摘要翻译:
本文提出将平滑、模拟和筛分逼近相结合来求解一般动态离散选择(DDC)模型中的积分函数或期望值函数。我们使用重要性抽样来近似定义这两个函数的Bellman算子。随机Bellman算子及其相应的解一般是非光滑的,这是不可取的。为了避免这个问题,我们引入了随机Bellman算子的平滑版本,并用筛选方法求解了相应的平滑值函数。我们表明,通过推广和调整Rust(1997)的“自近似”方法,我们可以避免使用筛子。我们给出了近似解的渐近理论,并证明了它们以根-n-速率收敛于高斯过程,其中$n$是Monte Carlo画法的个数。我们通过一组数值实验检验了它们在实际中的性能,发现这两种方法都有很好的性能,其中筛法在计算速度和精度方面尤其引人注目。
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英文标题:
《Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods》
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作者:
Dennis Kristensen and Patrick K. Mogensen and Jong Myun Moon and
Bertel Schjerning
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最新提交年份:
2020
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分类信息:
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: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: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 propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce a smoothed version of the random Bellman operator and solve for the corresponding smoothed value function using sieve methods. We show that one can avoid using sieves by generalizing and adapting the `self-approximating' method of Rust (1997) to our setting. We provide an asymptotic theory for the approximate solutions and show that they converge with root-N-rate, where $N$ is number of Monte Carlo draws, towards Gaussian processes. We examine their performance in practice through a set of numerical experiments and find that both methods perform well with the sieve method being particularly attractive in terms of computational speed and accuracy.
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PDF链接:
https://arxiv.org/pdf/1904.05232