Related papers: Attribute Estimation and Testing Quasi-Symmetry
Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
Procedures are given below to construct symmetric and anti-symmetric quantum functions. If hidden in an oracle, such functions can be identified exactly, without iterative interrogation. This is another example of quantum search. The…
We give a $\mathrm{poly}(\log n, 1/\epsilon)$-query adaptive algorithm for testing whether an unknown Boolean function $f: \{-1,1\}^n \to \{-1,1\}$, which is promised to be a halfspace, is monotone versus $\epsilon$-far from monotone. Since…
Given an element in a finite-dimensional real vector space, $V$, that is a nonnegative linear combination of basis vectors for some basis $B$, we compute the probability that it is furthermore a nonnegative linear combination of basis…
The asymmetric objective function is proposed as an alternative to Huber objective function to model skewness and obtain robust estimators for the location, scale and skewness parameters. The robustness and asymptotic properties of the…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…
We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. The central result of this thesis, developed in Chapter 3, is that a natural correspondence…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…