r$r8r=rrrrr%r r r3r3s  000EEE*;;;,<>>>>>r r3c2eZdZdZd dZdZdZdZdZdS) RamsayEz Ramsay's Ea for M estimation. Parameters ---------- a : float, optional The tuning constant for Ramsay's Ea function. The default value is 0.3. See Also -------- statsmodels.robust.norms.RobustNorm 333333?c||_dSr6arrRs r r8zRamsayE.__init__)r9r ctj|}dtj|j tj|zd|jtj|zzzz |jdzz S)a  The robust criterion function for Ramsay's Ea. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = a**-2 * (1 - exp(-a*\|z\|)*(1 + a*\|z\|)) rrr+r,exprRr<rs r rz RamsayE.rho,se JqMMBFDF7RVAYY.//TVbfQii'')),0FAI6 6r ctj|}|tj|j tj|zzS)a The psi function for Ramsay's Ea estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*exp(-a*\|z\|) rUrs r rz RamsayE.psi>s7 JqMM2646'BF1II-....r ctj|}tj|j tj|zS)a" Ramsay's Ea weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = exp(-a*\|z\|) rUrs r rzRamsayE.weightsQs2" JqMMvtvgq )***r c|j}tj| tj|z}| |ztj|z}|}d}||z||zzS)z The derivative of Ramsay's Ea psi function. Notes ----- Used to estimate the robust covariance matrix. r)rRr+rVr<r)rrrRrdxydys r rzRamsayE.psi_derives\ F FA2q > " "R!Vbgajj   2vBr N)rO) r!r"r#r$r8rrrrr%r r rNrNsn  666$///&+++(     r rNc8eZdZdZd dZdZdZdZdZdZ d S) AndrewWavea Andrew's wave for M estimation. Parameters ---------- a : float, optional The tuning constant for Andrew's Wave function. The default value is 1.339. See Also -------- statsmodels.robust.norms.RobustNorm Cl?c||_dSr6rQrSs r r8zAndrewWave.__init__r9r ctj|}tjtj||jtjzS)zI Andrew's wave is defined piecewise over the range of z. )r+r,r;r<rRpirs r r=zAndrewWave._subsets3 JqMM}RVAYY777r c|j}tj|}||}||dzzdtj||z z zd|z |dzzdzzS)a{ The robust criterion function for Andrew's wave. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray The elements of rho are defined as: .. math:: rho(z) & = a^2 *(1-cos(z/a)), |z| \leq a\pi \\ rho(z) & = 2a, |z|>q\pi rr)rRr+r,r=cosrrrRr@s r rzAndrewWave.rhosg( F JqMM||Aq!t q26!a%==01TQT!A%& 'r c|j}tj|}||}||ztj||z zS)aR The psi function for Andrew's wave The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = a * sin(z/a) for \|z\| <= a*pi psi(z) = 0 for \|z\| > a*pi )rRr+r,r=sinres r rzAndrewWave.psisB& F JqMM||Aax"&Q--''r c|j}tj|}||}||z }tj|tjtjjk}tj|rCtj |}|}||}||tj |z|z ||<n|tj |z|z }|S)a} Andrew's wave weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = sin(z/a) / (z/a) for \|z\| <= a*pi weights(z) = 0 for \|z\| > a*pi ) rRr+r,r=r<finfodoubleepsany ones_likerg)rrrRr@ratiosmallrlarges r rzAndrewWave.weightss$ F JqMM||AAu  3 3 77 6%== 3l5))GFE%LE!%[26%==85@GENNRVE]]*U2Gr cj||}|tj||jz zS)z The derivative of Andrew's wave psi function Notes ----- Used to estimate the robust covariance matrix. )r=r+rdrRr?s r rzAndrewWave.psi_derivs.||AbfQZ((((r N)r_rLr%r r r^r^us~  888'''4(((0@ ) ) ) ) )r r^c8eZdZdZd dZdZdZdZdZdZ d S) TrimmedMeana Trimmed mean function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Ramsay's Ea function. The default value is 2.0. See Also -------- statsmodels.robust.norms.RobustNorm @c||_dSr6crrws r r8zTrimmedMean.__init__r9r ctj|}tjtj||jS)zN Least trimmed mean is defined piecewise over the range of z. )r+r,r;r<rwrs r r=zTrimmedMean._subsets- JqMM}RVAYY///r ctj|}||}||dzzdzd|z |jdzzdzzS)aA The robust criterion function for least trimmed mean. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 for \|z\| <= c rho(z) = (1/2.)*c**2 for \|z\| > c rr)rr+r,r=rwr?s r rzTrimmedMean.rhosL" JqMM||Aad{S AH #9C#???r c^tj|}||}||zS)aQ The psi function for least trimmed mean The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= c psi(z) = 0 for \|z\| > c r+r,r=r?s r rzTrimmedMean.psis)$ JqMM||Aaxr cXtj|}||}|S)an Least trimmed mean weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= c weights(z) = 0 for \|z\| > c r}r?s r rzTrimmedMean.weights2s%$ JqMM||A r c0||}|S)z The derivative of least trimmed mean psi function Notes ----- Used to estimate the robust covariance matrix. )r=r?s r rzTrimmedMean.psi_derivHs||A r N)rtrLr%r r rsrss  000@@@*,,     r rsc8eZdZdZd dZdZdZdZd Zd Z d S) Hampela; Hampel function for M-estimation. Parameters ---------- a : float, optional b : float, optional c : float, optional The tuning constants for Hampel's function. The default values are a,b,c = 2, 4, 8. See Also -------- statsmodels.robust.norms.RobustNorm rt@ @c0||_||_||_dSr6)rRbrw)rrRrrws r r8zHampel.