View More View Less
  • 1 Russian-Armenian University, 123 Hovsep Emin St, Yerevan 0051, Armenia
  • 2 Boston University, 111 Cummington Mall, Boston, MA 02215, USA
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00


In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

  • [1]

    Adenstedt, R. K., On large-sample estimation for the mean of a stationary random sequence, Ann. Stat., 2 (1974), 10951107.

  • [2]

    Adenstedt, R. K. and Eisenberg, B., Linear estimation of regression coefficients, Quart. Appl. Math., 32(3) (1974), 317327.

  • [3]

    Babayan, N. M., On asymptotic behavior of the prediction error in the singular case, Theory Probab. Appl, 29(1), 147150 (1985).

  • [4]

    Goluzin, G. M., Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence, 1969.

  • [5]

    Grenander, U., Stochastic processes and statistical inference, Ark. Mat., 1(17) (1950), 195277.

  • [6]

    Grenander, U., On Toeplitz forms and stationary processes, Ark. Mat., 1(37) (1952), 555571.

  • [7]

    Grenander, U. and Szegő, G., Toeplitz Forms and Their Applications, University of California Press, Berkeley, 1958.

  • [8]

    Mazurkievicz, S., Un theoreme sur les polynomes, Ann. Soc. Polon. Math., 18 (1945), 113118.

  • [9]

    Rosenblatt, M., Some Purely Deterministic Processes, J. of Math. and Mech., 6 (1957), 801810.

  • [10]

    Samarov, A. and Taqqu, M. S., On the efficiency of the sample mean in longmemory noise, J. Time Series Analysis, 9 (1988), 191200.

  • [11]

    Vitale, R. A., An asymptotically efficient estimate in time series analysis, Quart. Appl. Math., 30 (1973), 421440.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE


  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • The ISI Alerting Services


Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333