An Universal, Simple, Circular Statistics-Based Estimator of alpha for Symmetric Stable Family

Download

index.pdf

Date

2019-12-01

Author

SenGupta, Ashis
Roy, Moumita

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

73
views

45
downloads

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter alpha lies between 1 and 2. A similar approach can be adopted when alpha (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.

Subject Keywords

Index parameter, Efficiency, Asymptotic, Characteristic function-based estimator, Hill estimator, Wrapped stable, Estimation

URI

https://hdl.handle.net/11511/64513

Journal

JOURNAL OF RISK AND FINANCIAL MANAGEMENT

DOI

https://doi.org/10.3390/jrfm12040171

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

On the Cramér-Rao lower bound under model mismatch Fritsche, Carsten; Orguner, Umut; Özkan, Emre; Gustafsson, Fredrik (2014-04-24) Cram´er-Rao lower bounds (CRLBs) are proposed for deterministic parameter estimation under model mismatch conditions where the assumed data model used in the design of the estimators differs from the true data model. The proposed CRLBs are defined for the family of estimators that may have a specified bias (gradient) with respect to the assumed model. The resulting CRLBs are calculated for a linear Gaussian measurement model and compared to the performance of the maximum likelihood estimator for the corresp...
Guaranteed Exponential Convergence without Persistent Excitation in Adaptive Control Yayla, Metehan; Kutay, Ali Türker (2016-09-02) In this paper, a new adaptive control framework for linear systems in which the matched uncertainty can be linearly parameterized is introduced to guarantee the global exponential stability of reference tracking error and parameter convergence error without requiring restrictive persistent excitation condition. The framework uses time histories of control input and system signals to construct least-squares problem based on recorded data. Then, unique solution to least-squares problem is computed, and assign...
Robust time series: Some engineering applications Tiku, ML; Kestel, Sevtap Ayşe (2000-01-01) AR(1) models in time series with nonnormal errors represented by two families of distributions: (i) Gamma with support IR:(0,infinity), and (ii) Student's t with support IR:(-infinity,infinity) are considered. Since the maximum likelihood (ML) estimators are intractable, the modified maximum likelihood (MML) estimators of the parameters are derived and it is shown that they are remarkably efficient besides being easy to compute. It is also shown that the least squares (LS) estimators have very low efficienc...
Waterfall region analysis for iterative decoding Yılmaz, Ali Özgür (2004-12-01) Finite length analysis of iterative decoders can be done by using probabilistic models based on EXIT charts. The validity of these models will be investigated by checking the performance of iterative decoding under various scenarios.
On investigating the performance of various turbo decoding algorithms based on the finite-EXIT chart method Yilmaz, AO (2004-04-30) Finite length analysis of iterative decoders can be done by using probabilistic models based on EXIT charts. The validity of these models will be investigated by checking the performance of iterative decoding under various scenarios.

Citation Formats

A. SenGupta and M. Roy, “An Universal, Simple, Circular Statistics-Based Estimator of alpha for Symmetric Stable Family,” JOURNAL OF RISK AND FINANCIAL MANAGEMENT, pp. 0–0, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64513.