Related papers: On Conditional Chisini Means and Risk Measures
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…
In this short note, we introduce probabilistic Cauchy functional equations, specifically, functional equations of the following form: $$ f(X_1 + X_2) \stackrel{d}{=} f(X_1) + f(X_2), $$ where $X_1$ and $X_2$ represent two independent…
We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the…
Nielsen [quant-ph/0108020] introduced a model of quantum computation by measurement-based simulation of unitary computations. In this model, a consequence of the non-determinism of quantum measurement is the probabilistic termination of…
We propose a variance-penalized formulation of Bayesian optimal experimental design for nonlinear models that augments the classical expected utility criterion with a penalty on utility variability, yielding a mean--variance objective that…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work…
We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
We define so-called residual means, which have a Taylor expansion of the form $M(x)=\bar x +\tfrac12 \xi_M(\bar x) \text{Var}(x)+o(\|x-\bar x\|^\alpha)$ for some $\alpha>2$ and a single-variable function $\xi_M$ ($\bar x$ stands for the…
Many typical Bell experiments can be described as follows. A source repeatedly distributes particles among two spacelike separated observers. Each of them makes a measurement, using an observable randomly chosen out of several possible…
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function…
Consider a stationary real-valued time series $\{X_n\}_{n=0}^{\infty}$ with a priori unknown distribution. The goal is to estimate the conditional expectation $E(X_{n+1}|X_0,..., X_n)$ based on the observations $(X_0,..., X_n)$ in a…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
Simulation and its variants (e.g., bisimulation and degree-preserving simulation) are useful in a wide spectrum of applications. However, all simulation variants are coarse "yes-or-no" indicators that simply confirm or refute whether one…