ABSTRACT
Considered a regression model Y(n) = X(n)I3 + s(n), where 13 is a pxl vektor of unknown parameterse(n) is an nxl unobservable vektor of random errors. The problem in regression analysis is how to estimate the parameter vektor 13 based on the observable data.
For the regression model, let *(m) be the least squares estimate based on the resample: 13 *Om) = X(m)TXOn»-I MmirY*(m), The distribution of -1,1m (0 *0:0-13 (u)), which can be computed directly from
the data consistent for the distribution of (n)-f3). For the correlation
model, the least squares estimate is R *(m) = {X*(m)TX*(m)r
A A
X*(m)TY*(m) and the law of ( *(m)-13 (u)) close to the law of
-4n (13 (n) - 13). It is shown that under mild conditions, the bootstrap
approximation to the distribution of the least squares estimates is valid. The bootstrap give the same asymtotic result as normal approximation.
Key Words: Regression, correlation, least squares estimation, bootstrap
,
