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A note on identifying heterogeneous sharing rules

异质性家庭分配规则识别札记

In this note, we address nonparametric identification of a collective model of household behavior in the presence of additive unobserved heterogeneity in the sharing rule. We show that the (nonstochastic part of the) sharing rule is nonparametrically identified. Moreover, under independence assumptions, individual Engel curves and the random distributions are identified except in special cases (i.e., linear Engel curves).

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Oracle inequalities for network models and sparse graphon estimation

网络模型的预言不等式与稀疏 graphon 估计

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. Taking the stochastic block model as an approximation, we construct estimators of network connection probabilities—the ordinary block constant least squares estimator, and its restricted version.…

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Fractional order statistic approximation for nonparametric conditional quantile inference

非参数条件分位数推断的分数阶次序统计量近似

Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed (Hutson, 1999) confidence intervals for population quantiles using L-statistics as endpoints. We derive an analytic expression for the n−1 term, which may be used to calibrate the nominal coverage level to get O(n−3/2[log(n)]3) coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for…

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R-estimation in semiparametric dynamic location-scale models

半参数动态位置—尺度模型的秩估计

We propose rank-based estimation (R-estimators) as an alternative to Gaussian quasi-likelihood and standard semiparametric estimation in time series models, where conditional location and/or scale depend on a Euclidean parameter of interest, while the unspecified innovation density is a nuisance. We show how to construct R-estimators achieving semiparametric efficiency at some predetermined reference density while preserving root-n consistency and asymptotic normality…

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UNIFORM BAHADUR REPRESENTATION FOR NONPARAMETRIC CENSORED QUANTILE REGRESSION: A REDISTRIBUTION-OF-MASS APPROACH

非参数删失分位数回归的一致 Bahadur 表示:质量再分配方法

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability , vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local…

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SMOOTHED ESTIMATING EQUATIONS FOR INSTRUMENTAL VARIABLES QUANTILE REGRESSION

工具变量分位数回归的平滑估计方程

The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth h . We show that the mean squared error (MSE) of the vector of the SEE is minimized for some h > 0, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal h also minimizes the higher-order type I error of a…

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Nonparametric regression with nearly integrated regressors under long-run dependence

长期依赖下含近单位根解释变量的非参数回归

We study the nonparametric estimation of a regression function with nonstationary (integrated or nearly integrated) covariates and the error series of the regressor process following a fractional integrated autoregressive moving average model. A local linear estimation method is developed to estimate the unknown regression function. The asymptotic results of the resulting estimator at both interior points and boundaries are obtained. The asymptotic distribution is mixed…

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Itemwise conditionally independent nonresponse modelling for incomplete multivariate data

不完整多变量数据的逐项条件独立无应答建模

We introduce a nonresponse mechanism for multivariate missing data in which each study variable and its nonresponse indicator are conditionally independent given the remaining variables and their nonresponse indicators. This is a nonignorable missingness mechanism, in that nonresponse for any item can depend on values of other items that are themselves missing. We show that under this itemwise conditionally independent nonresponse assumption, one can define and identify…

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Fast Approximate Inference for Arbitrarily Large Semiparametric Regression Models via Message Passing

通过消息传递实现大规模半参数回归的快速近似推断

We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling arbitrarily large models of particular types once a set of primitive operations is established. The approach is founded upon a message passing formulation of mean field variational Bayes that utilizes factor graph representations of…

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A Directional Mixed Effects Model for Compositional Expenditure Data

组成性支出数据的方向混合效应模型

Compositional data are vectors of proportions defined on the unit simplex and this type of constrained data occur frequently in Government surveys. It is also possible for the compositional data to be correlated due to the clustering or grouping of the observations within small domains or areas. We propose a new class of the mixed model for compositional data based on the Kent distribution for directional data, where the random effects also have Kent distributions. One…

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Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency

杠杆效应的非参数估计:稳健性与效率的权衡

We consider two new approaches to nonparametric estimation of the leverage effect. The first approach uses stock prices alone. The second approach uses the data on stock prices as well as a certain volatility instrument, such as the Chicago Board Options Exchange (CBOE) volatility index (VIX) or the Black–Scholes implied volatility. The theoretical justification for the instrument-based estimator relies on a certain invariance property, which can be exploited when…

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Semiparametric Modeling and Estimation of the Terminal Behavior of Recurrent Marker Processes Before Failure Events

带标记复发过程在失效事件前的终末行为:半参数建模与估计

Recurrent event processes with marker measurements are mostly and largely studied with forward time models starting from an initial event. Interestingly, the processes could exhibit important terminal behavior during a time period before occurrence of the failure event. A natural and direct way to study recurrent events prior to a failure event is to align the processes using the failure event as the time origin and to examine the terminal behavior by a backward time model.…

