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In this paper, we study the confounder detection problem in the linear model, where the target variable $Y$ is predicted using its $n$ potential causes $X_n=(x_1,...,x_n)^T$. Based on an assumption of rotation invariant generating process…
Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling…
We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…
Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…
In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…
This paper considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, $n$, and the number of time periods, $T$, are large. We first clarify the probability…
When the target parameter for inference is a real-valued, continuous function of probabilities in the $k$-sample multinomial problem, variance estimation may be challenging. In small samples or when the function is nondifferentiable at the…
Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this…
Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise in industrial organization and labor economics settings where data are collected using an input-based sampling…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
This paper considers statistical inference for the explained variance $\beta^{\intercal}\Sigma \beta$ under the high-dimensional linear model $Y=X\beta+\epsilon$ in the semi-supervised setting, where $\beta$ is the regression vector and…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
An artificial intelligence (AI) model can be viewed as a function that maps inputs to outputs in high-dimensional spaces. Once designed and well trained, the AI model is applied for inference. However, even optimized AI models can produce…
Combining information from multiple samples is often needed in biomedical and economic studies, but the differences between these samples must be appropriately taken into account in the analysis of the combined data. We study estimation for…