Related papers: Reverse Mathematics and parameter-free Transfer
In transformation regression models the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA0, ATR0, and Pi11-Comprehension.
Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…
This is a Research and Instructional Development Project from the U. S. Naval Academy. In this monograph, the basic methods of nonstandard analysis for n-dimensional Euclidean spaces are presented. Specific rules are deveoped and these…
An alternative way of looking at the Riemann hypothesis from the viewpoint of mathematical control theory is considered. A control theoretic transfer function is constructed by inverting the values of the Riemann zeta-function from which…
This paper reports a modified axiomatic foundation of the analytic hierarchy process (AHP), where the reciprocal property of paired comparisons is broken. The novel concept of reciprocal symmetry breaking is proposed to characterize the…
In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the…
Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with independent random sample size have been originated by…
This paper develops a rigorous probabilistic framework that extends denoising diffusion models to the setting of noncommutative random variables. Building on Voiculescu's theory of free entropy and free Fisher information, we formulate…
In many economic applications, multiple source datasets are available, but their effective combination is challenging due to heterogeneity across datasets. To address this problem, we study a parameter-transfer framework that shares only…
Recent AI regulations call for data that remain useful for innovation while resistant to misuse, balancing utility with protection at the model level. Existing approaches either perturb data to make it unlearnable or retrain models to…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
Odds ratios and log-linear parameters are not collapsible, meaning that including a variable into the analysis or omitting one from it, may change the strength of association among the remaining variables. Even the direction of association…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…
We establish a class of sufficient conditions, ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this result to construct a set of explicit counterexamples,…
We study the reverse mathematics of countable analogues of several maximality principles that are equivalent to the axiom of choice in set theory. Among these are the principle asserting that every family of sets has a $\subseteq$-maximal…
We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…