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We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…
In the classic measurement error framework, covariates are contaminated by independent additive noise. This paper considers parameter estimation in such a linear errors-in-variables model where the unknown measurement error distribution is…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…
Instrumental variable analysis is a powerful tool for estimating causal effects when randomization or full control of confounders is not possible. The application of standard methods such as 2SLS, GMM, and more recent variants are…
We in this paper utilize P-GMM (Cheng and Liao, 2015) moment selection procedure to select valid and relevant moments for estimating and testing forecast rationality under the flexible loss proposed by Elliott et al. (2005). We motivate the…
Epidemiologic screening programs often make use of tests with small, but non-zero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect…
Structural estimation in economics often makes use of models formulated in terms of moment conditions. While these moment conditions are generally well-motivated, it is often unknown whether the moment restrictions hold exactly. We consider…
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…
We consider a generalized method of moments framework in which a part of the data vector is missing for some units in a completely unrestricted, potentially endogenous way. In this setup, the parameters of interest are usually only…
The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple…
We introduce a new method for estimating the mean of an outcome variable within groups when researchers only observe the average of the outcome and group indicators across a set of aggregation units, such as geographical areas. Existing…
Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include…
In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator…
Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This…
Inferring the means in the multivariate normal model $X \sim N_n(\theta, I)$ with unknown mean vector $\theta=(\theta_1,...,\theta_n)' \in \mathbb{R}^n$ and observed data $X=(X_1,...,X_n)'\in {\mathbb R}^n$ is a challenging task, known as…
Traditional covariate selection methods for causal inference focus on achieving unbiasedness and asymptotic efficiency. In many practical scenarios, researchers must estimate causal effects from observational data with limited sample sizes…
We consider estimation in moment condition models and show that under any bound on identification strength, asymptotically admissible (i.e. undominated) estimators in a wide class of estimation problems must be uniformly continuous in the…
We develop tools to do valid post-selective inference for a family of model selection procedures, including choosing a model via cross-validated Lasso. The tools apply universally when the following random vectors are jointly asymptotically…
A common approach to constructing a Synthetic Control unit is to fit on the outcome variable and covariates in pre-treatment time periods, but it has been shown by Ferman and Pinto (2019) that this approach does not provide asymptotic…