arXiv subjects

R. M. Crujeiras

Publications and source records attributed to R. M. Crujeiras.

3 recordsLinked to original sources

arXiv2026

Long range dependence spectral testing from discretely observed functional time series in manifolds

A specification test for long range dependence (LRD) in functional time series in manifolds has been formulated in \cite{Ruiz-MedinaCrujeiras24} in the spectral domain for fully observed functional data. The asymptotic Gaussian distribution of the proposed test statistics, based on the weighted periodogram operator, under the null hypothesis, and the consistency of the test have been derived. In this paper, we analyze the asymptotic properties of this LRD spectral testing procedure, when the functional data are contaminated, and discretely observed through random uniform spatial sampling.

math.ST↗

arXiv2025

Testing LRD in the spectral domain for functional time series in manifolds

A statistical hypothesis test for long range dependence (LRD) is formulated in the spectral domain for functional time series in manifolds. The elements of the spectral density operator family are assumed to be invariant with respect to the group of isometries of the manifold. The proposed test statistic is based on the weighted periodogram operator. A Central Limit Theorem is derived to obtain the asymptotic Gaussian distribution of the proposed test statistic operator under the null hypothesis. The rate of convergence to zero, in the Hilbert--Schmidt operator norm, of the bias of the integrated empirical second and fourth order cumulant spectral density operators is obtained under the alternative hypothesis. The consistency of the test follows from the consistency of the integrated weighted periodogram operator under LRD. Practical implementation of our testing approach is based on the random projection methodology. A simulation study illustrates, in the context of spherical functional time series, the asymptotic normality of the test statistic under the null hypothesis, and its consistency under the alternative. The empirical size and power properties are also computed for different functional sample sizes, and under different scenarios.

math.ST↗

arXiv2012

A plug-in rule for bandwidth selection in circular density estimation

A new plug-in rule procedure for bandwidth selection in kernel circular density estimation is introduced. The performance of this proposal is checked throughout a simulation study considering a variety of circular distributions exhibiting multimodality, peakedness and/or skewness. The plug-in rule behaviour is also compared with other existing bandwidth selectors. The method is illustrated with two classical datasets of cross-beds layers and animal orientation.

stat.ME↗