Related papers: Can Tests for Jumps be Viewed as Tests for Cluster…
We introduce a method for validation of results obtained by clustering analysis of data. The method is based on resampling the available data. A figure of merit that measures the stability of clustering solutions against resampling is…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
This paper studies inference in cluster randomized trials where treatment status is determined according to a "matched pairs" design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the…
Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters remains a challenge. Here our goal is posterior inference on…
We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward…
We propose a change-point detection method for large scale multiple testing problems with data having clustered signals. Unlike the classic change-point setup, the signals can vary in size within a cluster. The clustering structure on the…
Consider a population consisting of clusters of sampling units, evolving temporally, spatially, or according to other dynamics. We wish to monitor the evolution of its means, medians, or other parameters. For administrative convenience and…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…
Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they…
We study structural equation modeling (SEM) for diffusion processes with jumps. Based on high-frequency data, we consider the parameter estimation and the goodness-of-fit test in the SEM. Using a threshold method, we propose the…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
We present in this paper an empirical framework motivated by the practitioner point of view on stability. The goal is to both assess clustering validity and yield market insights by providing through the data perturbations we propose a…
This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an…
Evaluation of default correlation is an important task in credit risk analysis. In many practical situations, it concerns the joint defaults of several correlated firms, the task that is reducible to a first passage time (FPT) problem. This…
Understanding the dependence structure of asset returns is fundamental in risk assessment and is particularly relevant in a portfolio diversification strategy. We propose a clustering approach where evidence accumulated in a multiplicity of…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…
Cross-level interactions among fixed effects in linear mixed models (also known as multilevel models) are often complicated by the variances stemming from random effects and residuals. When these variances change across clusters, tests of…
In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering…