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S‐Estimation in the Linear Regression Model with Long‐memory Error Terms Under Trend
Author(s) -
Sibbertsen Philipp
Publication year - 2001
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00228
Subject(s) - mathematics , estimator , asymptotic distribution , statistics , polynomial regression , linear regression , covariance , rate of convergence , linear model , minimum variance unbiased estimator , convergence (economics) , best linear unbiased prediction , channel (broadcasting) , economic growth , computer science , economics , selection (genetic algorithm) , artificial intelligence , electrical engineering , engineering
The asymptotic distribution of S‐estimators in the linear regression model with long‐memory error terms is obtained under mild regularity conditions to the regressors which are sufficiently weak to cover, for example, polynomial trends and i.i.d. carriers. It turns out that S‐estimators are asymptotically normal in the case of deterministic regressors with a variance–covariance structure similar to the structure in the i.i.d. case. Also, the rate of convergence for S‐estimators is the same as for the least‐squares estimator (LSE) and the best linear unbiased estimator (BLUE).