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We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…
Calibrating blackbox machine learning models to achieve risk control is crucial to ensure reliable decision-making. A rich line of literature has been studying how to calibrate a model so that its predictions satisfy explicit finite-sample…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…
The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the…
In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on…
In this paper we prove the asymptotic efficiency of the model selection procedure proposed by the authors in the first part. To this end we introduce the robust risk as the least upper bound of the quadratical risk over a broad class of…
The analysis of high-dimensional time series data has become increasingly important across a wide range of fields. Recently, a method for constructing the minimum information Markov kernel on finite state spaces was established. In this…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
This paper proposes a new method and algorithm for predicting multivariate responses in a regression setting. Research into classification of High Dimension Low Sample Size (HDLSS) data, in particular microarray data, has made considerable…
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from…
We consider the problem of Adverse Selection and optimal derivative design within a Principal-Agent framework. The principal's income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She…
We study prediction-powered conditional inference in the setting where labeled data are scarce, unlabeled covariates are abundant, and a black-box machine-learning predictor is available. The goal is to perform statistical inference on…
Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…