__init__fsr c`tjtj|}tj||j}tj||jtj||jz}tj||jtj||jz}|||fS)zL Hampel's function is defined piecewise over the range of z )r+r<r,r;rRrgreaterrw)rrt1t2t3s r r=zHampel._subsetks F2:a== ! ! ]1df % % ]1df % % 1df(=(= = ]1df % % 1df(=(= =2rzr c&|j|j|j}}}tj|}tj|}||\}}}||z} tj|jd} tj |j | } tj |}||dzdz| |<|||z|dzdzz | |<||||z dzz||z z dz| |<| | xx|||z|z zdzz cc<|r| d} | S)a The robust criterion function for Hampel's estimator Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = z**2 / 2 for \|z\| <= a rho(z) = a*\|z\| - 1/2.*a**2 for a < \|z\| <= b rho(z) = a*(c - \|z\|)**2 / (c - b) / 2 for b < \|z\| <= c rho(z) = a*(b + c - a) / 2 for \|z\| > c rKdtyperr)gr rRrrwr+rDrEr= promote_typesrzerosr/r<) rrrRrrwrFrrrt34dtrHs r rz Hampel.rhous"(&$&$&a1[^^ M!  \\!__ BRj  agw / / HQWB ' ' ' F1II"q3"QrUQTCZ'"Q2YN"a!e,5" #!q1uqy/C''  !Ar c|j|j|j}}}tj|}tj|}||\}}}tj|jd} tj |j | } tj |} tj |} ||| |<|| |z| |<|| |z|| |z z||z z | |<|r| d} | S)a The psi function for Hampel's estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= a psi(z) = a*sign(z) for a < \|z\| <= b psi(z) = a*sign(z)*(c - \|z\|)/(c-b) for b < \|z\| <= c psi(z) = 0 for \|z\| > c rKrr rRrrwr+rDrEr=rrrr/rr<) rrrRrrwrFrrrrrHszas r rz Hampel.psis,&$&$&a1[^^ M!  \\!__ B  agw / / HQWB ' ' ' GAJJ VAYY""AbE "AbE QBZ(AE2"  !Ar c|j|j|j}}}tj|}tj|}||\}}}tj|jd} tj |j | } d| |<tj |} || |z | |<| |} ||| z z| ||z zz | |<|r| d} | S)a$ Hampel weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= a weights(z) = a/\|z\| for a < \|z\| <= b weights(z) = a*(c - \|z\|)/(\|z\|*(c-b)) for b < \|z\| <= c weights(z) = 0 for \|z\| > c rKrrCrr) rrrRrrwrFrrrrrHabs_zabs_zt3s r rzHampel.weightss,&$&$&a1[^^ M!  \\!__ B  agw / / HQWB ' ' '"q E"I ")Q[!WA%67"  !Ar c|j|j|j}}}tj|}tj|}||\}}}tj|jd} tj |j | } d| |<||} |tj | z| z tj | ||z zz | |<|r| d} | S)zGDerivative of psi function, second derivative of rho function. rKrrCrr) rrrRrrwrFr_rrdzt3s r rzHampel.psi_derivs&$&$&a1[^^ M!  LLOO Ar  agw / / HQWB ' ' '"ebgcll"S()RVC[[AE-BC"  !Ar N)rtrrrLr%r r rrTs" '''R'''R'''Rr rc8eZdZdZd dZdZdZdZdZdZ d S) TukeyBiweighta Tukey's biweight function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Tukey's Biweight. The default value is c = 4.685. Notes ----- Tukey's biweight is sometime's called bisquare. = ףp@c||_dSr6rvrxs r r8zTukeyBiweight.__init__r9r ctjtj|}tj||jS)zK Tukey's biweight is defined piecewise over the range of z )r+r<r,r;rwrs r r=zTukeyBiweight._subsets/ F2:a== ! !}Q'''r c||}|jdzdz }d||jz dzz dz |z|z|zS)a^ The robust criterion function for Tukey's biweight estimator Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = -(1 - (z/c)**2)**3 * c**2/6. for \|z\| <= R rho(z) = 0 for \|z\| > R rg@rr=rw)rrsubsetfactors r rzTukeyBiweight.rhosN aRa$&j1_$q((61F:VCCr ctj|}||}|d||jz dzz dzz|zS)ar The psi function for Tukey's biweight estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*(1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R rrr{rrrs r rzTukeyBiweight.psi3sD& JqMMaATVa'!