Rosenblatt distribution subordinated to gaussian random fields with long-range dependence

The Karhunen-Lo\`eve expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on R^d displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d=1. Several properties of this new distribution are obtained. Specifically, its series representation in terms of independent chi-squared random variables is given, the asymptotic behavior of the eigenvalues, its L\`evy-Khintchine representation, as well as its membership to the Thorin subclass of self-decomposable distributions. The existence and boundedness of its probability density is then a direct consequence.Comment: This paper has 40 pages and it has already been submitte

On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure

Sojourn functionals for spatiotemporal random fields with long-memory

This paper addresses the asymptotic analysis of sojourn functionals of spatiotemporal Gaussian random fields with long-range dependence (LRD) in time also known as long memory. Specifically, reduction theorems are derived for local functionals of nonlinear transformation of such fields, with Hermite rank m larger than or equal to 1, under general covariance structures. These results are proven to hold, in particular, for a family of non--separable covariance structures belonging to Gneiting class. For m=2, under separability of the spatiotemporal covariance function in space and time, the properly normalized Minkowski functional, involving the modulus of a Gaussian random field, converges in distribution to the Rosenblatt type limiting distribution for a suitable range of the long memory parameter.Comment: This paper is regular article to be submitted to a regular journa

Standardization of molecular monitoring for chronic myeloid leukemia in Latin America using locally produced secondary cellular calibrators

Residual disease in chronic myeloid leukemia (CML) patients undergoing therapy with tyrosine kinase inhibitors (TKIs) is measured by assessing the quantity of transcripts of the BCR-ABL1 fusion gene in peripheral white blood cells. This analysis is based on reverse-transcription quantitative PCR (RT–qPCR) technology; however, the wide array of methods used worldwide has led to large variation in quantitative BCR-ABL1 measurements, which hamper inter-laboratory comparative studiesFil: Ruiz, María Sol. Fundación Cáncer. Centro de Investigaciones Oncológicas; ArgentinaFil: Medina, M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Medicina Experimental. Academia Nacional de Medicina de Buenos Aires. Instituto de Medicina Experimental; ArgentinaFil: Tapia, I.. Fundación Cáncer. Centro de Investigaciones Oncológicas; ArgentinaFil: Mordoh, Jose. Fundación Cáncer. Centro de Investigaciones Oncológicas; ArgentinaFil: Cross, N. C. P.. Universidad de Southampton Uk; Reino UnidoFil: Larripa, Irene Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Medicina Experimental. Academia Nacional de Medicina de Buenos Aires. Instituto de Medicina Experimental; ArgentinaFil: Bianchini, Michele. Fundación Cáncer. Centro de Investigaciones Oncológicas; Argentin