Least squares, preliminary test and Stein‐type estimation in general vector <i>AR</i>(<i>p</i>) models

Ahmed, S. Ejaz; Basu, A. K.

doi:10.1111/1467-9574.00125

Cited by 10 publications

(7 citation statements)

References 9 publications

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“…The distributions of corresponding linear predictors constructed after model selection were studied in [10,11]. Related work can also be found in [1,5,7,8,9,15,19,24].…”

mentioning

confidence: 99%

Can one estimate the conditional distribution of post-model-selection estimators?

Leeb¹,

Pötscher²

2006

Ann. Statist.

205

148

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We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion such as AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for this distribution. Similar impossibility results are also obtained for the conditional distribution of linear functions (e.g., predictors) of the post-model-selection estimator.

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“…The distributions of corresponding linear predictors constructed after model selection were studied in [10,11]. Related work can also be found in [1,5,7,8,9,15,19,24].…”

mentioning

confidence: 99%

Can one estimate the conditional distribution of post-model-selection estimators?

Leeb¹,

Pötscher²

2006

Ann. Statist.

205

148

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“…The finite sample distribution theory of these SEs is not simple to obtain. This difficulty has been largely overcome by asymptotic methods (A hmed and B asu 2000; A hmed , 2001; Saleh 2006 and others). These asymptotic methods relate primarily to convergence in distribution which may not generally guarantee convergence in quadratic risk.…”

Section: Estimation Strategiesmentioning

confidence: 99%

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

Nkurunziza¹,

Ahmed²

2011

Statistica Neerlandica

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We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators.We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes.

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“…Preliminary test estimation in elliptical models has been considered in the contexts of linear regression and of principal component analysis; see Arashi et al (2014) and Paindaveine et al (2017), respectively. It has also been widely considered in time series analysis; see, for example, Ahmed and Basu (2000), Maeyama et al (2011), and the references therein. For a general overview of the topic, we refer to Giles and Giles (1993) and Saleh (2006).…”

Section: Introductionmentioning

confidence: 99%

Preliminary test estimation in uniformly locally asymptotically normal models

Paindaveine

Rasoafaraniaina

Verdebout

2021

Scandinavian J Statistics

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Preliminary test estimation is a methodology that combines goodness-of-fit testing and estimation. It is a classical procedure when it is suspected that the parameter to be estimated satisfies some prespecified constraints.In the present paper, we establish general results on the asymptotic behavior of preliminary test estimators. More precisely, we show that, in uniformly locally asymptotically normal (ULAN) models, a general asymptotic theory can be derived for preliminary test estimators based on estimators admitting generic Bahadur-type representations. This allows for a detailed comparison between classical estimators and preliminary test estimators in ULAN models. Our results, that, in standard linear regression models, are shown to reduce to some classical results, are also illustrated in more modern and involved setups, such as the multisample one where m covariance matrices 1 , … , m are to be estimated when it is suspected that these matrices might be equal, might be proportional, or might share a common "scale". Simulation results confirm our theoretical findings and an illustration on a real data example is provided.

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Least squares, preliminary test and Stein‐type estimation in general vector AR(p) models

Cited by 10 publications

References 9 publications

Can one estimate the conditional distribution of post-model-selection estimators?

Can one estimate the conditional distribution of post-model-selection estimators?

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

Preliminary test estimation in uniformly locally asymptotically normal models

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