B ZvP@sddlmZddlZGdddeZGdddeZGdddeZGd d d eZGd d d eZ Gd ddeZ GdddeZ GdddeZ dddZ dS))rangeNc@s8eZdZdZddZddZddZdd Zd d Zd S) RobustNorma1 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. Parameters ---------- None : Some subclasses have optional tuning constants. 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. See Also -------- statsmodels.rlm for more information on how the estimators are used and the inputs for the methods of RobustNorm and subclasses. Notes ----- Currently only M-estimators are available. cCstdS)z| The robust criterion estimator function. Abstract method: -2 loglike used in M-estimator N)NotImplementedError)selfzr7lib/python3.7/site-packages/statsmodels/robust/norms.pyrho&szRobustNorm.rhocCstdS)z Derivative of rho. Sometimes referred to as the influence function. Abstract method: psi = rho' N)r)rrrrrpsi0szRobustNorm.psicCstdS)z_ Returns the value of psi(z) / z Abstract method: psi(z) / z N)r)rrrrrweights:szRobustNorm.weightscCstdS)z Deriative of psi. Used to obtain robust covariance matrix. See statsmodels.rlm for more information. Abstract method: psi_derive = psi' N)r)rrrrr psi_derivDs zRobustNorm.psi_derivcCs ||S)zH Returns the value of estimator rho applied to an input )r )rrrrr__call__PszRobustNorm.__call__N) __name__ __module__ __qualname____doc__r r r r r rrrrrs     rc@s0eZdZdZddZddZddZdd Zd S) LeastSquaresz Least squares rho for M-estimation and its derived functions. See also -------- statsmodels.robust.norms.RobustNorm for the methods. cCs |ddS)z The least squares estimator rho function Parameters ----------- z : array 1d array Returns ------- rho : array rho(z) = (1/2.)*z**2 g?r)rrrrrr `szLeastSquares.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 : array psi(z) = z )npasarray)rrrrrr qszLeastSquares.psicCst|}t|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 : array weights(z) = np.ones(z.shape) )rronesshapefloat64)rrrrrr s zLeastSquares.weightscCst|jtjS)z The derivative of the least squares psi function. Returns ------- psi_deriv : array ones(z.shape) Notes ----- Used to estimate the robust covariance matrix. )rrrr)rrrrrr s zLeastSquares.psi_derivN)rrrrr r r r rrrrrVs rc@sBeZdZdZdddZddZddZd d Zd d Zd dZ dS)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?cCs ||_dS)N)t)rrrrr__init__szHuberT.__init__cCst|}tt||jS)zE Huber's T is defined piecewise over the range for z )rr less_equalfabsr)rrrrr_subsets zHuberT._subsetcCsJt|}||}|d|dd|t||jd|jdS)a6 The robust criterion function for Huber's t. Parameters ---------- z : array-like 1d array Returns ------- rho : array rho(z) = .5*z**2 for \|z\| <= t rho(z) = \|z\|*t - .5*t**2 for \|z\| > t g?r)rrrrr)rrtestrrrr s  z HuberT.rhocCs4t|}||}||d||jt|S)aC The psi function for Huber's t estimator The analytic derivative of rho Parameters ---------- z : array-like 1d array Returns ------- psi : array psi(z) = z for \|z\| <= t psi(z) = sign(z)*t for \|z\| > t r )rrrrsign)rrr!rrrr s  z HuberT.psicCs<t|}||}t|}d||<|d||j|S)a_ Huber's t weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array-like 1d array Returns ------- weights : array weights(z) = 1 for \|z\| <= t weights(z) = t/\|z\| for \|z\| > t g?r )rrrrr)rrr!Zabszrrrr s    zHuberT.weightscCstt||jS)z The derivative of Huber's t psi function Notes ----- Used to estimate the robust covariance matrix. )rrrr)rrrrrr szHuberT.psi_derivN)r) rrrrrrr r r r rrrrrs  rc@s:eZdZdZdddZddZddZd d Zd d Zd S)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?cCs ||_dS)N)a)rr%rrrrszRamsayE.