Zeitschriftenartikel: „Misspecified bounds“

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Liu, Changyu, Yuling Jiao, Junhui Wang und Jian Huang. „Nonasymptotic Bounds for Adversarial Excess Risk under Misspecified Models“. SIAM Journal on Mathematics of Data Science 6, Nr. 4 (01.10.2024): 847–68. http://dx.doi.org/10.1137/23m1598210.

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2

Teichner, Ron, und Ron Meir. „Kalman smoother error bounds in the presence of misspecified measurements“. IFAC-PapersOnLine 56, Nr. 2 (2023): 10252–57. http://dx.doi.org/10.1016/j.ifacol.2023.10.907.

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3

Fudenberg, Drew, Giacomo Lanzani und Philipp Strack. „Pathwise concentration bounds for Bayesian beliefs“. Theoretical Economics 18, Nr. 4 (2023): 1585–622. http://dx.doi.org/10.3982/te5206.

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We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated‐utility” models, and extend our analysis to outcomes that are perceived to follow a Markov process.

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Lu, Shuai, Peter Mathé und Sergiy Pereverzyev. „Analysis of regularized Nyström subsampling for regression functions of low smoothness“. Analysis and Applications 17, Nr. 06 (23.09.2019): 931–46. http://dx.doi.org/10.1142/s0219530519500039.

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This paper studies a Nyström-type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood in spite of its practical importance. To model such a case, the smoothness of target functions is described in terms of general source conditions. It is surprising that almost for the whole range of the source conditions, describing the misspecified case, the corresponding learning rate bounds can be achieved with just one value of the regularization parameter. This observation allows a formulation of mild conditions under which the plain Nyström subsampling can be realized with subquadratic cost maintaining the guaranteed learning rates.

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Wang, Ke, und Hong Yue. „Sampling Time Design with Misspecified Cramer-Rao Bounds under Input Uncertainty“. IFAC-PapersOnLine 58, Nr. 14 (2024): 622–27. http://dx.doi.org/10.1016/j.ifacol.2024.08.406.

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6

Fortunati, Stefano, Fulvio Gini, Maria S. Greco und Christ D. Richmond. „Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications“. IEEE Signal Processing Magazine 34, Nr. 6 (November 2017): 142–57. http://dx.doi.org/10.1109/msp.2017.2738017.

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7

Salmon, Mark. „EDITOR'S INTRODUCTION“. Macroeconomic Dynamics 6, Nr. 1 (Februar 2002): 1–4. http://dx.doi.org/10.1017/s1365100502027013.

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The papers collected in this issue are united in a common view that it is rational to recognize that we have a poor perception of the constraints we face when making economic decisions and hence we employ decision rules that are robust. Robustness can be interpreted in different ways but generally it implies that our decision rules should not depend critically on an exact description of these constraints but they should perform well over a prespecified range of potential variations in the assumed economic environment. So, we are interested in deriving optimal and hence rational decisions where our utility or loss function incorporates the need for robustness in the face of a misspecified model. This misspecification can involve placing simple bounds on deviations from the parameters we assume for a nominal model, or misspecified dynamics, neglected nonlinearities, time variation, or quite general arbitrary misspecification in the transfer function between the input uncertainties and the output variables in which we are ultimately interested.

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Cheng, Xu, Zhipeng Liao und Ruoyao Shi. „On uniform asymptotic risk of averaging GMM estimators“. Quantitative Economics 10, Nr. 3 (2019): 931–79. http://dx.doi.org/10.3982/qe711.

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This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite‐sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. The results apply to quadratic loss functions. This uniform asymptotic dominance is established in non‐Gaussian semiparametric nonlinear models.

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Banerjee, Imon, Vinayak A. Rao und Harsha Honnappa. „PAC-Bayes Bounds on Variational Tempered Posteriors for Markov Models“. Entropy 23, Nr. 3 (06.03.2021): 313. http://dx.doi.org/10.3390/e23030313.

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Datasets displaying temporal dependencies abound in science and engineering applications, with Markov models representing a simplified and popular view of the temporal dependence structure. In this paper, we consider Bayesian settings that place prior distributions over the parameters of the transition kernel of a Markov model, and seek to characterize the resulting, typically intractable, posterior distributions. We present a Probably Approximately Correct (PAC)-Bayesian analysis of variational Bayes (VB) approximations to tempered Bayesian posterior distributions, bounding the model risk of the VB approximations. Tempered posteriors are known to be robust to model misspecification, and their variational approximations do not suffer the usual problems of over confident approximations. Our results tie the risk bounds to the mixing and ergodic properties of the Markov data generating model. We illustrate the PAC-Bayes bounds through a number of example Markov models, and also consider the situation where the Markov model is misspecified.

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Ortega, Lorenzo, Corentin Lubeigt, Jordi Vilà-Valls, und Eric Chaumette. „On GNSS Synchronization Performance Degradation under Interference Scenarios: Bias and Misspecified Cramér-Rao Bounds“. NAVIGATION: Journal of the Institute of Navigation 70, Nr. 4 (2023): navi.606. http://dx.doi.org/10.33012/navi.606.

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11

Armstrong, Timothy B., und Michal Kolesár. „Sensitivity analysis using approximate moment condition models“. Quantitative Economics 12, Nr. 1 (2021): 77–108. http://dx.doi.org/10.3982/qe1609.

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We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.

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Armstrong, Timothy B., und Michal Kolesár. „Sensitivity analysis using approximate moment condition models“. Quantitative Economics 12, Nr. 1 (2021): 77–108. http://dx.doi.org/10.3982/qe1609.

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We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.

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Mennad, Abdelmalek, Stefano Fortunati, Mohammed Nabil El Korso, Arezki Younsi, Abdelhak M. Zoubir und Alexandre Renaux. „Slepian-Bangs-type formulas and the related Misspecified Cramér-Rao Bounds for Complex Elliptically Symmetric distributions“. Signal Processing 142 (Januar 2018): 320–29. http://dx.doi.org/10.1016/j.sigpro.2017.07.029.

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14

Fortunati, Stefano, Fulvio Gini und Maria S. Greco. „The Constrained Misspecified Cramér–Rao Bound“. IEEE Signal Processing Letters 23, Nr. 5 (Mai 2016): 718–21. http://dx.doi.org/10.1109/lsp.2016.2546383.

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15

Waldorp, L. J., H. M. Huizenga und R. P. P. P. Grasman. „The Wald test and Crame/spl acute/r-Rao bound for misspecified models in electromagnetic source analysis“. IEEE Transactions on Signal Processing 53, Nr. 9 (September 2005): 3427–35. http://dx.doi.org/10.1109/tsp.2005.853213.

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16

Fortunati, Stefano, Fulvio Gini und Maria S. Greco. „The Misspecified Cramer-Rao Bound and Its Application to Scatter Matrix Estimation in Complex Elliptically Symmetric Distributions“. IEEE Transactions on Signal Processing 64, Nr. 9 (Mai 2016): 2387–99. http://dx.doi.org/10.1109/tsp.2016.2526961.

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17

van de Geer, Sara, Peter Bühlmann und Shuheng Zhou. „The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso)“. Electronic Journal of Statistics 5 (2011): 688–749. http://dx.doi.org/10.1214/11-ejs624.

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18

Ranger, Jochen, Jörg Tobias Kuhn und Tuulia M. Ortner. „Modeling Responses and Response Times in Tests With the Hierarchical Model and the Three-Parameter Lognormal Distribution“. Educational and Psychological Measurement 80, Nr. 6 (17.03.2020): 1059–89. http://dx.doi.org/10.1177/0013164420908916.

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The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels—one for the responses and one for the response times—that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a skew distribution with a support from zero to infinity. Such a support is unrealistic as the solution process demands a minimal processing time that sets a response time threshold. Ignoring this response time threshold misspecifies the model and threatens the validity of model-based inferences. In this article, the response time model of van der Linden is replaced by a model that is based on the three-parameter lognormal distribution. The three-parameter lognormal distribution extends the lognormal distribution by an additional location parameter that bounds the support away from zero. Two different approaches to model fitting are proposed and evaluated with regard to parameter recovery in a simulation study. The extended model is applied to two data sets. In both data sets, the extension improves the fit of the hierarchical model.

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Fudenberg, Drew, Giacomo Lanzani und Philipp Strack. „Pathwise Concentration Bounds for Misspecified Bayesian Beliefs“. SSRN Electronic Journal, 2021. http://dx.doi.org/10.2139/ssrn.3805083.

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20

Betz, Timm, Scott J. Cook und Florian M. Hollenbach. „Bias from Network Misspecification Under Spatial Dependence“. Political Analysis, 23.11.2020, 1–7. http://dx.doi.org/10.1017/pan.2020.26.

