Related papers: Equality between two general ridge estimators and …
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…
We study regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We provide a detailed proof of asymptotic normality of the covariate-adjusted estimator under minimal…
Missing data often result in undesirable bias and loss of efficiency. These issues become substantial when the response mechanism is nonignorable, meaning that the response model depends on unobserved variables. To manage nonignorable…
We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator? (2) how to correctly use cross-validation to choose the regularization parameter? and (3) how to accelerate computation…
Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
There are a variety of settings where vague prior information may be available on the importance of predictors in high-dimensional regression settings. Examples include ordering on the variables offered by their empirical variances (which…
We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first order bias emerges when the number of \textit{included} covariates is "large" relative to the…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Auxiliary information can increase the efficiency of survey estimators through an assisting model when the model captures some of the relationship between the auxiliary data and the study variables. Despite their superior properties,…
The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…
Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…
We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…
We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present…
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive…
A growing statistical literature focuses on causal inference in the context of experiments where the target of inference is the average treatment effect in a finite population and random assignment determines which subjects are allocated to…
In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…