Estimating the Structural Dimension of Regressions Via Parametric Inverse Regression

Bura, Efstathia; Cook, R. Dennis

doi:10.1111/1467-9868.00292

Cited by 118 publications

(98 citation statements)

References 26 publications

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“…Likelihood-based SDR methods can be compared to likelihood based estimation methods for DFM however we do not pursue such comparison in this paper for clarity purposes. 13 The rank of β is the structural dimension of the regression and d = 0 signifies that y t+h is independent of xt.…”

Section: The Sdr Forecasting Frameworkmentioning

confidence: 99%

“…Cook and his collaborators formalized the field in several papers (e.g. Cook and Weisberg (1991) [31]; Cook (1994), (1998b), (2007) [22][24] [26]; Cook and Lee (1999) [29]; Cook (2001a and2001b) [13] [14]; Cook and Yin (2001) [32]; Chiaromonte, Cook and Li (2002) [20]; Cook and Ni (2005) [30]; Forzani (2008 and [27] [28]) and a book (Cook 1998a [23]), where much of the SDR terminology was introduced.…”

Section: Introductionmentioning

confidence: 99%

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A Unified Framework for Dimension Reduction in Forecasting

Barbarino

Bura²

2017

FEDS

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Factor models are widely used in summarizing large datasets with few underlying latent factors and in building time series forecasting models for economic variables. In these models, the reduction of the predictors and the modeling and forecasting of the response y are carried out in two separate and independent phases. We introduce a potentially more attractive alternative, Sufficient Dimension Reduction (SDR), that summarizes x as it relates to y, so that all the information in the conditional distribution of y|x is preserved. We study the relationship between SDR and popular estimation methods, such as ordinary least squares (OLS), dynamic factor models (DFM), partial least squares (PLS) and RIDGE regression, and establish the connection and fundamental differences between the DFM and SDR frameworks. We show that SDR significantly reduces the dimension of widely used macroeconomic series data with one or two sufficient reductions delivering similar forecasting performance to that of competing methods in macro-forecasting. JEL Classification Number: C32, C53, C55, E17

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Section: The Sdr Forecasting Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Unified Framework for Dimension Reduction in Forecasting

Barbarino

Bura²

2017

FEDS

Self Cite

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“…This entity can be estimated in a number of different ways, for instance, parametrically as in [Bura and Cook, 2001] or nonparametrically as in [Li, 1991, Bura, 2003. In this paper we will make use of the latter methods, which will be referred to as sliced and local inverse regression, abbreviated SIR and LIR, respectively.…”

Section: Inverse Regressionmentioning

confidence: 99%

Inverse Regression for the Wiener Class of Systems

Lyzell

Enqvist

2012

IFAC Proceedings Volumes

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The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.Keywords: System identification; Dimension reduction; Inverse regression. Inverse Regression for the Wiener Class of SystemsChristian Lyzell, Martin Enqvist 2011-11-14 AbstractThe concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.

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“…In the one-dimensional case, it is well known that if ϕ(t) is elliptically distributed, the linear least-squares estimate of B is consistent [Bussgang, 1952]. In this paper, we are going to consider a related method called sliced inverse regression (SIR) [Li, 1991], which has had a considerable influence in the field of dimension reduction in the statistical community [see, for example, Bura and Cook, 2001, Li and Wang, 2007, Bura and Yang, 2011.…”

Section: Introductionmentioning

confidence: 99%

Sliced Inverse Regression for the Identification of Dynamical Systems

Lyzell

Enqvist

2012

IFAC Proceedings Volumes

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The estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called sliced inverse regression is presented and a consistency analysis for dynamically dependent variables is given. The straightforward system identification application is the estimation of the number of linear subsystems in a Wiener class system and their corresponding impulse response.Keywords: System identification; Dimension reduction; Inverse regression. Sliced Inverse Regression for the Identification of Dynamical SystemsChristian Lyzell, Martin Enqvist 2011-11-14 AbstractThe estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called sliced inverse regression is presented and a consistency analysis for dynamically dependent variables is given. The straightforward system identification application is the estimation of the number of linear subsystems in a Wiener class system and their corresponding impulse response.

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Estimating the Structural Dimension of Regressions Via Parametric Inverse Regression

Cited by 118 publications

References 26 publications

A Unified Framework for Dimension Reduction in Forecasting

A Unified Framework for Dimension Reduction in Forecasting

Inverse Regression for the Wiener Class of Systems

Sliced Inverse Regression for the Identification of Dynamical Systems

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