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Abstract The prespecification of the network is one of the biggest hurdles for applied researchers in undertaking spatial analysis. In this letter, we demonstrate two results. First, we derive bounds for the bias in nonspatial models with omitted spatially-lagged predictors or outcomes. These bias expressions can be obtained without prior knowledge of the network, and are more informative than familiar omitted variable bias formulas. Second, we derive bounds for the bias in spatial econometric models with nondifferential error in the specification of the weights matrix. Under these conditions, we demonstrate that an omitted spatial input is the limit condition of including a misspecificed spatial weights matrix. Simulated experiments further demonstrate that spatial models with a misspecified weights matrix weakly dominate nonspatial models. Our results imply that, where cross-sectional dependence is presumed, researchers should pursue spatial analysis even with limited information on network ties.

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Katsumata, Hiroto. „How should we estimate inverse probability weights with possibly misspecified propensity score models?“ Political Science Research and Methods, 15.08.2024, 1–22. http://dx.doi.org/10.1017/psrm.2024.23.

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Abstract Inverse probability weighting is a common remedy for missing data issues, notably in causal inference. Despite its prevalence, practical application is prone to bias from propensity score model misspecification. Recently proposed methods try to rectify this by balancing some moments of covariates between the target and weighted groups. Yet, bias persists without knowledge of the true outcome model. Drawing inspiration from the quasi maximum likelihood estimation with misspecified statistical models, I propose an estimation method minimizing a distance between true and estimated weights with possibly misspecified models. This novel approach mitigates bias and controls mean squared error by minimizing their upper bounds. As an empirical application, it gives new insights into the study of foreign occupation and insurgency in France.

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Nakakita, Shogo. „Parametric estimation of stochastic differential equations via online gradient descent“. Japanese Journal of Statistics and Data Science, 27.07.2024. http://dx.doi.org/10.1007/s42081-024-00266-x.

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AbstractWe propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the estimators over a family of stochastic differential equations. Theoretical guarantees for the estimation of stochastic differential equations with discrete observations by online gradient descent are novel to our best knowledge.

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Le, Trung Thanh, Karim Abed Meraim und Nguyen Linhtrung. „Misspecified Cramer-Rao Bounds for Blind Channel Estimation under Channel Order Misspecification“. IEEE Transactions on Signal Processing, 2021, 1. http://dx.doi.org/10.1109/tsp.2021.3111558.

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24

Yang, Lixiong. „High dimensional threshold model with a time-varying threshold based on Fourier approximation“. Studies in Nonlinear Dynamics & Econometrics, 30.05.2022. http://dx.doi.org/10.1515/snde-2021-0047.

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Abstract This paper studies high-dimensional threshold models with a time-varying threshold approximated using a Fourier function. We develop a weighted LASSO estimator of regression coefficients as well as the threshold parameters. Our LASSO estimator can not only select covariates but also distinguish between linear and threshold models. We derive non-asymptotic oracle inequalities for the prediction risk, the l 1 and l ∞ bounds for regression coefficients, and provide an upper bound on the l 1 estimation error of the time-varying threshold estimator. The bounds can be translated easily into asymptotic consistency for prediction and estimation. We also establish the variable selection consistency and threshold detection consistency based on the l ∞ bounds. Through Monte Carlo simulations, we show that the thresholded LASSO works reasonably well in finite samples in terms of variable selection, and there is little harmness by the allowance for Fourier approximation in the estimation procedure even when there is no time-varying feature in the threshold. On the contrary, the estimation and variable selection are inconsistent when the threshold is time-varying but being misspecified as a constant. The model is illustrated with an empirical application to the famous debt-growth nexus.

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Tan, Zhiqiang. „Model-assisted sensitivity analysis for treatment effects under unmeasured confounding via regularized calibrated estimation“. Journal of the Royal Statistical Society Series B: Statistical Methodology, 03.05.2024. http://dx.doi.org/10.1093/jrsssb/qkae034.

