On multivariate records from random vectors with independent components

  title={On multivariate records from random vectors with independent components},
  author={Michael Falk and Amir Khorrami Chokami and Simone A. Padoan},
  journal={Journal of Applied Probability},
  pages={43 - 53}
Abstract Let X1, X2, . . . be independent copies of a random vector X with values in ℝd and a continuous distribution function. The random vector Xn is a complete record, if each of its components is a record. As we require X to have independent components, crucial results for univariate records clearly carry over. But there are substantial differences as well. While there are infinitely many records in the d = 1 case, they occur only finitely many times in the series if d ≥ 2. Consequently… 
Records for time-dependent stationary Gaussian sequences
The probability that the records and $(X_j,X_n)$ take place and the arrival time of the nth record are independent of the marginal distribution function, provided that it is continuous.
Functional Time Series Analysis Based on Records
This work proposes some nonparametric tools for functional data observed over time (functional time series) and uses the concept of record to use the trajectory of the number of record curves under different scenarios.
Generalized Records for Functional Time Series with Application to Unit Root Tests.
A generalization of the definition of records to functional data is proposed, based on ranking curves using a notion of functional depth, which allows to study the curves of the number of records over time.
General regular variation, Popa groups and quantifier weakening


Some Results on Joint Record Events
The Asymptotic Theory of Extreme Order Statistics
Abstract. Let X j denote the life length of the j th component of a machine. In reliability theory, one is interested in the life length Z n of the machine where n signifies its number of components.
In 2001, the Indian Sociological Society (ISS) and the Indian Council of Social Science Research (ICSSR) jointly set up an endowment fund in memory of the late Professor M.N. Srinivas, which was stipulated to be used every year for two main purposes.
Extreme Values, Regular Variation, and Point Processes
Contents: Preface * Preliminaries * Domains of Attraction and Norming Constants * Quality of Convergence * Point Processes * Records and Extremal Processes * Multivariate Extremes * References *
Records: Arnold/Records
Records in a partially ordered set
Many multivariate records
Extreme Value Theory in Higher Dimensions
  • Max-Stable Processes and Multivariate Records. Ph. D. thesis, University of Würzburg.
  • 2016
Many multivariate records. Stochastic Process
  • Appl
  • 1995
Many multivariate records . Stochastic Process