19,912 research outputs found

    Parameter estimation for a discrete-response model with double rules of sample selection: A Bayesian approach

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    We present a Bayesian sampling approach to parameter estimation in a discrete-response model with double rules of selectivity, where the dependent variables contain two layers of binary choices and one ordered response. Our investigation is motivated by an empirical study using such a double-selection rule for three labor-market outcomes, namely labor force participation, employment and occupational skill level. Full information maximum likelihood (FIML) estimation often encounters convergence problems in numerical optimization. The contribution of our investigation is to present a sampling algorithm through a new reparameterization strategy. We conduct Monte Carlo simulation studies and find that the numerical optimization of FIML fails for more than half of the simulated samples. Our Bayesian method performs as well as FIML for the simulated samples where FIML works. Moreover, for the simulated samples where FIML fails, Bayesian works as well as it does for the simulated samples where FIML works. We apply the proposed sampling algorithm to the double-selection model of labor-force participation, employment and occupational skill level. We derive the 95% Bayesian credible intervals for marginal effects of the explanatory variable on the three labor-force outcomes. In particular, the marginal effects of mental health factors on these three outcomes are discussed.Bayesian sampling; conditional posterior; marginal effects; mental illness; reparameterization.

    Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

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    Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced

    Penalized Likelihood and Bayesian Function Selection in Regression Models

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    Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive predictors has been considered only more recently. Several competing suggestions have been developed at about the same time and often do not refer to each other. This article provides a state-of-the-art review on function selection, focusing on penalized likelihood and Bayesian concepts, relating various approaches to each other in a unified framework. In an empirical comparison, also including boosting, we evaluate several methods through applications to simulated and real data, thereby providing some guidance on their performance in practice

    Prior distributions for objective Bayesian analysis

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    We provide a review of prior distributions for objective Bayesian analysis. We start by examining some foundational issues and then organize our exposition into priors for: i) estimation or prediction; ii) model selection; iii) highdimensional models. With regard to i), we present some basic notions, and then move to more recent contributions on discrete parameter space, hierarchical models, nonparametric models, and penalizing complexity priors. Point ii) is the focus of this paper: it discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models. We also present some recent contributions in the area of objective priors on model space.With regard to point iii) we only provide a short summary of some default priors for high-dimensional models, a rapidly growing area of research

    Sequential Design for Ranking Response Surfaces

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    We propose and analyze sequential design methods for the problem of ranking several response surfaces. Namely, given L2L \ge 2 response surfaces over a continuous input space X\cal X, the aim is to efficiently find the index of the minimal response across the entire X\cal X. The response surfaces are not known and have to be noisily sampled one-at-a-time. This setting is motivated by stochastic control applications and requires joint experimental design both in space and response-index dimensions. To generate sequential design heuristics we investigate stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging surrogates. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
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