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Abstract Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model. At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions. We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression. At the sample level, we develop new methods and theory for obtaining not only doubly robust point estimators for the relaxed population bounds with respect to misspecification of a propensity score model or an outcome mean regression model, but also model-assisted confidence intervals which are valid if the propensity score model is correctly specified, but the outcome quantile and mean regression models may be misspecified. The relaxed population bounds reduce to the sharp bounds if outcome quantile regression is correctly specified. For a linear outcome mean regression model, the confidence intervals are also doubly robust. Our methods involve regularized calibrated estimation, with Lasso penalties but carefully chosen loss functions, for fitting propensity score and outcome mean and quantile regression models. We present a simulation study and an empirical application to an observational study on the effects of right-heart catheterization. The proposed method is implemented in the R package RCALsa.

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Xia, Fan, und Kwun Chuen Gary Chan. „Decomposition, identification and multiply robust estimation of natural mediation effects with multiple mediators“. Biometrika, 08.02.2022. http://dx.doi.org/10.1093/biomet/asac004.

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Summary Natural mediation effects are desirable estimands for studying causal mechanisms in a population, but complications arise in defining and estimating natural indirect effects through multiple mediators with an unspecified causal ordering. We propose a decomposition of the natural indirect effect of multiple mediators into individual components, termed exit indirect effects, and a remainder interaction term, and study the similarities to and differences from existing natural and interventional effects in the literature. We provide a set of identification assumptions for estimating all components of the proposed natural effect decomposition and derive the semiparametric efficiency bounds for the effects. The efficient influence functions contain conditional densities that are variationally dependent, which is uncommon in existing problems and may lead to model incompatibility. By ensuring model compatibility through a reparameterization based on copulas, our estimator is quadruply robust, which means that it remains consistent and asymptotically normal under four types of possible misspecification, and also is locally semiparametric efficient. We further propose a stabilized quadruply robust estimator to improve practical performance under possibly misspecified models, as well as a nonparametric extension based on sample splitting.

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Meylahn, Janusz M., und Arnoud V. den Boer. „Learning to Collude in a Pricing Duopoly“. Manufacturing & Service Operations Management, 10.02.2022. http://dx.doi.org/10.1287/msom.2021.1074.

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Problem definition: This paper addresses the question whether or not self-learning algorithms can learn to collude instead of compete against each other, without violating existing competition law. Academic/practical relevance: This question is practically relevant (and hotly debated) for competition regulators, and academically relevant in the area of analysis of multi-agent data-driven algorithms. Methodology: We construct a price algorithm based on simultaneous-perturbation Kiefer–Wolfowitz recursions. We derive theoretical bounds on its limiting behavior of prices and revenues, in the case that both sellers in a duopoly independently use the algorithm, and in the case that one seller uses the algorithm and the other seller sets prices competitively. Results: We mathematically prove that, if implemented independently by two price-setting firms in a duopoly, prices will converge to those that maximize the firms’ joint revenue in case this is profitable for both firms, and to a competitive equilibrium otherwise. We prove this latter convergence result under the assumption that the firms use a misspecified monopolist demand model, thereby providing evidence for the so-called market-response hypothesis that both firms’ pricing as a monopolist may result in convergence to a competitive equilibrium. If the competitor is not willing to collaborate but prices according to a strategy from a certain class of strategies, we prove that the prices generated by our algorithm converge to a best-response to the competitor’s limit price. Managerial implications: Our algorithm can learn to collude under self-play while simultaneously learn to price competitively against a ‘regular’ competitor, in a setting where the price-demand relation is unknown and within the boundaries of competition law. This demonstrates that algorithmic collusion is a genuine threat in realistic market scenarios. Moreover, our work exemplifies how algorithms can be explicitly designed to learn to collude, and demonstrates that algorithmic collusion is facilitated (a) by the empirically observed practice of (explicitly or implicitly) sharing demand information, and (b) by allowing different firms in a market to use the same price algorithm. These are important and concrete insights for lawmakers and competition policy professionals struggling with how to respond to algorithmic collusion.

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Levy-Israel, Moshe, Joseph Tabrikian und Igal Bilik. „Misspecified Cramér-Rao bound for Terahertz automotive radar range estimation“. Science Talks, Juni 2024, 100373. http://dx.doi.org/10.1016/j.sctalk.2024.100373.

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29

Djeutem, Edouard, und Pierre Nguimkeu. „Robust learning in the foreign exchange market“. B.E. Journal of Macroeconomics 20, Nr. 1 (25.08.2018). http://dx.doi.org/10.1515/bejm-2017-0117.

