Optimality of equidistant sampling designs for the Brownian motion with a quadratic drift

被引：7

作者：

Harman, Radoslav ^{[1
]}

Stulajter, Frantisek ^{[1
]}

机构：

[1] Comenius Univ, Dept Appl Math & Stat, Fac Math Phys & Informat, Bratislava, Slovakia

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2011年 / 141卷 / 08期

关键词：

Brownian motion; Estimation; Loewner ordering; Optimal design; Prediction; Wiener process; CORRELATED ERRORS; REGRESSION PROBLEMS; PARAMETERS;

D O I：

10.1016/j.jspi.2011.02.025

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In the paper we show that the equidistant sampling designs are optimal for the model of Brownian motion with a quadratic drift and for any of its submodels. This result holds for all Loewner isotonic criteria of parametric optimality continuous on the set of regular information matrices, as well as for the mean squared error of the best linear unbiased predictor. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2750 / 2758

页数：9

共 11 条

[1]

[Anonymous], OPTIMAL DESIGN EXPT

[2]

Dette H, 2008, STAT SINICA, V18, P135

[3] BEST LINEAR UNBIASED PREDICTION IN GENERALIZED LINEAR-REGRESSION MODEL [J].

GOLDBERGER, AS .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1962, 57 (298) :369-&

[4]

HARMAN R, 2009, P 6 ST PET WORKSH SI, P1097

[5] Equidistant and D-optimal designs for parameters of Ornstein-Uhlenbeck process [J].

Kiselak, Jozef ;

Stehlik, Milan .

STATISTICS & PROBABILITY LETTERS, 2008, 78 (12) :1388-1396

[6] Exactly optimal sampling designs for processes with a product covariance structure [J].

Mukherjee, B .

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2003, 31 (01) :69-87

[7]

Pazman A., 1986, Foundations of optimum experimental design

[8] DESIGNS FOR REGRESSION PROBLEMS WITH CORRELATED ERRORS [J].

SACKS, J ;

YLVISAKE.D .

ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (01) :66-&

[9] DESIGNS FOR REGRESSION PROBLEMS WITH CORRELATED ERRORS - MANY PARAMETERS [J].

SACKS, J ;

YLVISAKER, D .

ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (01) :49-+

[10]

Stulajter F., 2002, PREDICTIONS TIME SER

← 1 2 →