相关论文: Data-driven goodness-of-fit tests
Artificial intelligence models trained from data can only be as good as the underlying data is. Biases in training data propagating through to the output of a machine learning model are a well-documented and well-understood phenomenon, but…
This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…
Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism…
We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
Nowadays, data analysis in the world of Big Data is connected typically to data mining, descriptive or exploratory statistics, e.~g.\ cluster analysis, classification or regression analysis. Aside these techniques there is a huge area of…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
We propose a family of tests to assess the goodness-of-fit of a high-dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and…
Given a pair of non-negative random variables $X$ and $Y$, we introduce a class of nonparametric tests for the null hypothesis that $X$ dominates $Y$ in the total time on test order. Critical values are determined using bootstrap-based…
We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses.…
Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…
Data-driven learning is generalized to consider history-dependent multi-fidelity data, while quantifying epistemic uncertainty and disentangling it from data noise (aleatoric uncertainty). This generalization is hierarchical and adapts to…
A common problem in physics is to fit regression data by a parametric class of functions, and to decide whether a certain functional form allows for a good fit of the data. Common goodness of fit methods are based on the calculation of the…
We introduce two new tools to assess the validity of statistical distributions. These tools are based on components derived from a new statistical quantity, the $comparison$ $curve$. The first tool is a graphical representation of these…
A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…
We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…
The problem of simple $M-$ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…