Abstract
Abstract. In this paper we shall consider the interpolation problem under the condition that the spectral density of a stationary process concerned is vaguely known (i.e., Huber's ε ‐contaminated model). Then we can get a minimax robust interpolator for the class of spectral densities S={ g:g(x)=(1‐ε)f(x)+εh(x)ε Ar Do, 0<ε<1}, where f(x) is a known spectral density and D0 is a certain class of spectral densities. Also we shall consider the time series regression problem under the condition that the residual spectral density is vaguely known. Then we can get a minimax robust regression coefficient estimate for the class of the residual spectral densities S.
| Original language | English |
|---|---|
| Pages (from-to) | 53-62 |
| Number of pages | 10 |
| Journal | Journal of Time Series Analysis |
| Volume | 2 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1981 |
| Externally published | Yes |
Keywords
- interpolation
- regression spectrum
- robust estimation
- spectral density
- spectrum element
- Stationary process
- time series regression
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics