In this correspondence, we prove that if X is a random variable with P(X=0)=0 and E|X|=∞, then there exists a continuous function G on (0,∞) with 0G(x)↑∞ and xG(x)↑∞ as 0x↑∞ such that E(|X|/G(|X|))=∞. An application of this result pertaining to the Kolmogorov strong law of...

In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell–TIS inequality to establish...

Semi-parametric and nonparametric modeling and inference have been widely studied duringthe last two decades. In this manuscript, we do statistical inference based on semi-parametricand nonparametric models in several different scenarios.Firstly, we develop a semi-parametric additivity test for...

The objective of this dissertation is to develop a suitable statistical methodologyfor functional data analysis. Modern advanced technology allows researchers to collectsamples as functional which means the ideal unit of samples is a curve. We considereach functional observation as the resulting...

We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time independent covariates with coefficients as functions of time dependent covariates. Based on spline smoothing, we propose data driven simultaneous...

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of high-dimensional data. However, in many applications such as risk quantification in finance or climatology, one is interested in capturing the tail variations rather than variation around the mean. In...

We propose a statistical procedure to determine the dimension of the nonstationary subspace of cointegrated functional time series taking values in the Hilbert space of square-integrable functions defined on a compact interval. The procedure is based on sequential application of a proposed test...

Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated by a continuous time stochastic process are called...