Gaussian semiparametric or local Whittle estimation of the memory parameter in standard long memory processes was proposed by Robinson [18]. This technique shows several advantages over the popular log- periodogram regression introduced by Geweke and Porter–Hudak [7]. In particular under milder assumptions than those needed in the log periodogram regression it is asymptotically more efficient. We analyse the asymptotic behaviour of the Gaussian semiparametric estimate of the memory parameter in...

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis $H_0$: “$f=f_0$” against the composite alternative $H_a$: “$f\ne f_0$” under the assumption that the true regression function $f$ is decreasing. The test statistic is based on the ${𝕃}_1$-distance between the isotonic estimator of $f$ and the function $f_0$, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under $H_0$. We study the asymptotic...

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the ${𝕃}_1$-distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0....

In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.