Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference

Nonparametric inference of photon energy distribution from indirect measurements

We consider a density estimation problem arising in nuclear physics. Gamma photons are impinging on a semiconductor detector, producing pulses of current. The integral of this pulse is equal to the total amount of charge created by the photon in the detector, which is linearly related to the photon energy. Because the inter-arrival of photons can be shorter than the charge collection time, pulses corresponding to different photons may overlap leading to a phenomenon known as pileup. The distortions on the photon energy spectrum estimate due to pileup become worse when the photon rate increases…

近端推断用于间接和中介效应在人群干预中的应用

Proximal Inference for Indirect and Intervening Effects in Population Interventions

本文提出了一种统一的识别和估计框架，用于在存在广泛未测量混杂因素的情况下估计人群干预间接效应及中介变量的因果效应，通过近端因果推断方法构建了三种不同的识别策略，并开发了稳健的估计器。

Minimum scoring rule inference

Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper we develop some basic scoring rule estimation theory, and explore robustness and interval estimation properties by means of theory and simulations.

带有（无）约束的间接推断

Indirect Inference With(Out) Constraints

本文研究了在间接推断（I-I）估计中如何处理辅助模型参数的约束问题，提出了一种新的I-I方法，通过适当修改无约束的辅助统计量来提高估计精度，并展示了其在GARCH等模型中的应用。

凸函数极小点与极小值的估计与推断：最优性、自适应性与不确定性原理

Estimation and inference for minimizer and minimum of convex functions: optimality, adaptivity and uncertainty principles

该研究在非渐近局部极小极大框架下探究凸回归函数极小点与极小值的估计推断，提出自适应高效算法并给出下界，还建立了二者同时估计的不确定性原理。

On minimum Bregman divergence inference

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new sub-class of Bregman divergences called the exponentially weighted divergence (EWD). Like the minimum DPD estimator, the minimum EWD estimator is recognised as an M-estimator. This characterisation is useful while discussing the asymptotic behaviour as well as the robustness properties of this class of estimators. Performances of the two classes are compared -- bo…

一类最小距离模型中带界的弱识别

Weak Identification with Bounds in a Class of Minimum Distance Models

针对现有弱识别推断方法无法结合参数界信息的问题，本文在一类最小距离模型中提出纳入界信息的识别稳健推断方法，并通过模型与实证应用验证了其价值。

Inference in Marginal Structural Models by Automatic Targeted Bayesian and Minimum Loss-Based Estimation

Two of the principle tasks of causal inference are to define and estimate the effect of a treatment on an outcome of interest. Formally, such treatment effects are defined as a possibly functional summary of the data generating distribution, and are referred to as target parameters. Estimation of the target parameter can be difficult, especially when it is high-dimensional. Marginal Structural Models (MSMs) provide a way to summarize such target parameters in terms of a lower dimensional working model. We introduce the semi-parametric efficiency bound for estimating MSM parameters in a general…

Gibbs posterior inference on the minimum clinically important difference

IIt is known that a statistically significant treatment may not be clinically significant. A quantity that can be used to assess clinical significance is called the minimum clinically important difference (MCID), and inference on the MCID is an important and challenging problem. Modeling for the purpose of inference on the MCID is non-trivial, and concerns about bias from a misspecified parametric model or inefficiency from a nonparametric model motivate an alternative approach to balance robustness and efficiency. In particular, a recently proposed representation of the MCID as the minimizer …

A Multi-resolution Theory for Approximating Infinite-$p$-Zero-$n$: Transitional Inference, Individualized Predictions, and a World Without Bias-Variance Trade-off

Transitional inference is an empiricism concept, rooted and practiced in clinical medicine since ancient Greece. Knowledge and experiences gained from treating one entity are applied to treat a related but distinctively different one. This notion of "transition to the similar" renders individualized treatments an operational meaning, yet its theoretical foundation defies the familiar inductive inference framework. The uniqueness of entities is the result of potentially an infinite number of attributes (hence $p=\infty$), which entails zero direct training sample size (i.e., $n=0$) because genu…

Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the parametric model is correctly specified, it is furthermore shown that the asymptotic variance-covariance matrix equals the inverse of the Fisher-information matrix. These results are based on uniform-in-parameters convergence rates and a uniform-in-parameters Donsker-type theorem for non-parametric maximum likelihood density estimators.