__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 : array rho(z) = a**-2 * (1 - exp(-a*\|z\|)*(1 + a*\|z\|)) r r)rrexpr%r)rrrrrr s z 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 : array psi(z) = z*exp(-a*\|z\|) )rrr&r%r)rrrrrr 2s 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 : array weights(z) = exp(-a*\|z\|) )rrr&r%r)rrrrrr Es zRamsayE.weightscCsJt|j t||dt|j t||j t|S)z The derivative of Ramsay's Ea psi function. Notes ----- Used to estimate the robust covariance matrix. r)rr&r%r)rrrrrr Ys zRamsayE.psi_derivN)r$) rrrrrr r r r rrrrr#s   r#c@sBeZdZdZdddZddZddZd d Zd d Zd dZ dS) AndrewWavea Andrew's wave for M estimation. Parameters ---------- a : float, optional The tuning constant for Andrew's Wave function. The default value is 1.339. See also -------- statsmodels.robust.norms.RobustNorm Cl?cCs ||_dS)N)r%)rr%rrrrtszAndrewWave.__init__cCs$t|}tt||jtjS)zI Andrew's wave is defined piecewise over the range of z. )rrrrr%Zpi)rrrrrrws zAndrewWave._subsetcCsD|j}t|}||}||dt||d|d|S)a> The robust criterion function for Andrew's wave. Parameters ---------- z : array-like 1d array Returns ------- rho : array rho(z) = a*(1-cos(z/a)) for \|z\| <= a*pi rho(z) = 2*a for \|z\| > a*pi r r)r%rrrcos)rrr%r!rrrr ~s   zAndrewWave.rhocCs,|j}t|}||}|t||S)aP The psi function for Andrew's wave The analytic derivative of rho Parameters ---------- z : array-like 1d array Returns ------- psi : array psi(z) = sin(z/a) for \|z\| <= a*pi psi(z) = 0 for \|z\| > a*pi )r%rrrsin)rrr%r!rrrr s  zAndrewWave.psicCs4|j}t|}||}|t||||S)aw Andrew's wave weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array-like 1d array Returns ------- weights : array weights(z) = sin(z/a)/(z/a) for \|z\| <= a*pi weights(z) = 0 for \|z\| > a*pi )r%rrrr*)rrr%r!rrrr s  zAndrewWave.weightscCs$||}|t||j|jS)z The derivative of Andrew's wave psi function Notes ----- Used to estimate the robust covariance matrix. )rrr)r%)rrr!rrrr s zAndrewWave.psi_derivN)r() rrrrrrr r r r rrrrr'es r'c@sBeZdZdZdddZddZddZd d Zd d Zd dZ dS) TrimmedMeana Trimmed mean function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Ramsay's Ea function. The default value is 2.0. See also -------- statsmodels.robust.norms.RobustNorm @cCs ||_dS)N)c)rr-rrrrszTrimmedMean.__init__cCst|}tt||jS)zN Least trimmed mean is defined piecewise over the range of z. )rrrrr-)rrrrrrs zTrimmedMean._subsetcCs$t|}||}||ddS)a5 The robust criterion function for least trimmed mean. Parameters ---------- z : array-like 1d array Returns ------- rho : array rho(z) = (1/2.)*z**2 for \|z\| <= c rho(z) = 0 for \|z\| > c rg?)rrr)rrr!rrrr s  zTrimmedMean.rhocCst|}||}||S)aP The psi function for least trimmed mean The analytic derivative of rho Parameters ---------- z : array-like 1d array Returns ------- psi : array psi(z) = z for \|z\| <= c psi(z) = 0 for \|z\| > c )rrr)rrr!rrrr s  zTrimmedMean.psicCst|}||}|S)am Least trimmed mean weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array-like 1d array Returns ------- weights : array weights(z) = 1 for \|z\| <= c weights(z) = 0 for \|z\| > c )rrr)rrr!rrrr s  zTrimmedMean.weightscCs||}|S)z The derivative of least trimmed mean psi function Notes ----- Used to estimate the robust covariance matrix. )r)rrr!rrrr .s zTrimmedMean.psi_derivN)r,) rrrrrrr r r r rrrrr+s  r+c@sBeZdZdZdddZddZd d Zd d Zd dZddZ dS)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 @@ @cCs||_||_||_dS)N)r%br-)rr%r2r-rrrrKszHampel.