The β-Model-Maximum Likelihood, Cramer-Rao Bounds, and Hypothesis Testing

被引：5
|
作者：
Wahlstrom, Johan [1 ]
Skog, Isaac [1 ]
La Rosa, Patricio S. [2 ,3 ]
Handel, Peter [1 ]
Nehorai, Arye [4 ]
机构：
[1] KTH Royal Inst Technol, ACCESS Linnaeus Ctr, Dept Signal Proc, S-11428 Stockholm, Sweden
[2] Monsanto Co, Global IT Analyt, St Louis, MO 63167 USA
[3] Washington Univ St Louis, Sch Engn, St Louis, MO 63130 USA
[4] Washington Univ St Louis, Dept Elect & Syst Engn, St Louis, MO 63130 USA
来源：
IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2017年 / 65卷 / 12期
关键词：
The beta-model; Cramer-Rao bounds; hypothesis testing; random graphs; dynamic social networks; RANDOM GRAPHS; ASYMPTOTICS; NUMBER;
D O I：
10.1109/TSP.2017.2691667
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
We study the maximum-likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level. The model generalizes the well-known beta-model for random graphs by replacing the constant model parameters with regression functions. Cramer-Rao bounds are derived for special cases of the undirected beta-model, the directed beta-model, and the covariate-based beta-model. The corresponding maximum-likelihood estimators are compared with the bounds by means of simulations. Moreover, examples are given on how to use the presented maximum-likelihood estimators to test for directionality and significance. Finally, the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers.
引用
收藏
页码：3234 / 3246
页数：13
相关论文
共 44 条
  • [1] Inertial Sensor Arrays, Maximum Likelihood, and Cramer-Rao Bound
    Skog, Isaac
    Nilsson, John-Olof
    Handel, Peter
    Nehorai, Arye
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2016, 64 (16) : 4218 - 4227
  • [2] Cramer-Rao bounds for synchronization of rotations
    Boumal, Nicolas
    Singer, Amit
    Absil, P. -A.
    Blondel, Vincent D.
    INFORMATION AND INFERENCE-A JOURNAL OF THE IMA, 2014, 3 (01) : 1 - 39
  • [3] Cramer-Rao bounds: an evaluation tool for quantitation
    Cavassila, S
    Deval, S
    Huegen, C
    van Ormondt, D
    Graveron-Demilly, D
    NMR IN BIOMEDICINE, 2001, 14 (04) : 278 - 283
  • [4] CRAMER-RAO BOUNDS FOR THE LOCALIZATION OF ANISOTROPIC SOURCES
    Monier, E.
    Chardon, G.
    2017 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2017, : 3281 - 3285
  • [5] Cramer-Rao bounds for fractional Brownian motions
    Coeurjolly, JF
    Istas, J
    STATISTICS & PROBABILITY LETTERS, 2001, 53 (04) : 435 - 447
  • [6] Accurate Cramer-Rao bounds for a laser Doppler anemometer
    Sobolev, VS
    Feshenko, AA
    IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 2006, 55 (02) : 659 - 665
  • [7] Cramer-Rao bounds for variance of Fourier magnitude measurements
    Holmes, Richard
    Calef, Brandoch
    Gerwe, David
    Dolne, Jean
    Crabtree, Peter
    UNCONVENTIONAL IMAGING AND WAVEFRONT SENSING 2013, 2013, 8877
  • [8] CRAMER-RAO BOUNDS AND INSTRUMENT OPTIMIZATION FOR SLITLESS SPECTROSCOPY
    Oktem, Figen S.
    Kamalabadi, Farzad
    Davila, Joseph M.
    2013 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2013, : 2169 - 2173
  • [9] Cramer-Rao bounds for circadian rhythm parameter estimation
    Zarowski, C
    Kropyvnytskyy, I
    IEEE CCEC 2002: CANADIAN CONFERENCE ON ELECTRCIAL AND COMPUTER ENGINEERING, VOLS 1-3, CONFERENCE PROCEEDINGS, 2002, : 1083 - 1086
  • [10] Cramer-Rao bound and maximum likelihood estimation of covariance matrices with non-homogeneous snapshots
    Besson, Olivier
    Bidon, Stephanie
    Yourneret, Jean-Yves
    CONFERENCE RECORD OF THE FORTY-FIRST ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS & COMPUTERS, VOLS 1-5, 2007, : 2213 - +
12345