Consistency of the LSE in Linear regression with stationary noise

• Autorzy: Guy Cohen , Michael Lin , Arkady Tempelman
• Języki publikacji: EN

Abstrakty

EN

We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also $L_{p}$-consistency when the noise is strict sense stationary with continuous spectrum and finite absolute pth moment, p ≥ 1 (even without finite variance).
When the spectral measure of the noise is not continuous, we assume that the non-random regressors are Hartman almost periodic, and obtain a spectral condition for L₂-consistency. An additional assumption on the regressors yields strong consistency for strictly stationary noise sequences.
We also treat the case when the regressors are random sequences, with trends having some good averaging properties and with additive stationary ergodic random fluctuations independent of the noise. When the noise and the fluctuations have disjoint point spectra and the noise is strict sense stationary, we obtain strong consistency of the LSE.
The results are applied to amplitude estimation in sums of harmonic signals with known frequencies.

Kategorie tematyczne

• 62J05: Linear regression
• 37A50: Relations with probability theory and stochastic processes
• 47A35: Ergodic theory
• 37A30: Ergodic theorems, spectral theory, Markov operators
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 100
• Numer: 1
• Strony: 29-71

Daty

wydano

2004

Twórcy

autor

Guy Cohen

• Department of Mathematics, Ben-Gurion University, Beer-Sheva, Israel

autor

Michael Lin

• Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel

autor

Arkady Tempelman

• Department of Statistics, Penn State University, University Park, PA 16802, U.S.A.

Identyfikatory

DOI

10.4064/cm100-1-5