Related papers: Untestability of Average Slutsky Symmetry
Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if $g(t)=\sum_{k=0}^m a_kt^k$ is a polynomial of degree $m$ with non-negative coefficients, then, for all positive operators $A,\,B$ and…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behaviour (cf. Heckman 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric…
We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
This paper develops and implements a nonparametric test of Random Utility Models. The motivating application is to test the null hypothesis that a sample of cross-sectional demand distributions was generated by a population of rational…
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the…
We consider the problem of computing the satisfaction probability of a formula for stochastic models with parametric uncertainty. We show that this satisfaction probability is a smooth function of the model parameters. This enables us to…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
We study distribution-free nonparametric regression following a notion of average smoothness initiated by Ashlagi et al. (2021), which measures the "effective" smoothness of a function with respect to an arbitrary unknown underlying…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
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…
In this paper, we build a new test of rational expectations based on the marginal distributions of realizations and subjective beliefs. This test is widely applicable, including in the common situation where realizations and beliefs are…
We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
Let $\mu$ be a matrix-valued measure with the essential spectrum a single interval and countably many point masses outside of it. Under the assumption that the absolutely continuous part of $\mu$ satisfies Szego's condition and the point…
This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the…
We highlight that match fixed effects, represented by the coefficients of interaction terms involving dummy variables for two elements, lack identification without specific restrictions on parameters. Consequently, the coefficients…