++f44r cX||}d||jz dzz dz|zS)a~ Tukey's biweight weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray psi(z) = (1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R rrrrs r rzTukeyBiweight.weightsJs2&aQZ!O#a'&00r c||}|d||jz dzz dzd|dzz|jdzz d||jz dzz zz zS)z The derivative of Tukey's biweight psi function Notes ----- Used to estimate the robust covariance matrix. rrrrs r rzTukeyBiweight.psi_deriv`sga!qx!m+a/adF4619,AdfHq=ABC Cr N)rrLr%r r rrs  (((DDD(555.111, C C C C Cr rc<eZdZdZdZdZdZdZdZdZ dZ d S) MQuantileNormuM-quantiles objective function based on a base norm This norm has the same asymmetric structure as the objective function in QuantileRegression but replaces the L1 absolute value by a chosen base norm. rho_q(u) = abs(q - I(q < 0)) * rho_base(u) or, equivalently, rho_q(u) = q * rho_base(u) if u >= 0 rho_q(u) = (1 - q) * rho_base(u) if u < 0 Parameters ---------- q : float M-quantile, must be between 0 and 1 base_norm : RobustNorm instance basic norm that is transformed into an asymmetric M-quantile norm Notes ----- This is mainly for base norms that are not redescending, like HuberT or LeastSquares. (See Jones for the relationship of M-quantiles to quantiles in the case of non-redescending Norms.) Expectiles are M-quantiles with the LeastSquares as base norm. References ---------- .. [*] Bianchi, Annamaria, and Nicola Salvati. 2015. “Asymptotic Properties and Variance Estimators of the M-Quantile Regression Coefficients Estimators.” Communications in Statistics - Theory and Methods 44 (11): 2416–29. doi:10.1080/03610926.2013.791375. .. [*] Breckling, Jens, and Ray Chambers. 1988. “M-Quantiles.” Biometrika 75 (4): 761–71. doi:10.2307/2336317. .. [*] Jones, M. C. 1994. “Expectiles and M-Quantiles Are Quantiles.” Statistics & Probability Letters 20 (2): 149–53. doi:10.1016/0167-7152(94)90031-0. .. [*] Newey, Whitney K., and James L. Powell. 1987. “Asymmetric Least Squares Estimation and Testing.” Econometrica 55 (4): 819–47. doi:10.2307/1911031. c"||_||_dSr6)q base_norm)rrrs r r8zMQuantileNorm.__init__s"r ct|}|dk}tj|}d|jz ||<|j||<|S)Nrr)lenr+emptyr)rrnobsmask_negqqs r _get_qzMQuantileNorm._get_qsD1vvE Xd^^46z8 H9  r cf||}||j|zS)z The robust criterion function for MQuantileNorm. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray )rrrrrrs r rzMQuantileNorm.rhos.[[^^DN&&q))))r cf||}||j|zS)z The psi function for MQuantileNorm estimator. The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray )rrrrs r rzMQuantileNorm.psis.[[^^DN&&q))))r cf||}||j|zS)a  MQuantileNorm weighting function for the IRLS algorithm The psi function scaled by z, psi(z) / z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray )rrrrs r rzMQuantileNorm.weightss.[[^^DN**1----r cf||}||j|zS)a The derivative of MQuantileNorm function Parameters ---------- z : array_like 1d array Returns ------- psi_deriv : ndarray Notes ----- Used to estimate the robust covariance matrix. )rrrrs r rzMQuantileNorm.psi_derivs."[[^^DN,,Q////r c,||Srrrs r rzMQuantileNorm.__call__r r N) r!r"r#r$r8rrrrrrr%r r rrms//b###*** ***$...$000(r rư>c |t}|tj||}n|}t|D]}|||z |z } tj| |z|tj| |z } tjtjtj|| z ||zr| cS| }td|z)a M-estimator of location using self.norm and a current estimator of scale. This iteratively finds a solution to norm.psi((a-mu)/scale).sum() == 0 Parameters ---------- a : ndarray Array over which the location parameter is to be estimated scale : ndarray Scale parameter to be used in M-estimator norm : RobustNorm, optional Robust norm used in the M-estimator. The default is HuberT(). axis : int, optional Axis along which to estimate the location parameter. The default is 0. initial : ndarray, optional Initial condition for the location parameter. Default is None, which uses the median of a. niter : int, optional Maximum number of iterations. The default is 30. tol : float, optional Toleration for convergence. The default is 1e-06. Returns ------- mu : ndarray Estimate of location Nz6location estimator failed to converge in %d iterations) r3r+medianrangersumalllessr< ValueError) rRscalenormaxisinitialmaxitertolmurWnmus r estimate_locationrsB |xx Yq$    7^^ LL!B$ & &fQqS$"&D//1 6"'"&c**ECK88 9 9 JJJBB M   r )NrNrr) numpyr+r r r'r3rNr^rsrrrrr%r r rs HHHHHHHHVN,N,N,N,N,:N,N,N,bj>j>j>j>j>Zj>j>j>\XXXXXjXXXvt)t)t)t)t)t)t)t)pddddd*dddNnnnnnZnnnbeCeCeCeCeCJeCeCeCPKKKKKJKKK\<@&-1 1 1 1 1 1 r