__init__cCs`tt|}t||j}t||jt||j}t||jt||j}|||fS)zL Hampel's function is defined piecewise over the range of z )rrrrr%r2Zgreaterr-)rrt1t2t3rrrrPs zHampel._subsetc Cst|}|j}|j}|j}||\}}}||dd||||dd|||||dd||d|ddd|||||||}|S)a The robust criterion function for Hampel's estimator Parameters ---------- z : array-like 1d array Returns ------- rho : array rho(z) = (1/2.)*z**2 for \|z\| <= a rho(z) = a*\|z\| - 1/2.*a**2 for a < \|z\| <= b rho(z) = a*(c*\|z\|-(1/2.)*z**2)/(c-b) for b < \|z\| <= c rho(z) = a*(b + c - a) for \|z\| > c rg?g@r )rrr%r2r-r) rrr%r2r-r3r4r5vrrrr Zs Z"z Hampel.rhoc Csxt|}|j}|j}|j}||\}}}t|}t|}|||||||||||||} | S)a The psi function for Hampel's estimator The analytic derivative of rho Parameters ---------- z : array-like 1d array Returns ------- psi : array 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 )rrr%r2r-rr"r) rrr%r2r-r3r4r5sr7rrrr xs    z Hampel.psic Cst|}|j}|j}|j}||\}}}|||t||||t|t|||}d|tt|<|S)a Hampel weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array-like 1d array Returns ------- weights : array 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 g?) rrr%r2r-rrwhereZisnan) rrr%r2r-r3r4r5r7rrrr s *zHampel.weightscCsB||\}}}|||jt||t||j|jS)N)rr%rr"rr-r2)rrr3r4r5rrrr szHampel.psi_derivN)r/r0r1) rrrrrrr r r r rrrrr.9s    r.c@sBeZdZdZdddZddZddZd d Zd d Zd dZ dS) 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@cCs ||_dS)N)r-)rr-rrrrszTukeyBiweight.__init__cCstt|}t||jS)zK Tukey's biweight is defined piecewise over the range of z )rrrrr-)rrrrrrszTukeyBiweight._subsetcCs4||}d||jdd ||jddS)a\ The robust criterion function for Tukey's biweight estimator Parameters ---------- z : array-like 1d array Returns ------- rho : array rho(z) = -(1 - (z/c)**2)**3 * c**2/6. for \|z\| <= R rho(z) = 0 for \|z\| > R r rg@)rr-)rrsubsetrrrr s zTukeyBiweight.rhocCs2t|}||}|d||jdd|S)ap The psi function for Tukey's biweight estimator The analytic derivative of rho Parameters ---------- z : array-like 1d array Returns ------- psi : array psi(z) = z*(1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R r r)rrrr-)rrr=rrrr s  zTukeyBiweight.psicCs$||}d||jdd|S)a| Tukey's biweight weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array-like 1d array Returns ------- weights : array psi(z) = (1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R r r)rr-)rrr=rrrr s zTukeyBiweight.weightscCsL||}|d||jddd|d|jdd||jdS)z The derivative of Tukey's biweight psi function Notes ----- Used to estimate the robust covariance matrix. r r)rr-)rrr=rrrr s *zTukeyBiweight.psi_derivN)r;) rrrrrrr r r r rrrrr:s r:ư>c Cs|dkrt}|dkr$t||}n|}xft|D]Z}||||} t| ||t| |} ttt|| ||r| S| }q2Wt d|dS)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 : array Array over which the location parameter is to be estimated scale : array 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 : array, 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 : array Estimate of location Nz6location estimator failed to converge in %d iterations) rrZmedianrr sumZalltrueZlessr ValueError) r%ZscaleZnormZaxisinitialmaxiterZtolZmuiterWZnmurrrestimate_location#s! rG)NrNr?r@)Zstatsmodels.compat.pythonrZnumpyrobjectrrrr#r'r+r.r:rGrrrrs PQgWlhg