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Classification via Bayesian Nonparametric Learning of Affine Subspaces

通过贝叶斯非参数仿射子空间学习进行分类

It has become common for data sets to contain large numbers of variables in studies conducted in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric procedures tend to be non-robust because of insufficient data on these high dimensional spaces. This is particularly true when interest lies in building efficient classifiers in the presence of many predictor variables.…

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Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information

无辅助信息的经典测量误差模型:非参数识别与半参数估计

Virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information (e.g., validation data, known error distributions, repeated measurements, or instruments). In contrast, we establish that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the model takes a very specific parametric form. This parametric family includes…

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DURATION DEPENDENCE VERSUS UNOBSERVED HETEROGENEITY IN TREATMENT EFFECTS: SWEDISH LABOR MARKET TRAINING AND THE TRANSITION RATE TO EMPLOYMENT

处理效应的持续期依赖与未观测异质性:瑞典就业培训与就业转移率

SUMMARY The effect of a treatment on the hazard rate of a duration outcome may depend on the elapsed time since treatment. In addition, treatment effects may be heterogeneous across agents. The former gives rise to duration dependence of the treatment effect, whereas unobserved heterogeneity gives rise to spurious duration dependence of the observable hazard rate. We develop a model allowing for duration dependence and unobserved heterogeneity in the treatment effect. The…

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Modeling structural equations with endogenous regressors and heterogeneity through derivative constraints

通过导数约束建模内生解释变量与异质性结构方程

In this paper, I present a general modeling framework for nonparametric models with endogenous regressors and heterogeneity. I show that many existing models in the literature can be derived from a structural equation with unobserved heterogeneity by imposing constancy assumptions on the first and second derivatives. I consider a less restrictive model that imposes constancy assumptions on the second partial derivative of the structural equation. Assuming the existence of…

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On the surjectivity of the mapping between utilities and choice probabilities

效用与选择概率映射的满射性

This note considers a standard multinomial choice model. It is shown that if the distribution of additive utility shocks has a density, then the mapping from deterministic components of utilities to choice probabilities is surjective. In other words, any vector of choice probabilities can be obtained by selecting suitable utilities for alternatives. This result has implications for at least three areas of interest to econometricians: the Hotz and Miller (1993) estimator for…

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Convergence of latent mixing measures in finite and infinite mixture models

有限与无限混合模型中潜在混合测度的收敛

This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of mixing measures and $f$-divergence functionals such as Hellinger and Kullback–Leibler distances on the space of mixture distributions is investigated in detail using various identifiability conditions. Convergence in Wasserstein metrics for…

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Identification of treatment response with social interactions

社会互动下处理反应的识别

This paper studies identification of potential outcome distributions when treatment response may have social interactions. Defining a person's treatment response to be a function of the entire vector of treatments received by the population, I study identification when non‐parametric shape restrictions and distributional assumptions are placed on response functions. An early key result is that the traditional assumption of individualistic treatment response is a polar case…

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Estimation of spatial autoregressive models with randomly missing data in the dependent variable

因变量随机缺失时空间自回归模型的估计

We suggest and compare different methods for estimating spatial autoregressive models with randomly missing data in the dependent variable. Aside from the traditional expectation-maximization (EM) algorithm, a nonlinear least squares method is suggested and a generalized method of moments estimation is developed for the model. A two-stage least squares estimation with imputation is proposed as well. We analytically compare these estimation methods and find that generalized…

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Identification and inference in a simultaneous equation under alternative information sets and sampling schemes

不同信息集与抽样方案下联立方程的识别和推断

In simple static linear simultaneous equation models the empirical distributions of IV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. We demonstrate that the limiting distribution of consistent IV is not affected by conditioning on exogenous regressors, whereas that of inconsistent OLS is. The OLS asymptotic and simulated actual variances are shown to diminish by extending the set of exogenous variables…

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Instrumental variables estimation and inference in the presence of many exogenous regressors

存在大量外生回归变量时的工具变量估计与推断

We consider a standard instrumental variables model contaminated by the presence of a large number of exogenous regressors. In an asymptotic framework where this number is proportional to the sample size, we study the impact of their ratio on the validity of existing estimators and tests. When the instruments are few, the inference using the conventional 2SLS estimator and associated t and J statistics, as well as the Anderson–Rubin and Kleibergen tests, is still valid. When…

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Partial identification in asymmetric auctions in the absence of independence

