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We learn mathematics subjectively and must apply it objectively. But sometimes, we apply it subjectively by using wrong intuitions which may be elusive to our eyes. The aim of this note is to disclose the secretes of two kinds of these…
Several systematic studies have suggested that a large fraction of published research is not reproducible. One probable reason for low reproducibility is insufficient sample size, resulting in low power and low positive predictive value. It…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a P-value, we construct a…
An important issue for many economic experiments is how the experimenter can ensure sufficient power for rejecting one or more hypotheses. Here, we apply methods developed mainly within the area of clinical trials for testing multiple…
We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that…
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…
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…
We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider…
Estimates based on 2x2 tables of frequencies are widely used in statistical applications. However, in many cases these tables are incomplete in the sense that the data required to compute the frequencies for a subset of the cells defining…
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised.…
This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process.…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would…
We introduce estimation and test procedures through divergence minimiza- tion for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with…
We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference…
In order to estimate causal effects in a randomized experiment where spillovers are suspected to occur, analysts must posit a model of interference. The most popular class of interference models are those based on exposure mappings. In…