Limiting Behavior of Posterior Distributions when the Model is Incorrect

Berk, Robert H.

doi:10.1214/aoms/1177699597

“…Neo-additive capacities are an analytically very 7 Convergence to the true parameter value only occurs if the prior is well-speci…ed, i.e., has this true value in its support; (the seminal contribution is Doob 1949). For a more general convergence result-including misspeci…ed priors-in terms of minimization of the Kullback-Leibler divergence, see Berk (1966). tractable class of non-additive probability measures which are used in the literature 8 to approximate inverse S-shaped probability weighting functions as typically elicited for CPT (cf., e.g., Tversky and Kahneman 1992;Wu and Gonzalez 1996;1999).…”

Section: Bayesian Learning Of Ambiguous Survival Beliefsmentioning

confidence: 99%

A Life-Cycle Model with Ambiguous Survival Beliefs

Groneck

¹

,

Ludwig

²

,

Zimper

³

2014

View full text Add to dashboard Cite

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Non-Technical SummaryOptimal tax and transfer systems are key for the design of modern economics. One of the workhorse models used by economists to evaluate the welfare benefits of (reforms to) these systems is the life-cycle model of consumption and savings. The model can, e.g., be used to investigate the reactions of households to savings subsidies or any other kind of reform to old-age insurance, or, more general, any institutional feature of the tax-transfer system.Yet, from a quantitative perspective, it is well known that the standard model produces several "puzzles" in a sense that the standard model cannot match certain facts in the data. It is well established that, relative to an optimal saving rate according to the model, households save too little in the data. Furthermore, the decumulation speed of assets in old-age is much lower in the data than predicted by the standard model. Finally, households behave dynamically inconsistent, in a sense that they generally save less during working life for retirement than they originally planned. Such inconsistencies cannot be accommodated by the standard model.In order to generate correct quantitative predictions it is therefore important to modify the standard model in order to account for these three empirical regularities. This is the aim of the present paper.The specific model element under investigation is the life-expectancy of households which is one of the most important ingredients of the model. Obviously, survival beliefs are of high relevance for savings behavior. The standard model uses objective data on survival beliefs, traced out from population wide survival tables. However, in several datasets that explicitly ask for subjective survival beliefs, substantial biases in survival beliefs relative to such objective data can be observed. E.g., young people strongly underestimate whereas old people (after retirement) strongly overestimate their chances to survive into the future. This paper addresses the question how these biases in survival beliefs may alter model savings behavior, thereby bringing model predictions closer to the data on household savings. On the one hand, underestimation of survival beliefs may lead to lower savings than in the standard model. On the other hand, overestimation in old-age may lead to the fact that households hold on to their assets longer in life than predicted by the standard model.To test whether the observed biases in survival be...

show abstract

“…Aside from large deviation results such as Thm. 1, there exist strong law results, see [39]. The following proof is obtained by combining ideas taken from [33] and [34].…”

Section: A Proof Of Theoremmentioning

confidence: 94%

On U-Statistics and Compressed Sensing I: Non-Asymptotic Average-Case Analysis

Lim

¹

,

Stojanović

²

2013

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime (relevant to practice). The aim is to address certain pessimisms of "worst-case" restricted isometry analyses, as observed by both Blanchard & Dossal, et. al.We show how U-statistics can obtain "average-case" analyses, by relating to statistical restricted isometry property (StRIP) type recovery guarantees. However unlike standard StRIP, random signal models are not required; the analysis here holds in the almost sure (probabilistic) sense. For Gaussian/bounded entry matrices, we show that both ℓ1-minimization and LASSO essentially require on the order of k · [log((n − k)/u) + 2(k/n) log(n/k)] measurements to respectively recover at least 1−5u fraction, and 1 − 4u fraction, of the signals. Noisy conditions are considered. Empirical evidence suggests our analysis to compare well to Donoho & Tanner's recent large deviation bounds for ℓ0/ℓ1-equivalence, in the regime of block lengths 1000 ∼ 3000 with high undersampling (50 ∼ 150 measurements); similar system sizes are found in recent CS implementation.In this work, it is assumed throughout that matrix columns are independently sampled.

show abstract

“…There is also evidence that explicitly modeling the serial correlation in the context of a Markov Switching model of leading indicators as a filter jeopardizes turning point predictions, see Lahiri and Wang (1994). Fortunately, P(θ|X T ) under this type of model misspecification can be asymptotically approximated by a multivariate normal distribution with the maximum likelihood estimatorθ as its mean and the inverse of the estimated negative Hessian matrix as its covariance (Berk (1966), Bunke and Milhaud (1998), and Geweke (2005)). However, Müller (2013) has shown that the asymptotic frequentist risk associated with the posterior inference is systematically lower if the asymptotic variance of the normal posterior is replaced by a sandwich covariance matrix, which is routinely used in obtaining robust standard errors in the frequentist approach.…”

Section: Robust Inferencementioning

confidence: 99%

A non-linear forecast combination procedure for binary outcomes

Lahiri

¹

,

Liu²

2016

Studies in Nonlinear Dynamics &Amp; Econometrics

3

0

View full text Add to dashboard Cite

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We develop a non-linear forecast combination rule based on copulas that incorporate the dynamic interaction between individual predictors. This approach is optimal in the sense that the resulting combined forecast produces the highest discriminatory power as measured by the receiver operating characteristic (ROC) curve. Under additional assumptions, this rule is shown to be equivalent to the quintessential linear combination scheme. To illustrate its usefulness, we apply this methodology to optimally aggregate two currently used leading indicators-the ISM new order diffusion index and the yield curve spread-to predict economic recessions in the United States. We also examine the sources of forecasting gains using a counterfactual experimental set up. Terms of use: Documents in

show abstract

Limiting Behavior of Posterior Distributions when the Model is Incorrect

Cited by 346 publications

References 4 publications

A Life-Cycle Model with Ambiguous Survival Beliefs

A Life-Cycle Model with Ambiguous Survival Beliefs

On U-Statistics and Compressed Sensing I: Non-Asymptotic Average-Case Analysis

A non-linear forecast combination procedure for binary outcomes

Contact Info

Product

Resources

About