o þ0Gf’aã@s°ddlZdd„ZGdd„dƒZGdd„deƒZGdd „d eƒZGd d „d eƒZGd d „d eƒZGdd„deƒZGdd„deƒZ Gdd„deƒZ Gdd„deƒZ  ddd„Z dS)éNcCs|jdkdd}||S)z®absolute 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. réé)Úreal)ÚxÚsign©rú8lib/python3.10/site-packages/statsmodels/robust/norms.pyÚ_cabssr c@s8eZdZdZdd„Zdd„Zdd„Zdd „Zd d „Zd S) Ú 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. cCót‚)z| The robust criterion estimator function. Abstract method: -2 loglike used in M-estimator ©ÚNotImplementedError©ÚselfÚzrrrÚrho*ózRobustNorm.rhocCr )z„ Derivative of rho. Sometimes referred to as the influence function. Abstract method: psi = rho' r rrrrÚpsi4rzRobustNorm.psicCr )z_ Returns the value of psi(z) / z Abstract method: psi(z) / z r rrrrÚweights>rzRobustNorm.weightscCr )z¶ Derivative of psi. Used to obtain robust covariance matrix. See statsmodels.rlm for more information. Abstract method: psi_derive = psi' r rrrrÚ psi_derivHs zRobustNorm.psi_derivcCó | |¡S©zH Returns the value of estimator rho applied to an input ©rrrrrÚ__call__Tó zRobustNorm.__call__N) Ú__name__Ú __module__Ú __qualname__Ú__doc__rrrrrrrrrr s   r c@s0eZdZdZdd„Zdd„Zdd„Zdd „Zd S) Ú LeastSquareszŠ Least squares rho for M-estimation and its derived functions. See Also -------- statsmodels.robust.norms.RobustNorm cCs |ddS)zâ The least squares estimator rho function Parameters ---------- z : ndarray 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 rçà?rrrrrrds zLeastSquares.rhocCs t |¡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 )ÚnpÚasarrayrrrrrus zLeastSquares.psicCst |¡}t |jtj¡S)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"ÚonesÚshapeÚfloat64rrrrrˆó zLeastSquares.weightscCst |jtj¡S)zî 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$r%rrrrrœs zLeastSquares.psi_derivN)rrrrrrrrrrrrr[s  rc@óBeZdZdZddd„Zdd„Zdd„Zd d „Zd d „Zd d„Z dS)ÚHuberTz÷ 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 ç…ëQ¸…õ?cCó ||_dS©N)Út)rr,rrrÚ__init__»ó zHuberT.__init__cCót |¡}t t |¡|j¡S)zE Huber's T is defined piecewise over the range for z )r!r"Ú less_equalÚabsr,rrrrÚ_subset¾s zHuberT._subsetcCsJt |¡}| |¡}|d|dd|t |¡|jd|jdS)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"r2r1r,©rrÚtestrrrrÅs  $ÿz HuberT.rhocCs4t |¡}| |¡}||d||jt |¡S)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"r2r,rr3rrrrÚs   z HuberT.psicCsVt |¡}t |¡}| |¡}t |¡}d||<|d||j|}|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 çð?rr)r!ÚisscalarÚ atleast_1dr2r1r,)rrÚ z_isscalarr4ZabszÚvrrrrðs    zHuberT.weightscCst t |¡|j¡ t¡S)zŽ The derivative of Huber's t psi function Notes ----- Used to estimate the robust covariance matrix. )r!r0r1r,ZastypeÚfloatrrrrrszHuberT.psi_derivN)r)© rrrrr-r2rrrrrrrrr(¬s  r(c@s:eZdZdZddd„Zdd„Zdd„Zd d „Zd d „Zd S)ÚRamsayEzú 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 ç333333Ó?cCr*r+©Úa©rr?rrrr-)r.zRamsayE.