Influence Function Analysis of the Restricted Minimum Divergence Estimators : A General Form

The minimum divergence estimators have proved to be useful tools in the area of robust inference. The robustness of such estimators are measured using the classical Influence functions. However, in many complex situations like testing a composite hypothesis using divergence require the estimators to be restricted into some subspace of the parameter space. The robustness of these restricted minimum divergence estimators are very important in order to have overall robust inference. In this paper we provide a comprehensive description of the robustness of such restricted estimators in terms of th…

Minimum divergence estimators, Maximum Likelihood and the generalized bootstrap

This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where minimization of those indexes between a model and some extension of the empirical measure of the data appears as its natural extension. This leads to the so called generalized bootstrap setting for which minimum divergence inference seems to replace Maximum Likelihood one. 1 Motivation and context Divergences between probability measures are widely used in Statistics …

Estimating Linear and Quadratic forms via Indirect Observations

In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on estimating a linear or quadratic form of an unknown "signal," known to belong to a given convex compact set, via noisy indirect observations of the signal. Most of the existing theoretical results on the subject deal with precisely stated statistical models and aim at designing statistical inferences and quantifying their performance in a closed analytic form. In con…

Random Graph Asymptotics for Treatment Effect Estimation under Network Interference

The network interference model for causal inference places all experimental units at the vertices of an undirected exposure graph, such that treatment assigned to one unit may affect the outcome of another unit if and only if these two units are connected by an edge. This model has recently gained popularity as means of incorporating interference effects into the Neyman--Rubin potential outcomes framework; and several authors have considered estimation of various causal targets, including the direct and indirect effects of treatment. In this paper, we consider large-sample asymptotics for trea…

基于最小方差加权的数据驱动统一推断：一般连续处理模型

Data-Driven Uniform Inference for General Continuous Treatment Models via Minimum-Variance Weighting

本文提出了一种数据驱动的方法，通过最小方差加权估计一般连续处理模型的GDRF，并构建统一置信带。

The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities …

The Logarithmic Super Divergence and its use in Statistical Inference

This paper introduces a new superfamily of divergences that is similar in spirit to the S-divergence family introduced by Ghosh et al. (2013). This new family serves as an umbrella that contains the logarithmic power divergence family (Renyi, 1961; Maji, Chakraborty and Basu 2014) and the logarithmic density power divergence family (Jones et al., 2001) as special cases. Various properties of this new family and the corresponding minimum distance procedures are discussed with particular emphasis on the robustness issue; these properties are demonstrated through simulation studies. In particular…

Asymptotic Properties of Minimum S-Divergence Estimator for Discrete Models

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class of divergence measures, namely the S-Divergence Family and discussed its usefulness in robust parametric estimation through some numerical illustrations. In this present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under discrete models.

Nonparametric inference for interventional effects with multiple mediators

Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects. Interventional direct and indirect effects provide one such decomposition. Existing estimators of these effects are based on parametric models with confidence interval estimation facilitated via the nonparametric bootstrap. We provide theory that allows for more flexible, possibly machine learning-based, estimation techniques to be considered. In particular, we establ…

Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach

In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately yields inefficient inference; 2) a possible lack of robustness to deviations from the underlying model structure. Motivated by these efficiency and robustness concerns, we construct a new Bayesian method that can deliver efficient estimators when the underlying model is well-specified, and which is simultaneously robust to certain forms of model misspecification…

Energy Scaling Laws for Distributed Inference in Random Fusion Networks

The energy scaling laws of multihop data fusion networks for distributed inference are considered. The fusion network consists of randomly located sensors distributed i.i.d. according to a general spatial distribution in an expanding region. Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field (MRF) hypotheses, the scheme with minimum average energy consumption is bounded below by average energy of fusion along the minimum spanning tree, and above by a suboptimal scheme, referred to as Data Fusion for Markov Random Fields (DFMRF). Sc…

Discrete-Time Statistical Inference for Multiscale Diffusions

We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization regimes, based on an appropriate misspecified model motivated by a second-order stochastic Taylor expansion of the slow process with respect to a function of the time-scale separation parameter. In the case of a fixed number of observations, we establish consistency, asymptotic normality, and asymptotic statistical efficiency of a minimum contrast estimator (MCE),…

统计推断中的无损变换与超额风险界

Lossless Transformations and Excess Risk Bounds in Statistical Inference

本文研究统计推断中由特征变换导致的最小超额风险，刻画无损变换并提出强一致的划分检验，同时给出统一的信息论风险上界及 δ-无损变换的充分条件。

隐扩散过程路径估计与参数推断的变分方法

A variational approach to path estimation and parameter inference of hidden diffusion processes

本文提出一种变分方法，用于估计隐扩散过程的路径并推断参数，通过高效推理方案提升对随机微分方程参数的估计精度。