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In the random-effects model of meta-analysis a canonical representation of the restricted likelihood function is obtained. This representation relates the mean effect and the heterogeneity variance estimation problems. An explicit form of…
Estimation of causal effects using machine learning methods has become an active research field in econometrics. In this paper, we study the finite sample performance of meta-learners for estimation of heterogeneous treatment effects under…
Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…
The limit distribution of the nonparametric maximum likelihood estimator for interval censored data with more than one observation time per unobservable observation, is still unknown in general. For the so-called separated case, where one…
In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…
Optimal estimation of a coin's bias using noisy data is surprisingly different from the same problem with noiseless data. We study this problem using entropy risk to quantify estimators' accuracy. We generalize the "add Beta" estimators…
We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…
We consider the problem of estimating the mean of a normal distribution under the following constraint: the estimator can access only a single bit from each sample from this distribution. We study the squared error risk in this estimation…
Risk prediction models are often advertised as deterministic functions that map covariates to predicted risks. However, they are typically trained using finite samples, and as such, their predictions are inherently uncertain. This…
We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, [HZ19] obtained a pointwise limit distribution theory for the so-called block max-min and min-max estimators [FLN17]…
Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…
The Statistical Learning Theory (SLT) provides the theoretical guarantees for supervised machine learning based on the Empirical Risk Minimization Principle (ERMP). Such principle defines an upper bound to ensure the uniform convergence of…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite…