M.estimate function

M-estimator of scale of a trapezoidal fuzzy sample

This function calculates the M-estimator of scale with loss function given in M for a matrix of trapezoidal fuzzy numbers F. For computing the M-estimator, a method called ``iterative reweighting'' is used. The employed metric in the M-equation can be the 1-norm distance, the mid/spr distance or the $(\varphi,\theta)$-wabl/ldev/rdev distance. The function first checks if the input matrix F is given in the correct form (tested by checkingTra).

M.estimate(F, M, est_initial, delta, epsilon, type, a = 1, b = 1, theta = 1/3)

Arguments

• F: matrix of dimension n x 4 containing n trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function implicitly checks if the matrix is in the correct form (tested by checkingTra).
• M: name of the loss function. It can be Huber'', Tukey'' or ``Cauchy''.
• est_initial: initial scale estimate.
• delta: number in (0,1). It is present in the M-equation.
• epsilon: number >0. It is the tolerance allowed in the algorithm.
• type: number 1, 2 or 3: if type==1, the 1-norm distance will be considered in the calculation of the M-estimator. If type==2, the mid/spr distance will be considered. By contrast, if type==3, the $(\varphi,\theta)$-wabl/ldev/rdev distance will be used.
• a: number >0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1] in the mid/spr distance or in the $(\varphi,\theta)$-wabl/ldev/rdev distance.
• b: number >0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1] in the mid/spr distance or in the $(\varphi,\theta)$-wabl/ldev/rdev distance.
• theta: number >0, by default theta=1/3. It is the weight of the spread in the mid/spr distance and the weight of the ldev and rdev in the $(\varphi,\theta)$-wabl/ldev/rdev distance.

Details

See examples

Returns

The function returns the value of the M-estimator of scale, which is a real number.

Author(s)

Asun Lubiano lubiano@uniovi.es, Sara de la Rosa de Saa rosasara@uniovi.es

Note

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

See Also

checkingTra, Rho1Tra, DthetaphiTra, DwablphiTra

Examples

# Example 1:
F=SimulCASE1(100)
U=Median1norm(F)
est_initial=MDD(F,U,1)
delta=0.5
epsilon=10^(-5)
M.estimate(F,"Huber",est_initial,delta,epsilon,1)