摘要翻译:
在各向异性光滑性条件下,考虑离散-连续混合分布的非参数估计,并考虑离散部分的支撑点数目可能增加的情况。对于这些设置,我们导出了估计率在总变差距离中的下界。其次,我们考虑了一个非参数混合法线模型,该模型对离散部分的观测数据使用连续的潜在变量。我们证明,在这个模型中,后验的收缩率等于导出的下界,直到一个对数因子。因此,贝叶斯混合正态模型可用于离散-连续混合分布的最优自适应估计。
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英文标题:
《Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions
under Smoothness and Sparsity》
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作者:
Andriy Norets and Justinas Pelenis
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最新提交年份:
2018
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Economics 经济学
二级分类:Econometrics 计量经济学
分类描述:Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论,微观计量经济学,宏观计量经济学,通过新方法发现的经济关系的实证内容,统计推论应用于经济数据的方法论方面。
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates in the total variation distance. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at rates that are equal to the derived lower bounds up to a log factor. Thus, Bayesian mixture of normals models can be used for optimal adaptive estimation of mixed discrete-continuous distributions.
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PDF链接:
https://arxiv.org/pdf/1806.07484