Minimum distance estimation in linear models with long-range dependent errors. (English) Zbl 0806.62071
Summary: This paper discusses the asymptotic representations of a class of \(L^ 2\)-distance estimators based on weighted empirical processes in a multiple linear regression model when the errors are a function of stationary Gaussian random variables that are long-range dependent. Unlike the independent errors case, the limiting distributions of the suitably normalized estimators are not always normal. The limiting distributions depend heavily on the Hermite rank of a certain class of random variables. Some goodness of fit tests for specified error distributions are also considered.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62J05 | Linear regression; mixed models |
| 62F12 | Asymptotic properties of parametric estimators |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
asymptotic uniform quadraticity; Hermite polynomials; L2-distance estimators; asymptotic representations; weighted empirical processes; multiple linear regression model; stationary Gaussian random variables; long-range dependent; limiting distributions; Hermite rank; goodness of fit testsReferences:
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