不假定独立性时非对称拍卖的部分识别

This paper examines identification in second‐price and ascending auctions within the private‐values framework. The first part of the paper considers an arbitrary type of dependence of bidders’ values and analyses identification under several observational scenarios, in which the highest bid is never observed. In a basic scenario, only the winner’s identity and the winning price are observed. The most informative is the scenario in which all the identities and all the bids…

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Set inference in latent variables models

潜变量模型中的集合推断

We propose a methodology for constructing valid confidence regions in incomplete models with latent variables satisfying moment equality restrictions. These include moment equality and inequality models with latent variables. The confidence regions are obtained by inverting tests based on the characterization of the identified set derived in Ekeland et al. (2010). A valid bootstrap approximation of the distribution of the test statistic is derived under mild conditions and…

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Moment condition tests for heavy tailed time series

重尾时间序列的矩条件检验

We develop an asymptotically chi-squared statistic for testing moment conditions E[mt(θ0)]=0, where mt(θ0) may be weakly dependent, scalar components of mt(θ0) may have an infinite variance, and E[mt(θ)] need not exist for any θ under the alternative. Score tests are a natural application, and in general a variety of tests can be heavy-tail robustified by our method, including white noise, GARCH affects, omitted variables, distribution, functional form, causation, volatility…

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Model identification for infinite variance autoregressive processes

无穷方差自回归过程的模型识别

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order…

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ANOTHER LOOK AT THE IDENTIFICATION AT INFINITY OF SAMPLE SELECTION MODELS

重新审视样本选择模型的无穷远识别

It is often believed that without instruments, endogenous sample selection models are identified only if a covariate with a large support is available (see, e.g., Chamberlain, 1986, Journal of Econometrics 32, 189–218; Lewbel, 2007, Journal of Econometrics 141, 777–806) . We propose a new identification strategy mainly based on the condition that the selection variable becomes independent of the covariates for large values of the outcome. No large support on the covariates…

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Estimation of dynamic panel data models with sample selection

存在样本选择的动态面板数据模型估计

SUMMARY We propose a new method for estimating dynamic panel data models with selection. The method uses backward substitution for the lagged dependent variable, which leads to an estimating equation that requires correcting for contemporaneous selection only. The estimator is valid under relatively weak assumptions about errors and permits avoiding the weak instruments problem associated with differencing. We also propose a simple test for selection bias that is based on…

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On the simultaneity problem in the aid and growth debate

援助与增长争论中的联立性问题

SUMMARY This paper shows that foreign aid has a significant positive average effect on real per capita gross domestic product (GDP) growth if, and only if, the quantitatively large negative reverse causal effect of per capita GDP growth on foreign aid is adjusted for in the growth regression. Instrumental variables estimates show that a 1 percentage point increase in GDP per capita growth decreased foreign aid by over 4%. Adjusting for this quantitatively large, negative…

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Testing for Common Conditionally Heteroskedastic Factors

共同条件异方差因子的检验

This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features property is expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter value and therefore the standard asymptotic results of Hansen (1982) do not apply. We show in this context that Hansen's (1982) J-test…

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On the Testability of Identification in Some Nonparametric Models With Endogeneity

若干含内生性的非参数模型中识别的可检验性

This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity. The first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions. These conditions are typically referred to as completeness conditions. The second and third hypothesis testing problems we examine…

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Connected Substitutes and Invertibility of Demand

连通替代关系与需求的可逆性

We consider the invertibility (injectivity) of a nonparametric nonseparable demand system. Invertibility of demand is important in several contexts, including identification of demand, estimation of demand, testing of revealed preference, and economic theory exploiting existence of an inverse demand function or (in an exchange economy) uniqueness of Walrasian equilibrium prices. We introduce the notion of “connected substitutes” and show that this structure is sufficient for…

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Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local-to-Continuity Theory for the Pre-Averaging Method

含噪高频数据中跳跃的稳健估计与推断:预平均方法的局部趋于连续理论

We develop an asymptotic theory for the pre-averaging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple bias-corrected estimators for jump power variations, and construct robust…

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Robust Predictions in Games With Incomplete Information

不完全信息博弈中的稳健预测

We analyze games of incomplete information and offer equilibrium predictions that are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in…

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Intersection Bounds: Estimation and Inference

交集界限:估计与推断

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is…

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Nonparametric Estimation in Random Coefficients Binary Choice Models

随机系数二元选择模型中的非参数估计

This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill-posed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier–Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields…

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