Curved Exponential Models in Econometrics

Garderen, Kees Jan van

doi:10.1017/s0266466600006253

Cited by 14 publications

(9 citation statements)

References 32 publications

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“…Note that the vector π k (β k ) has zeros for regressors that do not appear in the kth model. Garderen (1997) shows that this model is a curved exponential model provided that the matrix Π has some zero restrictions. Consider the assumptions of Section 4.11.…”

Section: Seemingly Unrelated Regression Equationsmentioning

confidence: 98%

Posterior inference in curved exponential families under increasing dimensions

Belloni¹,

Chernozhukov²

2013

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Summary This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in econometrics and others branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties of estimation and inference procedures based on the posterior. In the process we also revisit and improve upon previous results for the exponential family under increasing dimension by making use of concentration of measure. We also discuss a variety of applications to high-dimensional versions of the classical econometric models including the multinomial model with moment restrictions, seemingly unrelated regression equations, and single structural equation models. In our analysis, both the parameter dimension and the number of moments are increasing with the sample size.

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Section: Seemingly Unrelated Regression Equationsmentioning

confidence: 98%

Posterior inference in curved exponential families under increasing dimensions

Belloni¹,

Chernozhukov²

2013

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“…Van Garderen (1997) has shown that this model is a curved exponential model provided that the matrix has some zero restrictions. Let d z denote the total number of distinct covariates.…”

Section: Seemingly Unrelated Regression Equationsmentioning

confidence: 99%

“…and by using the (trace) inner product θ, X = tr(X 1 θ 1 ) + tr(X 2 θ 2 ); see, e.g., van Garderen (1997). This parametrization leads to the normalizing function…”

Section: Multivariate Linear Modelmentioning

confidence: 99%

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Posterior inference in curved exponential families under increasing dimensions

Belloni

Chernozhukov

2014

The Econometrics Journal

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In this paper, we study the large-sample properties of the posterior-based inference in the curved exponential family under increasing dimensions. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in econometrics and others branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties of estimation and inference procedures based on the posterior. In the process, we also revisit and improve upon previous results for the exponential family under increasing dimensions by making use of concentration of measure. We also discuss a variety of applications to high-dimensional versions of classical econometric models, including the multinomial model with moment restrictions, seemingly unrelated regression equations, and single structural equation models. In our analysis, both the parameter dimensions and the number of moments are increasing with the sample size.

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“…This density is said to belong to the exponential family model, with natural parameter θ , canonical parameter a (θ) and canonical statistic g (x) (e.g. [16]). The Gaussian, the Poisson and the Binomial distributions all belong to this family.…”

Section: Example 22mentioning

confidence: 99%

Nearest neighbor conditional estimation for Harris recurrent Markov chains

Sancetta

2009

Journal of Multivariate Analysis

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a b s t r a c tThis paper is concerned with consistent nearest neighbor time series estimation for data generated by a Harris recurrent Markov chain on a general state space. It is shown that nearest neighbor estimation is consistent in this general time series context, using simple and weak conditions. The results proved here, establish consistency, in a unified manner, for a large variety of problems, e.g. autoregression function estimation, and, more generally, extremum estimators as well as sequential forecasting. Finally, under additional conditions, it is also shown that the estimators are asymptotically normal.

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Curved Exponential Models in Econometrics

Cited by 14 publications

References 32 publications

Posterior inference in curved exponential families under increasing dimensions

Posterior inference in curved exponential families under increasing dimensions

Posterior inference in curved exponential families under increasing dimensions

Nearest neighbor conditional estimation for Harris recurrent Markov chains

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