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Abstract:

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates. © 2018, © 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Registro:

Documento: Artículo
Título:Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
Autor:Bura, E.; Duarte, S.; Forzani, L.; Smucler, E.; Sued, M.
Filiación:Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
Department of Statistics, George Washington University, Washington, DC, United States
Facultad de Ingeniería Química, UNL, Santa Fe, Argentina
Department of Statistics, University of British Columbia, Vancouver, BC, Canada
Instituto de Cálculo, UBA, Buenos Aires, Argentina
Palabras clave:exponential family; M-estimation; non-convex; parameter spaces; rank restriction
Año:2018
Volumen:52
Número:5
Página de inicio:1005
Página de fin:1024
DOI: http://dx.doi.org/10.1080/02331888.2018.1467420
Título revista:Statistics
Título revista abreviado:Statistics
ISSN:02331888
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02331888_v52_n5_p1005_Bura

Referencias:

  • Reinsel, G.C., Velu, R.P., (1998) Multivariate reduced rank regression, , New York: Springer
  • Anderson, T.W., Estimating linear restrictions on regression coefficients for multivariate normal distributions (1951) Ann Math Statist, 22, pp. 327-351
  • Izenman, A.J., Reduced-rank regression for the multivariate linear model (1975) J Multivariate Anal, 5, pp. 248-264
  • Izenman, A.J., (2008) Modern multivariate. Statistical techniques: regression, classification and manifold learning, , New York: Springer
  • Fan, J., Gong, W., Zhu, Z., http://https://arxiv.org/pdf/1710.08083.pdf, Generalized high-dimensional trace regression via nuclear norm regularization; 2017 [cited 2017 Oct 23]. pre-print, available from; Yee, T.W., Hastie, T.J., Reduced-rank vector generalized linear models (2003) Stat Model, 3, pp. 15-41
  • Yee, T.W., (2015) Vector generalized linear and additive models, , New York: Springer
  • Bura, E., Duarte, S., Forzani, L., Sufficient reductions in regressions with exponential family inverse predictors (2016) J Amer Statist Assoc, 111, pp. 1313-1329
  • Huber, P.J., The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, 1, 1; 1967. p. 221–233; Haberman, S.J., Concavity and estimation (1989) Ann Statist, 17, pp. 1631-1661
  • Niemiro, W., Asymptotics for M-estimators defined by convex minimization (1992) Ann Statist, 20, pp. 1514-1533
  • Hjort, N.L., Pollard, D., Asymptotics for minimisers of convex processes; 2011; Geyer, C.J., On the asymptotics of constrained M-estimation (1994) Ann Statist, 22, pp. 1993-2010
  • van der Vaart, A.W., (2000) Asymptotic statistics, , Cambridge: Cambridge University Press
  • Yee, T.W., http://https://CRAN.R-project.org/package=VGAM, VGAM: vector generalized linear and additive models. R package version 1.0-3. 2015 [cited 2018 Feb 7]. Available from; Wasserman, L., (2013) All of statistics: a concise course in statistical inference, , New York: Springer-Verlag
  • Duarte, S.L., Modelos lineales generalizados: regresión de rango reducido y reducción suficiente de dimensiones [Tesis Doctoral]. Argentina: Universidad Nacional del Litoral; 2016; Bura, E., Yang, J., Dimension estimation in sufficient dimension reduction: a unifying approach (2011) J Multivariate Anal, 102, pp. 130-142
  • Yee, T.W., Wild, C.J., Vector generalized additive models (1996) J R Stat Soc Ser B, 58 (3), pp. 481-493
  • Powers, S., Hastie, T., Tibshirani, R., Nuclear penalized multinomial regression with an application to predicting at-bat outcomes baseball. To appear special edition ‘Statistical Modelling for Sports Analytics,’ Statistical Modelling; 2018; Cook, R.D., Ni, L., Sufficient dimension reduction via inverse regression: a minimum discrepancy approach (2005) J Amer Statist Assoc, 100, pp. 410-428
  • Puntanen, S., Styan, G.P., Isotalo, J., (2011) Matrix tricks for linear statistical models: our personal top twenty, , Berlin Heidelberg: Springer Science and Business Media

Citas:

---------- APA ----------
Bura, E., Duarte, S., Forzani, L., Smucler, E. & Sued, M. (2018) . Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models. Statistics, 52(5), 1005-1024.
http://dx.doi.org/10.1080/02331888.2018.1467420
---------- CHICAGO ----------
Bura, E., Duarte, S., Forzani, L., Smucler, E., Sued, M. "Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models" . Statistics 52, no. 5 (2018) : 1005-1024.
http://dx.doi.org/10.1080/02331888.2018.1467420
---------- MLA ----------
Bura, E., Duarte, S., Forzani, L., Smucler, E., Sued, M. "Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models" . Statistics, vol. 52, no. 5, 2018, pp. 1005-1024.
http://dx.doi.org/10.1080/02331888.2018.1467420
---------- VANCOUVER ----------
Bura, E., Duarte, S., Forzani, L., Smucler, E., Sued, M. Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models. Statistics. 2018;52(5):1005-1024.
http://dx.doi.org/10.1080/02331888.2018.1467420