mathematical optimization – Nonlinear Model Fitting to Numerical Data with automatic elimination

I have an experimental data set {f,x,y,z} as

{{300., 2., 4., 6.}, {500., 0., 4., 25.}, {6600., 1., 15., 9.}, {100.,
5., 0., 2.}, {1100., 10., 8., 1.}, {1300., 7., 8., 18.}, {300.,
23., 5., 0.}, {400., 1., 5., 3.}, {900., 3., 7., 9.}, {800., 4., 7.,
2.}, {400., 4., 4., 11.}, {3300., 24., 12., 0.}, {600., 2., 6.,
8.}, {300., 2., 4., 6.}, {600., 22., 6., 7.}, {17900., 3., 21.,
44.}}

I need to find the best fitted parameters for the function:

f=a*(x*b)^0.3 + c*(y*d)^3 + e*(z*h)^g

where a, b, c, d, e, h, g is the fitted parameters.
The problem is how to drop a certain data line with a higher deviation than a certain value e.g greater than 10% and then restart the finding parameters to have the best fitted parameters.
The another problem is how to guess the initials (starting points) for the parameters.
Could you please advise how to solve the problem?
Thank you.