Nick Kloodt
The so far most general identification result in the context of nonparametric transformation models is proven. The result is constructive in the sense that it provides an explicit expression of the transformation function.
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Completely nonparametric transformation models with heteroscedastic errors are considered. Despite their flexibility, such models have rarely been used so far, since estimators of the model components have been missing and even identification of such models has not been clear until very recently. The results of Kloodt (2020) are used to construct the first two estimators of the transformation function in these models. While the first estimator converges to the true transformation function at a parametric rate, the second estimator can be obtained by an explicit formula and is less computationa…
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability matrices have full-rank and are ergodic, and if the state-dependent distributions are all distinct, but not necessarily linearly independent. Based on this identification result, we develop nonparametric maximum likelihood estimation theory. First, we show that the asymptotic contrast, the Kullback--Leibler divergence of the hidden Markov model, identifies the true…
We show nonparametric identification of the parameters in the dynamic stochastic block model as recently introduced in Matias and Miele (2017) in case of binary, finitely weighted and general edge states. We formulate conditions on the true parameters which guarantee actual point identification instead of mere generic identification, and which also lead to novel conclusions in the static case. In particular, our results justify in terms of identification the applications in Matias and Miele (2017) to finitely weighted edges with three edge states. We also give numerical illustrations via the v…
A Simplified Condition For Quantile Regression
本文针对经济金融风险预测中的异方差性问题，在三种概率模型下提出识别条件，从而建立了分位回归的简化条件。
This paper studies point identification of the distribution of the coefficients in some random coefficients models with exogenous regressors when their support is a proper subset, possibly discrete but countable. We exhibit trade-offs between restrictions on the distribution of the random coefficients and the support of the regressors. We consider linear models including those with nonlinear transforms of a baseline regressor, with an infinite number of regressors and deconvolution, the binary choice model, and panel data models such as single-index panel data models and an extension of the Ko…
This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for the parameter is positive or zero, respectively. I first characterize these cases in models with densities linear in a nonparametric parameter. I then introduce a novel "generalized Fisher information". If positive, it implies (possibly irregular) identification when other conditions hold. If zero, it implies impossibility results on rates of estimation. Thre…
Local Identification of Nonparametric and Semiparametric Models
该研究将参数非线性结构模型的经典局部识别满秩条件推广至非参数非线性场景，补充了避免非线性掩盖线性效应的邻域约束，并应用于三类重要模型得到新的原生识别条件。
This is a companion note to Zinde-Walsh (2010), arXiv:1009.4217v1[MATH.ST], to clarify and extend results on identification in a number of problems that lead to a system of convolution equations. Examples include identification of the distribution of mismeasured variables, of a nonparametric regression function under Berkson type measurement error, some nonparametric panel data models, etc. The reason that identification in different problems can be considered in one approach is that they lead to the same system of convolution equations; moreover the solution can be given under more general as…
Pivotal and identification-robust nonparametric inference in linear IV models
针对线性工具变量模型，提出对识别强度与异方差鲁棒且第一阶段非参数的新推断方法，包括渐近关键统计量、子向量推断和设定检验。
Nonparametric Identification of Demand without Exogenous Product Characteristics
本文提出在更弱的指数限制和‘信仰’条件下，通过重新中心化的工具非参数识别需求，解决了内生产品特征下的需求识别问题。
Principal Stratification with Continuous Post-Treatment Variables: Nonparametric Identification and Semiparametric Estimation
本文针对连续治疗后变量的主分层问题，提出非参数识别与半参数估计理论，利用工作模型近似因果效应曲面并构造双重稳健估计量，填补了现有方法主要限于二值治疗后变量的空白。
In branching diffusions with immigration (BDI), particles travel on independent diffusion paths in $\mathbb{R}^d$, branch at position-dependent rates and leave offspring -- randomly scattered around the parent's death position -- according to position-dependent laws. We specify a set of conditions which grants ergodicity such that the invariant occupation measure is of finite total mass and admits a continuous Lebesgue density. Under discrete-time observation, BDI configurations being recorded at discrete times $iΔ$ only, $i\in\mathbb{N}_0$, we lose information about particle identities betwee…
Max-Stable Survival Copulas under Dependent Censoring: Sharp Identification and Efficient Inference
该研究针对相依删失下的广义Cox首达时间框架，明确了极大稳定生存Copula的识别条件，提出可用于可识别分量的非参数估计、高效推断及相容性检验方法，经模拟与实际数据验证有效。
This paper analyzes the effect of a discrete treatment Z on a duration T. The treatment is not randomly assigned. The confounding issue is treated using a discrete instrumental variable explaining the treatment and independent of the error term of the model. Our framework is nonparametric and allows for random right censoring. This specification generates a nonlinear inverse problem and the average treatment effect is derived from its solution. We provide local and global identification properties that rely on a nonlinear system of equations. We propose an estimation procedure to solve this sy…
Bayesian Nonparametric Inference in Elliptic PDEs: Convergence Rates and Implementation
本文针对椭圆PDE中的扩散系数推断问题，提出基于高斯级数先验的贝叶斯非参数方法，推导后验一致性与收敛速率，并通过数值模拟验证理论。
We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to nonignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for $\sqrt{n}$-estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow va…
The efficiency of two Bayesian order estimators is studied. By using nonparametric techniques, we prove new underestimation and overestimation bounds. The results apply to various models, including mixture models. In this case, the errors are shown to be $O(e^{-an})$ and $O((\log n)^b/\sqrt{n})$ ($a,b>0$), respectively.
This paper discusses endogenous treatment models with duration outcomes, competing risks and random right censoring. The endogeneity issue is solved using a discrete instrumental variable. We show that the competing risks model generates a non-parametric quantile instrumental regression problem. The cause-specific cumulative incidence, the cause-specific hazard and the subdistribution hazard can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for…
We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterizing the model compared to existing strategies; in particular, it does not require any large support conditions on the regressors of our model. We apply the general identification result to additive random utility and competing risk models.
Is completeness necessary? Estimation in nonidentified linear models
本文探讨了非识别线性模型中正则化估计器的完备性需求，提出了一种在识别失败情况下仍能提供非标准渐近分布的理论框架。
The goal of this paper is to extend independent subspace analysis (ISA) to the case of (i) nonparametric, not strictly stationary source dynamics and (ii) unknown source component dimensions. We make use of functional autoregressive (fAR) processes to model the temporal evolution of the hidden sources. An extension of the ISA separation principle--which states that the ISA problem can be solved by traditional independent component analysis (ICA) and clustering of the ICA elements--is derived for the solution of the defined fAR independent process analysis task (fAR-IPA): applying fAR identific…
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