__init__cCsDt |¡}dt |j t |¡¡d|jt |¡|jdS)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\|)) rr©r!r"Úexpr?r1rrrrr,s ÿÿz RamsayE.rhocCs&t |¡}|t |j t |¡¡S)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\|) rArrrrr>s z RamsayE.psicCs"t |¡}t |j t |¡¡S)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\|) rArrrrrQs zRamsayE.weightscCsH|j}t | t |¡¡}| |t |¡}|}d}||||S)z‘ The derivative of Ramsay's Ea psi function. Notes ----- Used to estimate the robust covariance matrix. r)r?r!rBr1r)rrr?rZdxÚyZdyrrrres zRamsayE.psi_derivN)r=) rrrrr-rrrrrrrrr<s  r<c@r')Ú 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 ç•C‹lõ?cCr*r+r>r@rrrr-ƒr.zAndrewWave.__init__cCs$t |¡}t t |¡|jtj¡S)zI Andrew's wave is defined piecewise over the range of z. )r!r"r0r1r?Zpirrrrr2†s zAndrewWave._subsetcCsL|j}t |¡}| |¡}||ddt ||¡d||ddS)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)r?r!r"r2Úcos©rrr?r4rrrrs   ÿzAndrewWave.rhocCs0|j}t |¡}| |¡}||t ||¡S)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 )r?r!r"r2ÚsinrGrrrr§s  zAndrewWave.psicCs|j}t |¡}| |¡}||}t |¡t tj¡jk}t |¡r=t  |¡}|}||}||t  |¡|||<|S|t  |¡|}|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 ) r?r!r"r2r1ZfinfoZdoubleZepsÚanyZ ones_likerH)rrr?r4ZratioZsmallrZlargerrrr¿s    ÿzAndrewWave.weightscCs| |¡}|t ||j¡S)z’ The derivative of Andrew's wave psi function Notes ----- Used to estimate the robust covariance matrix. )r2r!rFr?r3rrrrßs zAndrewWave.psi_derivN)rEr;rrrrrDus  rDc@r')Ú 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 ç@cCr*r+©Úc©rrMrrrr-ür.zTrimmedMean.__init__cCr/)zN Least trimmed mean is defined piecewise over the range of z. )r!r"r0r1rMrrrrr2ÿs zTrimmedMean._subsetcCs:t |¡}| |¡}||ddd||jddS)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 r©r!r"r2rMr3rrrrs  &zTrimmedMean.rhocCst |¡}| |¡}||S)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"r2r3rrrrs  zTrimmedMean.psicCst |¡}| |¡}|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 rPr3rrrr2s  zTrimmedMean.weightscCs| |¡}|S)z— The derivative of least trimmed mean psi function Notes ----- Used to estimate the robust covariance matrix. )r2r3rrrrHs zTrimmedMean.psi_derivN)rKr;rrrrrJís  rJc@sBeZdZdZddd„Zdd„Zd d „Zd d „Zd d„Zdd„Z dS)ÚHampela; 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 rKç@ç @cCs||_||_||_dSr+)r?ÚbrM)rr?rTrMrrrr-fs zHampel.__init__cCs`t t |¡¡}t ||j¡}t ||j¡t ||j¡}t ||j¡t ||j¡}|||fS)zL Hampel's function is defined piecewise over the range of z )r!r1r"r0r?rTZgreaterrM)rrÚt1Út2Út3rrrr2ks  zHampel._subsetc Csð|j|j|j}}}t |¡}t |¡}| |¡\}}}||B} t |jd¡} tj |j | d} t  |¡}||dd| |<||||dd| |<||||d||d| |<| | ||||d7<|rv| d} | S)aí 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 r:©Údtyperr gà¿r© r?rTrMr!r6r7r2Ú promote_typesrYÚzerosr$r1) rrr?rTrMr8rUrVrWZt34Údtr9rrrrus    $ z Hampel.rhoc Cs¼|j|j|j}}}t |¡}t |¡}| |¡\}}}t |jd¡} tj |j | d} t  |¡} t  |¡} ||| |<|| || |<|| ||| |||| |<|r\| d} | S)aû 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 r:rXr© r?rTrMr!r6r7r2r[rYr\r$rr1) rrr?rTrMr8rUrVrWr]r9ÚsZzarrrržs     $z Hampel.psic Cs®|j|j|j}}}t |¡}t |¡}| |¡\}}}t |jd¡} tj |j | d} d| |<t  |¡} || || |<| |} ||| | ||| |<|rU| d} | S)a$ 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 r:rXr5rrZ) rrr?rTrMr8rUrVrWr]r9Zabs_zZabs_zt3rrrrÇs   zHampel.weightsc Cs¢|j|j|j}}}t |¡}t |¡}| |¡\}}}t |jd¡} tj |j | d} d| |<||} |t  | ¡|  t  | ¡||| |<|rO| d} | S)zGDerivative of psi function, second derivative of rho function. r:rXr5rr^) rrr?rTrMr8rUÚ_rWr]ÚdZzt3rrrrðs  *zHampel.psi_derivN)rKrRrSr;rrrrrQTs  )) )rQc@r')Ú 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. ç= ×£p½@cCr*r+rLrNrrrr-r.zTukeyBiweight.__init__cCst t |¡¡}t ||j¡S)zK Tukey's biweight is defined piecewise over the range of z )r!r1r"r0rMrrrrr2szTukeyBiweight._subsetcCs<| |¡}|jdd}d||jdd |||S)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@ré©r2rM)rrÚsubsetZfactorrrrrs $zTukeyBiweight.rhocCs2t |¡}| |¡}|d||jdd|S)ar The psi function for Tukey's biweight estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*(1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R rrrO©rrrfrrrr3s  zTukeyBiweight.psicCs$| |¡}d||jdd|S)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 rrrergrrrrJs zTukeyBiweight.weightscCsL| |¡}|d||jddd|d|jdd||jdS)z• The derivative of Tukey's biweight psi function Notes ----- Used to estimate the robust covariance matrix. rrérergrrrr`s &ÿzTukeyBiweight.psi_derivN)rcr;rrrrrbs  rbc@sHeZdZdZdd„Zdd„Zdd„Zdd „Zd d „Zd d „Z dd„Z dS)Ú MQuantileNormu•M-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. cCs||_||_dSr+)ÚqÚ base_norm)rrjrkrrrr-Ÿs zMQuantileNorm.__init__cCs8t|ƒ}|dk}t |¡}d|j||<|j||<|S)Nrr)Úlenr!Úemptyrj)rrZnobsZmask_negÚqqrrrÚ_get_q£s   zMQuantileNorm._get_qcCó| |¡}||j |¡S)zÌ The robust criterion function for MQuantileNorm. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray )rorkr©rrrnrrrr¬s zMQuantileNorm.rhocCrp)zñ The psi function for MQuantileNorm estimator. The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray )rorkrrqrrrr¼ó zMQuantileNorm.psicCrp)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 )rorkrrqrrrrÎrrzMQuantileNorm.weightscCrp)a The derivative of MQuantileNorm function Parameters ---------- z : array_like 1d array Returns ------- psi_deriv : ndarray Notes ----- Used to estimate the robust covariance matrix. )rorkrrqrrrràr&zMQuantileNorm.psi_derivcCrrrrrrrrôrzMQuantileNorm.__call__N) rrrrr-rorrrrrrrrrrims1  riéçíµ ÷Æ°>c Csœ|durtƒ}|durt ||¡}n|}t|ƒD]/}| |||¡} t | ||¡t | |¡} t t t || ¡||¡¡rE| S| }qt d|ƒ‚)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) r(r!ZmedianÚrangerÚsumÚallZlessr1Ú ValueError) r?ZscaleZnormZaxisÚinitialÚmaxiterZtolZmur`ÚWZnmurrrÚestimate_locationûs!  ÿr|)NrNrsrt) Znumpyr!r r rr(r<rDrJrQrbrir|rrrrÚs  KQn[xg2hÿ