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We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient,…

In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV…

Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while…

We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require…

We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures…

We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…

Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…

Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works…

Partial mean with generated regressors arises in several econometric problems, such as the distribution of potential outcomes with continuous treatments and the quantile structural function in a nonseparable triangular model. This paper…

Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However (partially) linear models for example, which would deliver these, may fit poorly to the data. On the other hand, an…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

Obtaining valid treatment effect inference remains a challenging problem when dealing with numerous instruments and non-sparse control variables. In this paper, we propose a novel ridge regularization-based instrumental variables method for…

The partially linear binary choice model can be used for estimating structural equations where nonlinearity may appear due to diminishing marginal returns, different life cycle regimes, or hectic physical phenomena. The inference procedure…

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

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…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

In many areas of science, complex phenomena are modeled by stochastic parametric simulators, often featuring high-dimensional parameter spaces and intractable likelihoods. In this context, performing Bayesian inference can be challenging.…

This paper introduces a straightforward sieve-based approach for estimating and conducting inference on regression parameters in panel data models with interactive fixed effects. The method's key assumption is that factor loadings can be…

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for…

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…