Related papers: Testing predictor contributions in sufficient dime…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty.…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualization in a low-dimension framework. However, some popular dimension reduction methodologies fail to achieve this aim when…
This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…
Covariate-adaptive randomization is widely used in clinical trials to balance prognostic factors, and regression adjustments are often adopted to further enhance the estimation and inference efficiency. In practice, the covariates may…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
This paper presents a goodness-of-fit test for parametric regression models with scalar response and directional predictor, that is, a vector on a sphere of arbitrary dimension. The testing procedure is based on the weighted squared…
We study the problem of lossless feature selection for a $d$-dimensional feature vector $X=(X^{(1)},\dots ,X^{(d)})$ and label $Y$ for binary classification as well as nonparametric regression. For an index set $S\subset \{1,\dots ,d\}$,…
In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…