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Functional strong law of large numbers for Betti numbers in the tail
The objective of this paper is to investigate the layered structure of topological complexity in the tail of a probability distribution. We establish...
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Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds
To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric...
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Strong convergence of a nonparametric relative error regression estimator under missing data with functional predictors
In this paper, we develop a nonparametric estimator of the regression function for a functional explanatory variable and a scalar response variable...
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A Limit Theorem for Fluctuations
To motivate the results of this chapter, consider the classical strong law of large numbers: Let...
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Variable selection for multivariate functional data via conditional correlation learning
Variable selection involves selecting truly important predictors from p -dimensional multivariate functional predictors in functional predictive...
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Rates of the Strong Uniform Consistency for the Kernel-Type Regression Function Estimators with General Kernels on Manifolds
AbstractIn the present paper, we develop strong uniform consistency results for the generic kernel (including the kernel density estimator) on...
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Strong uniform consistency of the local linear relative error regression estimator under left truncation
This paper is concerned with a nonparametric estimator of the regression function based on the local linear method when the loss function is the mean...
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Testing normality of a large number of populations
This paper studies the problem of simultaneously testing that each of k independent samples come from a normal population. The means and variances of...
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Uniform consistency and uniform in number of neighbors consistency for nonparametric regression estimates and conditional U-statistics involving functional data
U -statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U -statistics...
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Limiting Canonical Distribution of Two Large-Dimensional Random Vectors
In multivariate analysis, canonical correlation analysis is a powerful tool to deal with the relationship between two random vectors. In this paper,...
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Testing independence and goodness-of-fit jointly for functional linear models
A conventional regression model for functional data involves expressing a response variable in terms of the predictor function. Two assumptions, that...
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Applications of Correlation
This chapter gives a bird’s eye view of application of correlation in various fields. A large number of R packages for this purposes are given in...
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Fourier approach to goodness-of-fit tests for Gaussian random processes
A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the...
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Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations
In this paper, we study so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit...
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Variational inference: uncertainty quantification in additive models
Markov chain Monte Carlo (MCMC)-based simulation approaches are by far the most common method in Bayesian inference to access the posterior...
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Measures of Association
This chapter starts with a discussion on the historical development of correlation coefficients. It then discusses the population and sample...
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Structural properties of generalised Planck distributions
A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is...
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Estimating Finite-Time Ruin Probability of Surplus with Long Memory via Malliavin Calculus
We consider a surplus process of a drifted fractional Brownian motion with the Hurst index...
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Application of the Cramér–Wold theorem to testing for invariance under group actions
We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a...
