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import numpy as N
class RobustNorm:
def __call__(self, z):
return self.rho(z)
class LeastSquares(RobustNorm):
"""
Least squares rho for M estimation.
DC Montgomery, EA Peck. \'Introduction to Linear Regression Analysis\',
John Wiley and Sons, Inc., New York, 2001.
"""
def rho(self, z):
return N.power(z, 2) * 0.5
def psi(self, z):
return N.asarray(z)
def weights(self, z):
return N.ones(z.shape, N.float64)
class HuberT(RobustNorm):
"""
Huber\'s T for M estimation.
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.
"""
t = 1.345
def subset(self, z):
z = N.asarray(z)
return N.less_equal(N.fabs(z), HuberT.t)
def rho(self, z):
z = N.asarray(z)
test = self.subset(z)
return (test * 0.5 * N.power(z, 2) +
(1 - test) * (N.fabs(z) * HuberT.t - 0.5 * HuberT.t**2))
def psi(self, z):
z = N.asarray(z)
test = self.subset(z)
return test * z + (1 - test) * HuberT.t * N.sign(z)
def weights(self, z):
z = N.asarray(z)
test = self.subset(z)
return test + (1 - test) * HuberT.t / N.fabs(z)
class RamsayE(RobustNorm):
"""
Ramsay\'s Ea for M estimation.
DC Montgomery, EA Peck. \'Introduction to Linear Regression Analysis\',
John Wiley and Sons, Inc., New York, 2001.
"""
a = 0.3
def rho(self, z):
z = N.asarray(z)
return (1 - N.exp(-RamsayE.a * N.fabs(z)) *
(1 + RamsayE.a * N.fabs(z))) / RamsayE.a**2
def psi(self, z):
z = N.asarray(z)
return z * N.exp(-RamsayE.a * N.fabs(z))
def weights(self, z):
z = N.asarray(z)
return N.exp(-RamsayE.a * N.fabs(z))
class AndrewWave(RobustNorm):
"""
Andrew\'s wave for M estimation.
DC Montgomery, EA Peck. \'Introduction to Linear Regression Analysis\',
John Wiley and Sons, Inc., New York, 2001.
"""
a = 1.339
def subset(self, z):
z = N.asarray(z)
return N.less_equal(N.fabs(z), RamsayE.a * N.pi)
def rho(self, z):
a = AndrewWave.a
z = N.asarray(z)
test = self.subset(z)
return (test * a * (1 - N.cos(z / a)) +
(1 - test) * 2 * a)
def psi(self, z):
a = AndrewWave.a
z = N.asarray(z)
test = self.subset(z)
return test * N.sin(z / a)
def weights(self, z):
a = AndrewWave.a
z = N.asarray(z)
test = self.subset(z)
return test * N.sin(z / a) / (z / a)
class TrimmedMean(RobustNorm):
"""
Trimmed mean function for M-estimation.
R Venables, B Ripley. \'Modern Applied Statistics in S\'
Springer, New York, 2002.
"""
c = 2
def subset(self, z):
z = N.asarray(z)
return N.less_equal(N.fabs(z), TrimmedMean.c)
def rho(self, z):
z = N.asarray(z)
test = self.subset(z)
return test * N.power(z, 2) * 0.5
def psi(self, z):
z = N.asarray(z)
test = self.subset(z)
return test * z
def weights(self, z):
z = N.asarray(z)
test = self.subset(z)
return test
class Hampel(RobustNorm):
"""
Hampel function for M-estimation.
R Venables, B Ripley. \'Modern Applied Statistics in S\'
Springer, New York, 2002.
"""
a = 2
b = 4
c = 8
def subset(self, z):
z = N.fabs(N.asarray(z))
t1 = N.less_equal(z, Hampel.a)
t2 = N.less_equal(z, Hampel.b) * N.greater(z, Hampel.a)
t3 = N.less_equal(z, Hampel.c) * N.greater(z, Hampel.b)
return t1, t2, t3
def psi(self, z):
z = N.asarray(z)
a = Hampel.a; b = Hampel.b; c = Hampel.c
t1, t2, t3 = self.subset(z)
s = N.sign(z); z = N.fabs(z)
v = s * (t1 * z +
t2 * a +
t3 * a * (c - z) / (c - b))
return v
def rho(self, z):
z = N.fabs(z)
a = Hampel.a; b = Hampel.b; c = Hampel.c
t1, t2, t3 = self.subset(z)
v = (t1 * z**2 * 0.5 +
t2 * (a * z - a**2 * 0.5) +
t3 * (a * (c * z - z**2 * 0.5) / (c - b) - 7 * a**2 / 2.) +
(1 - t1 + t2 + t3) * a * (b + c - a))
return v
def weights(self, z):
z = N.asarray(z)
test = N.not_equal(z, 0)
return self.psi(z) * test / z + (1 - test)
class TukeyBiweight(RobustNorm):
"""
Tukey\'s biweight function for M-estimation.
R Venables, B Ripley. \'Modern Applied Statistics in S\'
Springer, New York, 2002.
"""
R = 4.685
def subset(self, z):
z = N.fabs(N.asarray(z))
return N.less_equal(z, self.R)
def psi(self, z):
z = N.asarray(z)
subset = self.subset(z)
return z * (1 - (z / self.R)**2)**2 * subset
def rho(self, z):
subset = self.subset(z)
return -(1 - (z / self.R)**2)**3 * subset * self.R**2 / 6
def weights(self, z):
subset = self.subset(z)
return (1 - (z / self.R)**2)**2 * subset
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