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

Leeb, Hannes; Pötscher, Benedikt M.

doi:10.1214/009053606000000821

Cited by 205 publications

(161 citation statements)

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“…Then Theorem 2.3 and the discussion following Proposition 2.5 show that the non-uniformity phenomenon always arises in this estimation problem in case O = 0. In case O > 0, the non-uniformity problem is generically also present, except in the degenerate case where C (q) ∞ = 0, for all q satisfying O < q ≤ P (in which case Proposition 4.4 in Leeb and Pötscher (2006b) shows that the least-squares predictors from all models M p , O ≤ p ≤ P , perform asymptotically equally well).…”

Section: Performance Limits and Impossibility Resultsmentioning

confidence: 99%

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Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators?

2007

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We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. 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 like 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 the unconditional 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 the distribution; performance is here measured by the probability that the estimation error exceeds a given threshold. These lower bounds are shown to approach 1/2 or even 1 in large samples, depending on the situation considered. Similar impossibility results are also obtained for the distribution of linear functions (e.g., predictors) of the post-model-selection estimator.

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Section: Performance Limits and Impossibility Resultsmentioning

confidence: 99%

“…Remark A.6.] A precursor to Proposition B.1(a) is Corollary 5.5 of Leeb and Pötscher (2003) Leeb and Pötscher (2006b).…”

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Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators?

2007

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“…Leeb and Pötscher (2006; show that the sampling distributions of post-model-selection parameter estimates are likely to be unknown, and probably unknowable, even asymptotically. Moreover, it does not seem to matter what kind of model selection approach 2 There are also the well-known difficulties that can follow from undertaking a large number of statistical tests.…”

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Statistical Inference After Model Selection

2009

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Conventional statistical inference requires that a model of how the data were generated be known before the data are analyzed. Yet in criminology, and in the social sciences more broadly, a variety of model selection procedures are routinely undertaken followed by statistical tests and confidence intervals computed for a "final" model. In this paper, we examine such practices and show how they are typically misguided. The parameters being estimated are no longer well defined, and post-model-selection sampling distributions are mixtures with properties that are very different from what is conventionally assumed. Confidence intervals and statistical tests do not perform as they should. We examine in some detail the specific mechanisms responsible. We also offer some suggestions for better practice and show though a criminal justice example using real data how proper statistical inference in principle may be obtained. Abstract Conventional statistical inference requires that a model of how the data were generated be known before the data are analyzed. Yet in criminology, and in the social sciences more broadly, a variety of model selection procedures are routinely undertaken followed by statistical tests and confidence intervals computed for a "final" model. In this paper, we examine such practices and show how they are typically misguided. The parameters being estimated are no longer well defined, and post-model-selection sampling distributions are mixtures

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“…Otro desarrollo del modelo lineal clásico de la regresión, enriquecido con el análisis factorial, ha evolucionado hacia el establecimiento y estimación de modelos de ecuaciones estructurales, que comprende una extensa literatura (Berk 2004;Berk, Brown y Zhao, 2010a;Box 1976;Breiman 2001;Freedman 1987Freedman , 2005Holland 1986;Leeb y Pötscher, 2006).…”

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La metodología cuantitativa aplicada al estudio de la reincidencia en menores infractores

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This dissertation advances the outstanding importance about the use of the quantitative methodology in order to study the variables that lead to recidivism among young offenders. The quantitative research in criminology has been scarce in Spain. Two reasons explain this fact. First the lack of exhaustive and on-going statistics data base, at the national level as in the Anglo-Saxon countries. Second the short tradition in social empiric transversal and longitudinal cohort studies.Methodologically, a distinction has been drawn between studies on judicial practice (files opened, offences committed, cautions, etc..) with young offenders and studies on juvenile delinquency and re-offending that rest more heavily upon the examinations and evaluation of young offenders carried out by the service professionals (psychologists and social workers), in the Juvenile Courts. This study belongs to this last category. The chief advantage coming from official records is that they provide thorough, unique information that can be used in analyses in many different ways Empirical studies on re-offending in the field of juvenile delinquency reflect the great complexity of the existing literature. Contradictory findings have been achieved due to differences in data collection and methodological problems (research design and statistical processing).Hence, the aim of this research is twofold. First, it intends to apply the Ordinal Logistic Regression, selecting the proportional odds model or cumulative logit model to demonstrate its utility. To accomplish this objective, the SPSS statistics module, that implements the Polytomic Universal Model is used. Second, it also seeks to determine the influence of psychological, behaviour, school, work and social variables on rates of recidivism in young offenders in order to advance a predictive integrated reliable model with internal and ecological validity. 6The sample consisted of 2369 young male offenders and 617 young female offenders, that is, a total of 2986 subjects, with ages ranging from 12 to 21 years. The mean is 15 years and 8 months and the standard deviation 15,12 months. The number of young offenders who had committed more than one offence accounted for 10,9% of the total sampleThe instrument used in this study is the Youth Assessment Report, drawn up by the service professionals in Castellón's Juvenile Court.The dependent variable is brought about by means of the "number of further offences committed". The cases of re-offending are a sequence of frequencies, which can be interpreted as an ordinal-type accumulative categorical scale.The independent variables are Gender, Age at the time of first offence, Poor social skills, Impulsiveness, Anxiety, Academic failure, Substance abuse and the interaction between Impulsiviness and Substance abuse.All of the single independent variables have statistical significance as they also do when integrated in a joint model that has internal and ecological validity reflected in the concordance between the empirical and predicted data.The...

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

Cited by 205 publications

References 23 publications

Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators?

Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators?

Statistical Inference After Model Selection

La metodología cuantitativa aplicada al estudio de la reincidencia en menores infractores

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