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False Discovery Variance Reduction in Large Scale Simultaneous Hypothesis Tests
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it...
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Different Views of Interpretability
Interpretability, in the context of machine learning, means understanding the predictions made by the machine learning algorithm, with the aim to...
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Application of Bernstein Polynomials on Estimating a Distribution and Density Function in a Triangular Array
In this paper, we study some asymptotic properties for the Bernstein estimators of the limit distribution function and the limit density function...
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Law of large numbers for discretely observed random functions
A strong law of large numbers for continuous random functions, and associated tensor product surfaces is established in the setup of discretely...
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Applications of Generating Functions
There are many applications of GFs in algebra. GFs can be used to find the number of solutions to a single linear equation. Consider a simple example...
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Limit theorems for branching processes with immigration in a random environment
We investigate branching processes with immigration in a random environment. Using Goldie’s implicit renewal theory we prove that under a generalized...
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Strong convergence rates of probabilistic integrators for ordinary differential equations
Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation error, at scales no larger than...
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Testing marginal homogeneity in Hilbert spaces with applications to stock market returns
This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The...
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eXplainable AI with GPT4 for story analysis and generation: A novel framework for diachronic sentiment analysis
The recent development of Transformers and large language models (LLMs) offer unique opportunities to work with natural language. They bring a degree...
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Foundations of Statistical Inference
Historically, ruin theory has been mainly studied from a probabilistic point of view; the statistical aspect has not been focused on so much....
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Bootstrap and Subsampling Methods
The bootstrap, subsampling, and other resampling methods provide methods for inference, especially in problems where large-sample approximations are...
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Tests of Fit for Wrapped Stable Distributions Based on the Characteristic Function
We consider composite goodness-of-fit tests for wrapped stable distributions on the circle with unknown parameters, based on the empirical...
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Tests for circular symmetry of complex-valued random vectors
We propose tests for the null hypothesis that the law of a complex-valued random vector is circularly symmetric. The test criteria are formulated as
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Modeling and inferences for bounded multivariate time series of counts
This paper considers modeling bounded multivariate time series of counts and the inferential procedures of this model. For modeling, we introduce a...
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Spatial extremes and stochastic geometry for Gaussian-based peaks-over-threshold processes
Geometric properties of exceedance regions above a given quantile level provide meaningful theoretical and statistical characterizations for...
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Improper versus finitely additive distributions as limits of countably additive probabilities
The Bayesian paradigm with proper priors can be extended either to improper distributions or to finitely additive probabilities (FAPs). Improper...
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Comparative evaluation of point process forecasts
Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant...
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A nonparametric inverse probability weighted estimation for functional data with missing response data at random
This paper considers the nonparametric inverse probability weighted estimation for functional data with missing response data at random. Under mild...
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Applications of Relative Entropy
In this chapter we first introduce the concept of the relative entropy and prove the entropy projection theorem for probability measures. Then, as an...