Related papers: Regression rank scores in nonlinear models

Regressing a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its…

In this paper, we consider a partially linear model of the form $Y_t=X_t^{\tau}\theta_0+g(V_t)+\epsilon_t$, $t=1,...,n$, where $\{V_t\}$ is a $\beta$ null recurrent Markov chain, $\{X_t\}$ is a sequence of either strictly stationary or…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Let $X_{1}=(W_{1},Y_{1}),\ldots,X_{n}=(W_{n},Y_{n})$ be $n$ pairs of independent random variables. We assume that, for each $i\in\{1,\ldots,n\}$, the conditional distribution of $Y_{i}$ given $W_{i}$ belongs to a one-parameter exponential…

We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…

We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…

We consider in this paper the multivariate regression problem, when the target regression matrix $A$ is close to a low rank matrix. Our primary interest in on the practical case where the variance of the noise is unknown. Our main…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…

Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical…

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and…

We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

The order of smoothness chosen in nonparametric estimation problems is critical. This choice balances the tradeoff between model parsimony and data overfitting. The most common approach used in this context is cross-validation. However,…

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…

Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…