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Semiparametric Estimation of Risk–Return Relationships

风险与收益关系的半参数估计

This article proposes semiparametric generalized least-squares estimation of parametric restrictions between the conditional mean and the conditional variance of excess returns given a set of parametric factors. A distinctive feature of our estimator is that it does not require a fully parametric model for the conditional mean and variance. We establish consistency and asymptotic normality of the estimates. The theory is nonstandard due to the presence of estimated factors.…

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Efficient Augmented Inverse Probability Weighted Estimation in Missing Data Problems

缺失数据问题中高效的增广逆概率加权估计

When analyzing data with missing data, a commonly used method is the inverse probability weighting (IPW) method, which reweights estimating equations with propensity scores. The popularity of the IPW method is due to its simplicity. However, it is often being criticized for being inefficient because most of the information from the incomplete observations is not used. Alternatively, the regression method is known to be efficient but is nonrobust to the misspecification of…

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Nonparametric Inference for Time-Varying Coefficient Quantile Regression

时变系数分位数回归的非参数推断

The article considers nonparametric inference for quantile regression models with time-varying coefficients. The errors and covariates of the regression are assumed to belong to a general class of locally stationary processes and are allowed to be cross-dependent. Simultaneous confidence tubes (SCTs) and integrated squared difference tests (ISDTs) are proposed for simultaneous nonparametric inference of the latter models with asymptotically correct coverage probabilities and…

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Modeling Dependence in High Dimensions With Factor Copulas

用因子 Copula 建模高维依赖结构

This article presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for relatively high-dimensional applications, involving 50 or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied…

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Confidence Corridors for Multivariate Generalized Quantile Regression

多元广义分位数回归的置信带

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest, which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem, and exponential tail inequalities for Gaussian random fields. As a byproduct…

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Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective

收入动态中的未观测异质性:经验贝叶斯视角

Empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The new convex optimization formulation of the nonparametric (Kiefer–Wolfowitz) maximum likelihood estimator for mixture models is employed to construct nonparametric Bayes rules for compound decisions. The methods are first illustrated with some simulation examples and then with an application to models of income dynamics. Using panel data, we estimate a simple…

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Hamiltonian Monte Carlo Sampling in Bayesian Empirical Likelihood Computation

贝叶斯经验似然计算中的哈密顿蒙特卡洛抽样

Summary We consider Bayesian empirical likelihood estimation and develop an efficient Hamiltonian Monte Carlo method for sampling from the posterior distribution of the parameters of interest. The method proposed uses hitherto unknown properties of the gradient of the underlying log-empirical-likelihood function. We use results from convex analysis to show that these properties hold under minimal assumptions on the parameter space, prior density and the functions used in the…

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Laplace Deconvolution on the Basis of Time Domain Data and its Application to Dynamic Contrast-Enhanced Imaging

基于时域数据的拉普拉斯反卷积及其动态对比增强成像应用

Summary We consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over a Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using a regression setting. The expansion results in a small system of…

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Classification of Non-Parametric Regression Functions in Longitudinal Data Models

Summary We investigate a longitudinal data model with non-parametric regression functions that may vary across the observed individuals. In a variety of applications, it is natural to impose a group structure on the regression curves. Specifically, we may suppose that the observed individuals can be grouped into a number of classes whose members all share the same regression function. We develop a statistical procedure to estimate the unknown group structure from the data.…

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Inference in semiparametric conditional moment models with partial identification

部分识别半参数条件矩模型的统计推断

This paper develops inference methods for conditional moment models in which the unknown parameter is possibly partially identified and may contain infinite-dimensional components. For a conjectured restriction on the parameter, we consider testing the hypothesis that the restriction is satisfied by at least one element of the identified set. We propose using the sieve minimum of a Kolmogorov–Smirnov type statistic as the test statistic, derive its asymptotic distribution,…

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Estimating smooth structural change in cointegration models

协整模型中平滑结构变化的估计

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the…

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Statistical inference for independent component analysis: Application to structural VAR models

独立成分分析的统计推断及其结构 VAR 应用

The well-known problem of non-identifiability of structural VAR models disappears if the structural shocks are independent and if at most one of them is Gaussian. In that case, the relevant estimation technique is the Independent Component Analysis (ICA). Since the introduction of ICA by Comon (1994), various semi-parametric estimation methods have been proposed for “orthogonalizing” the error terms. These methods include pseudo maximum likelihood (PML) approaches and…

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