FuzzyStatTra (version 1.0)

M.estimate:

Description

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).

Usage

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.

Value

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

Details

See examples

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)