Asymptotic Normality of the Whittle Estimator in Linear Regression Models with Long Memory Errors

This paper establishes the asymptotic normality of the Whittle estimator of the unknown dependence parameters in a linear regression model with long memory moving average errors. The design variables are taken to be deterministic or random. In the latter case they are assumed to have a moving average representation that includes both short and long memory. In all cases, it is observed that the rate of consistency of the regression parameter estimator has an effect on the asymptotic normality of the Whittle estimator.     

The transfer of natural (226Ra,?232Th, 40K) and artificial (137Cs, 90Sr) radionuclides from soil to the wood of a Scots pine (Pinus sylvestris L.)

On the Stabatishke site near to Ignalina Nuclear Power Plant a near surface repository for low and intermediate-level short-lived radioactive waste is being constructed to store the waste which was produced during the decommissioning of the Ignalina Nuclear Power Plant. A possible spread of radionuclides from the near surface repository and the radiation level of expression are one at the most important aspects while evaluating the safety of the repository. The article examines the specific activity of artificial (¹³⁷Cs, ⁹⁰Sr) and natural (²²⁶Ra, ²³²Th, ⁴⁰K) radionuclides in the soil of Stabatishke site of Ignalina NPP in pinewood; the spread of these radionuclides is determined in the system “soil-tree”. The change of long term soil pollution with artificial radionuclides was estimated. This is a background soil pollution which had been there before the exploitation of the near surface waste repository. The transfer factors of natural (²²⁶Ra, ²³²Th, ⁴⁰K) and artificial (¹³⁷Cs, ⁹⁰Sr) radionuclides from the 0-to-20-cm soil layer to different annual pinewood rings were measured. After estimation of the position of pine roots in accordance to the soil vertical and the annual change of the plant biomass, the transfer factor of ¹³⁷Cs movement to different annual pinewood rings from the separate 0 to 20-cm soil layers was determined.     

Interpolation, correlation identities, and inequalities for infinitely divisible variables

We present an interpolation formula for the expectation of functions of infinitely divisible (i.d.) variables. This is then applied to study the association problem for i.d. vectors and to present new covariance expansions and correlation inequalities. Acknowledgements and Notes. The research of C. Houdré was supported in part by an NSF Mathematical Sciences Post-Doctoral Fellowship and by an NSF-NATO Postdoctoral Fellowship and by the NSF grant No. DMS-98032039. This research was completed while V. Pérez-Abreu was visiting the Georgia Institute of Technology.     

Testing a sub-hypothesis in linear regression models with long memory covariates and errors

This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be n ^1/2-consistent for all values of the long memory parameters of the design and error processes. Research of the first author was partly supported by the NSF DMS Grant 0701430. Research of the second author was partly supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation grant T-15/07.