Nonparametric estimation in alpha-series processes

AYDOĞDU H., Kara M.

COMPUTATIONAL STATISTICS & DATA ANALYSIS, cilt.56, sa.1, ss.190-201, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.csda.2011.06.037
  • Dergi Adı: COMPUTATIONAL STATISTICS & DATA ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.190-201
  • Anahtar Kelimeler: alpha-series process, Trend, Linear regression
  • Ankara Üniversitesi Adresli: Evet

Özet

A counting process {N(t), t >= 0} with the interoccurrence times X-1, X-2, ... is an alpha-series process if there exists a real number alpha such that (k(alpha)X(k))(k=1.2,) (...) forms a renewal process. The nonparametric inference problem in an alpha-series process is taken into consideration. The Mann test is applied for trend analysis and a graphical technique is presented in order to test whether the data come from an alpha-series process. Some nonparametric estimators for three important parameters of the alpha-series process are obtained by using a linear regression method. The consistency and asymptotic normality properties are investigated. The performances of the estimators are evaluated by a simulation study. Some suggestions on the choice of the estimators are made based on the theoretical and simulation results. Further, the method is illustrated through a real-life example. (C) 2011 Elsevier B.V. All rights reserved.