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We consider the problem to estimate the generalized cepstral coefficients of a stationary stochastic process or stationary multidimensional random field. It turns out that a naive version of the periodogram-based estimator for the…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this…
Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…
This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we…
We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…
In this paper, we apply doubly robust approach to estimate, when some covariates are given, the conditional average treatment effect under parametric, semiparametric and nonparametric structure of the nuisance propensity score and outcome…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…
We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We…
Structural assumptions are central to the causal inference literature. In practice, it is often crucial to assess their validity or to test implications that follow from them. In many settings, such tests can be framed as evaluating whether…
In parametric estimation of covariance function of Gaussian processes, it is often the case that the true covariance function does not belong to the parametric set used for estimation. This situation is called the misspecified case. In this…
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
Directed information and its causally conditioned variations are often used to measure causal influences between random processes. In practice, these quantities must be measured from data. Non-asymptotic error bounds for these estimates are…
Using deep latent variable models in causal inference has attracted considerable interest recently, but an essential open question is their ability to yield consistent causal estimates. While they have demonstrated promising results and…
When estimating causal effects from observational studies, researchers often need to adjust for many covariates to deconfound the non-causal relationship between exposure and outcome, among which many covariates are discrete. The behavior…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…