Fitted curve to measured data - statistical properties of the fit error

  • Thread starter cmunikat
  • Start date
  • #1
1
0

Main Question or Discussion Point

Dear all,

I have a set of measurements {xm(Ti,mi)=x(Ti)+e(Ti,mi)}, where:

_xm is the measured value
_x is the actual value
_e is a random measurement error for the measurement mi
_Ti is a parameter

I need to fit a curve to this data by some method. For example, if I use least squares best fit, the following value D is minimized:

D=Ʃ Di2

Where:
_Di=X(T=Ti)-xm(Ti)
_X is the continuous curve

Now, I define the error between the curve X(T) and the actual data x(Ti):

ef(Ti) = X(T) - x(Ti)

And here is the problem:

I need to know, for any parameter Tj, the mean and variance of this error ef(Tj), in terms of the mean and variance of the measurement errors "e(Ti,mi)" defined at the beggining.

Thank you in advance

Cmunikat
 

Answers and Replies

Related Threads on Fitted curve to measured data - statistical properties of the fit error

Replies
10
Views
2K
Replies
11
Views
9K
Replies
0
Views
1K
Replies
5
Views
2K
Replies
7
Views
3K
Replies
3
Views
524
Replies
4
Views
6K
  • Last Post
Replies
3
Views
727
  • Last Post
Replies
24
Views
984
Top