單調(diào)性下的非參數(shù)工具變量估計(jì)

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摘要翻譯：
在非參數(shù)工具變量模型中恢復(fù)回歸函數(shù)的逆問題的不適定性導(dǎo)致估計(jì)量可能遭受非常慢的對(duì)數(shù)收斂速度。在本文中，我們證明了將問題限制在具有單調(diào)回歸函數(shù)和單調(diào)工具的模型上，顯著地削弱了問題的不適定性。與現(xiàn)有文獻(xiàn)形成鮮明對(duì)比的是，單調(diào)工具的存在意味著我們的不適定性測(cè)度在局限于單調(diào)函數(shù)空間時(shí)的有界性。在此基礎(chǔ)上，我們給出了約束估計(jì)的一個(gè)新的非漸近誤差界。對(duì)于給定的樣本量，只要回歸函數(shù)不太陡，其界與不適定性無關(guān)。作為一個(gè)蘊(yùn)涵，這個(gè)界允許我們證明約束估計(jì)量在常數(shù)函數(shù)的一個(gè)大的但緩慢收縮的鄰域中以快速的多項(xiàng)式速度收斂，而與不適定性無關(guān)。我們的模擬研究表明，即使在回歸函數(shù)遠(yuǎn)不是常數(shù)的情況下，施加單調(diào)性也能顯著地提高有限樣本的性能。我們將約束估計(jì)量應(yīng)用于從美國(guó)數(shù)據(jù)估計(jì)汽油需求函數(shù)的問題。
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英文標(biāo)題：
《Nonparametric instrumental variable estimation under monotonicity》
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作者：
Denis Chetverikov and Daniel Wilhelm
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最新提交年份：
2015
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分類信息：

一級(jí)分類：Statistics        統(tǒng)計(jì)學(xué)
二級(jí)分類：Applications        應(yīng)用程序
分類描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物學(xué)，教育學(xué)，流行病學(xué)，工程學(xué)，環(huán)境科學(xué)，醫(yī)學(xué)，物理科學(xué)，質(zhì)量控制，社會(huì)科學(xué)
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一級(jí)分類：Economics        經(jīng)濟(jì)學(xué)
二級(jí)分類：Econometrics        計(jì)量經(jīng)濟(jì)學(xué)
分類描述：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.
計(jì)量經(jīng)濟(jì)學(xué)理論，微觀計(jì)量經(jīng)濟(jì)學(xué)，宏觀計(jì)量經(jīng)濟(jì)學(xué)，通過新方法發(fā)現(xiàn)的經(jīng)濟(jì)關(guān)系的實(shí)證內(nèi)容，統(tǒng)計(jì)推論應(yīng)用于經(jīng)濟(jì)數(shù)據(jù)的方法論方面。
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一級(jí)分類：Mathematics        數(shù)學(xué)
二級(jí)分類：Statistics Theory        統(tǒng)計(jì)理論
分類描述：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
應(yīng)用統(tǒng)計(jì)、計(jì)算統(tǒng)計(jì)和理論統(tǒng)計(jì)：例如統(tǒng)計(jì)推斷、回歸、時(shí)間序列、多元分析、數(shù)據(jù)分析、馬爾可夫鏈蒙特卡羅、實(shí)驗(yàn)設(shè)計(jì)、案例研究
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一級(jí)分類：Statistics        統(tǒng)計(jì)學(xué)
二級(jí)分類：Statistics Theory        統(tǒng)計(jì)理論
分類描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的別名。漸近，貝葉斯推論，決策理論，估計(jì)，基礎(chǔ)，推論，檢驗(yàn)。
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英文摘要：
  The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem. In stark contrast to the existing literature, the presence of a monotone instrument implies boundedness of our measure of ill-posedness when restricted to the space of monotone functions. Based on this result we derive a novel non-asymptotic error bound for the constrained estimator that imposes monotonicity of the regression function. For a given sample size, the bound is independent of the degree of ill-posedness as long as the regression function is not too steep. As an implication, the bound allows us to show that the constrained estimator converges at a fast, polynomial rate, independently of the degree of ill-posedness, in a large, but slowly shrinking neighborhood of constant functions. Our simulation study demonstrates significant finite-sample performance gains from imposing monotonicity even when the regression function is rather far from being a constant. We apply the constrained estimator to the problem of estimating gasoline demand functions from U.S. data.
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PDF鏈接：
https://arxiv.org/pdf/1507.05270

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關(guān)鍵詞：工具變量 非參數(shù) 單調(diào)性 econometrics instrumental 收縮 變量 無關(guān) estimator functions