A Unified Approach to Estimating Tail Behavior

Abstract

Tail estimators are proposed which make minimal assumptions and let the data dictate the form of the probability model. These estimators use only the observations in the tail and are based on a unifying density-quantile model. The fundamental result in this work is a representation (1) motivates a unified parameterization for tail estimators of the underlying probability model; (2) motivates methods for obtaining parameter estimates; and (3) simplifies the derivation of the asymptotic properties of the proposed parameter estimates. Parameter estimates may be obtained using a Generalized Pareto Distribution or a Generalized Extreme Value Distribution model of the exceedences. Assuming the underlying distribution can be correctly classified as either short tailed or long tailed, other estimates are formed. The asymptotic properties of these estimates are derived under rate of convergence conditions to show the effect of threshold selection on parameters properties.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1989
Accession Number
ADA210961

Entities

People

  • Scott D. Grimshaw

Organizations

  • Texas A&M University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Asymptotic Normality
  • Computations
  • Data Mining
  • Data Science
  • Estimators
  • Information Science
  • Knowledge Management
  • Order Statistics
  • Probability
  • Random Variables
  • Standards
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics
  • Surveys

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Statistical inference.