Related papers: Interval Effect Algebras and Holevo Instruments
For an effect algebra $A$, we examine the category of all morphisms from finite Boolean algebras into $A$. This category can be described as a category of elements of a presheaf $R(A)$ on the category of finite Boolean algebras. We prove…
Instrumental variables (IVs) are often continuous, arising in diverse fields such as economics, epidemiology, and the social sciences. Existing approaches for continuous IVs typically impose strong parametric models or assume homogeneous…
Using a one-to-one correspondence between observables and their spectral resolutions, we introduce the sum of any two bounded observables of a $\sigma$-MV-effect algebra. This sum is commutative, associative and with neutral element. Under…
This paper develops a Mean Group Instrumental Variables (MGIV) estimator for spatial dynamic panel data models with interactive effects, under large N and T asymptotics. Unlike existing approaches that typically impose slope-parameter…
Effect algebras were introduced as an abstract algebraic model for Hilbert space effects representing quantum mechanical measurements. We study additional structures on an effect algebra $E$ that enable us to define spectrality and spectral…
In the context of having an instrumental variable, the standard practice in causal inference begins by targeting an effect of interest and proceeds by formulating assumptions enabling its identification. We turn this around by adhering to…
A sequential effect algebra (SEA) is an effect algebra equipped with a sequential product operation modeled after the L\"uders product $(a,b)\mapsto \sqrt{a}b\sqrt{a}$ on C*-algebras. A SEA is called normal when it has all suprema of…
The unit interval in a partially ordered abelian group with order unit forms an interval effect algebra (IEA) which can be regarded as an algebraic model for the semantics of a formal deductive logic. There is a categorical equivalence…
For convex and sequential effect algebras, we study spectrality in the sense of Foulis. We show that under additional conditions (strong archimedeanity, closedness in norm and a certain monotonicity property of the sequential product), such…
The algebra of observables of planar electrons subject to a constant background magnetic field B is given by A_theta(R^2) x A_theta(R^2) the product of two mutually commuting Moyal algebras. It describes the free Hamiltonian and the guiding…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
The instrumental variable (IV) design is a common approach to address hidden confounding bias. For validity, an IV must impact the outcome only through its association with the treatment. In addition, IV identification has required a…
One of shortcomings of stepwise interval methods is the following. The intervals determining the solution of a system are often expanded in the course of time irrespective of the method and step used (the {\em Moore effect}). We introduce…
Many of the most fundamental observables | position, momentum, phase-point, and spin-direction | cannot be measured by an instrument that obeys the orthogonal projection postulate. Continuous-in-time measurements provide the missing…
This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to…
Algebraic effects are computational effects that can be represented by an equational theory whose operations produce the effects at hand. The free model of this theory induces the expected computational monad for the corresponding effect.…
Standard instrumental variables (IV) methods identify a Local Average Treatment Effect under monotonicity, which rules out defiers. In many empirical environments, however, distinct instruments may induce heterogeneous and even opposing…
We connect through the Fourier transform shift-invariant Sobolev type spaces $V_s\subset H^s$, $s\in\mathbb R,$ and the spaces of periodic distributions and analyze the properties of elements in such spaces with respect to the product. If…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
Many treatment variables used in empirical applications nest multiple unobserved versions of a treatment. I show that instrumental variable (IV) estimands for the effect of a composite treatment are IV-specific weighted averages of effects…