biwtInternalFunctions {biwt}

Functions used internally for the biwt package

Description

Tukey's biweight gives robust estimates of a p-dimensional mean vector and covariance matrix. These functions are used internally within the biweight estimation function.

Usage

chi.int2.p(p, a, c1)
chi.int2(p,a,c1)
chi.int.p(p,a,c1)
chi.int(p,a,c1)
erho.bw.p(p,c1)
erho.bw(p,c1)
ksolve(d,p,c1,b0)
psibw(x,c1)
rhobw(x,c1)
vbw(x,c1)
wtbw(x,c1)
rejpt.bw(p,r)
vect2diss(v)

Arguments

p

the dimension of the data (should be two if computing correlations. Unlike Pearson correlation, pairwise correlations will not be the same if computed on the entire data set as compared to one pair at a time.)

a

degrees of freedom for the chi square distribution

c1

cutoff value at which the biweight function gives zero weight to any data point

d

vector of distances from each data point to mean vector

b0

expected value of the \rho function for the biweight estimator (under normality)

x

value at which the biweight (\rho, \psi, v, w) should be evaluated

r

breakdown (k/n where k is the largest number of observations that can be replaced with arbitrarily large values while keeping the estimates bounded)

v

a vector (presumably from biwt.cor) consisting of the lower triangle of a symmetric dissimilarity or similarity matrix

Details

These functions are used internally for the biwt.est and biwt.cor functions in the biwt package.

Value

The following functions evaluate partial integrals of the \chi^2 distribution: chi.int, chi.in2, chi.int.p, chi.int2.p.

The following functions evaluate the biweight functions: psibw, rhobw, wbw, vbw.

The following functions caluclate the expected value of the \rho function under the assumption of normally distribued data: erho.bw, erho.bw.p.

The function ksolve keeps the estimates from imploding by setting the mean value of \rho equal to its expected value under normality.

The function rejpt.bw gives the asymptotic rejection point.

The function vect2diss converts a vector consisting of a lower triangle of a matrix into a symmetric dissimilarity or similarity matrix. The function is similar to dissmatrix in the hopach package, except that vect2diss fills in the lower triangle first while dissmatrix fills in the upper triangle first.

Author(s)

Jo Hardin [e-mail]

References

Hardin, J., Mitani, A., Hicks, L., VanKoten, B.; A Robust Measure of Correlation Between Two Genes on a Microarray, BMC Bioinformatics, 8:220; 2007.

See Also

biwt.est , biwt.cor

Examples

## These are not user level functions
## See examples for biwt.est or biwt.cor
## ?biwt.est
## ?biwt.cor