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Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the…
This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for…
Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…
The Y-test is a useful tool for detecting missing confounders in the context of a multivariate regression.However, it is rarely used in practice since it requires identifying multiple conditionally independent instruments, which is often…
In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of…
A longstanding problem of existing empirical process-based tests for regressions is that when the number of covariates is greater than one, they either have no tractable limiting null distributions or are not omnibus. To attack this…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
Due to its strong interpretability, linear regression is widely used in social science, from which significance test provides the significance level of models or coefficients in the traditional statistical inference. However, linear…
This thesis contains a series of independent contributions to statistics, unified by a model-free perspective. The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction…
A criterion is proposed for testing hypothesis about the nature of the error variance in the dependent variable in linear model, which separates correctly and incorrectly specified models. In the former only measurement errors determine the…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Suppose the nonparametric regression function of a response variable $Y$ on covariates $X$ and $Z$ is an affine function of $X$ such that the slope $\beta$ and the intercept $\alpha$ are real valued measurable functions on the range of the…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
Distinguishing causal connections from correlations is important in many scenarios. However, the presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing commonly employed in…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…