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Risk concentration under second order regular variation
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second...
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A formula for hidden regular variation behavior for symmetric stable distributions
We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the...
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Optimal two-level regular fractional factorial split-plot designs when the effects of subplot factors are more important
Robust parameter design (RPD) is an engineering methodology that focuses on reducing the variation of a process by appropriately selecting the...
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Test Pass/Fail Judgment and Japanese Compact Cars and Regular Cars
I introduce two self-evident LSDs. The pass/fail judgments of exams are self-evident LSD. Suppose two scores, T1 and T2, and 50 points is the passing...
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Geometric Mean Type of Proportional Reduction in Variation Measure for Two-Way Contingency Tables
Traditional analysis of two-way contingency tables with explanatory and response variables focuses on the independence of two variables. However, if...
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Exact variation and drift parameter estimation for the nonlinear fractional stochastic heat equation
This work concerns the statistical inference for stochastic partial differential equations. We consider the fractional stochastic heat equation...
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Non-regular Frameworks and the Mean-of-Order p Extreme Value Index Estimation
Most of the estimators of parameters of rare and large events, among which we distinguish the extreme value index (EVI) for maxima, one of the...
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Estimation of Tempered Stable Lévy Models of Infinite Variation
Truncated realized quadratic variations (TRQV) are among the most widely used high-frequency-based nonparametric methods to estimate the volatility...
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Random networks with heterogeneous reciprocity
Users of social networks display diversified behavior and online habits. For instance, a user’s tendency to reply to a post can depend on the user...
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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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Epidemics Models and Data Using R
This book is designed to be a practical study in infectious disease dynamics. It offers an easy-to-follow implementation and analysis of mathematical...
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Tail-dependence, exceedance sets, and metric embeddings
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the...
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Tail probabilities of random linear functions of regularly varying random vectors
We provide a new extension of Breiman’s Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In...
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Asymptotic Behavior of Common Connections in Sparse Random Networks
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In...
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Asymptotics of convolution with the semi-regular-variation tail and its application to risk
In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to...
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Convergence of extreme values of Poisson point processes at small times
We study the behaviour of large values of extremal processes at small times, obtaining an analogue of the Fisher-Tippet-Gnedenko Theorem. Thus,...
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Multi-normex distributions for the sum of random vectors. Rates of convergence
We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It...
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Bias Reduction in Kernel Tail Index Estimation for Randomly Truncated Pareto-Type Data
A bias reduction to a kernel estimator of the tail index of randomly right-truncated Pareto-type distributions is made. The asymptotic normality of...
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Time Series
Time series refers to any group of statistical information accumulated at regular intervals. It is a quantitative method used to determine patterns...