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Abstract This paper studies risk premia in the foreign exchange market when investors entertain multiple models for consumption growth. Investors confront two sources of uncertainty: (1) individual models might be misspecified, and (2) it is not known which of these potentially misspecified models is the best approximation to the actual data-generating process. Following Hansen and Sargent (Hansen, L. P., and T. J. Sargent. 2010. “Fragile Beliefs and the Price of Uncertainty.” Quantitative Economics 1 (1): 129–162.), agents formulate “robust” portfolio policies. These policies are implemented by applying two risk-sensitivity operators. One is forward-looking, and pessimistically distorts the state dynamics of each individual model. The other is backward-looking, and pessimistically distorts the probability weights assigned to each model. A robust learner assigns higher weights to worst-case models that yield lower continuation values. The magnitude of this distortion evolves over time in response to realized consumption growth. It is shown that robust learning not only explains unconditional risk premia in the foreign exchange market, it can also explain the dynamics of risk premia. In particular, an empirically plausible concern for model misspecification and model uncertainty generates a stochastic discount factor that uniformly satisfies the spectral Hansen-Jagannathan bound of Otrok et al. (Otrok, C., B. Ravikumar, and C. H. Whiteman. 2007. “A Generalized Volatility Bound for Dynamic Economies.” Journal of Monetary Economics 54 (8): 2269–2290.).

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Swinburne, Thomas, und Danny Perez. „Parameter uncertainties for imperfect surrogate models in the low-noise regime“. Machine Learning: Science and Technology, 16.12.2024. https://doi.org/10.1088/2632-2153/ad9fce.

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Abstract Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, this loss ignores model form error, or misspecification, meaning parameter uncertainties are significantly underestimated and vanish in the large data limit. As misspecification is the main source of uncertainty for surrogate models of low-noise calculations, such as those arising in atomistic simulation, predictive uncertainties are systematically underestimated. We analyze the true generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show that posterior parameter distributions must cover every training point to avoid a divergence in the generalization error and design a compatible \textit{ansatz} which incurs minimal overhead for linear models. The approach is demonstrated on model problems before application to thousand-dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors in terms of parameter uncertainties, allowing this important source of uncertainty to be incorporated in multi-scale computational workflows.

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GUPTA, RANGAN, ANANDAMAYEE MAJUMDAR, JACOBUS NEL und SOWMYA SUBRAMANIAM. „GEOPOLITICAL RISKS AND THE HIGH-FREQUENCY MOVEMENTS OF THE US TERM STRUCTURE OF INTEREST RATES“. Annals of Financial Economics 16, Nr. 03 (September 2021). http://dx.doi.org/10.1142/s2010495221500123.

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We use daily data for the period 25th November 1985 to 10th March 2020 to analyze the impact of newspapers-based measures of geopolitical risks (GPRs) on United States (US) Treasury securities by considering the level, slope and curvature factors derived from the term structure of interest rates of maturities covering 1 to 30 years. No evidence of predictability of the overall GPRs (or for threats and acts) is detected using linear causality tests. However, evidence of structural breaks and nonlinearity is provided by statistical tests performed on the linear model, which indicates that the Granger causality cannot be relied upon, as they are based on a misspecified framework. As a result, we use a data-driven approach, specifically a nonparametric causality-in-quantiles test, which is robust to misspecification due to regime changes and nonlinearity, to reconsider the predictive ability of the overall and decomposed GPRs on the three latent factors. Moreover, the zero lower bound situation, visible in our sample period, is captured by the lower quantiles, as this framework allows us to capture the entire conditional distribution of the three factors. Using this robust model, we find overwhelming evidence of causality from the GPRs, with relatively stronger effects from threats than acts, for the entire conditional distribution of the three factors, with higher impacts on medium- and long-run maturities, i.e., curvature and level factors, suggesting the predictability of the entire US term structure based on information contained in GPRs. Our results have important implications for academics, investors and policymakers.

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Roueff, Antoine, Jérôme Pety, Maryvonne Gerin, Léontine E. Ségal, Javier R. Goicoechea, Harvey S. Liszt, Pierre Gratier et al. „Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model. Application to the estimation of the gas temperature and volume density“. Astronomy & Astrophysics, 03.04.2024. http://dx.doi.org/10.1051/0004-6361/202449148.

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Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines. We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them. We focus on the CO and isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cramér-Rao lower bound. Column densities can be estimated with 30<!PCT!> accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases. Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future.

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Zeitschriftenartikel zum Thema „Misspecified bounds“

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