Related papers: The First-stage F Test with Many Weak Instruments
Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
Factor analysis is over a century old, but it is still problematic to choose the number of factors for a given data set. The scree test is popular but subjective. The best performing objective methods are recommended on the basis of…
Motivated by the inquiries of weak signals in underpowered genome-wide association studies (GWASs), we consider the problem of retaining true signals that are not strong enough to be individually separable from a large amount of noise. We…
Randomized controlled trials generate experimental variation that can credibly identify causal effects, but often suffer from limited scale, while observational datasets are large, but often violate desired identification assumptions. To…
Optomechanical systems are often used for the measurement of weak forces. Feedback loops can be used in these systems for achieving noise reduction. Here we show that even though feedback is not able to improve the signal to noise ratio of…
Weak measurement [1,19] combined with quantum delayed-choice experiment that use quantum beam splitter instead of the beam splitter give rise to a surprising amplification effect, i.e., counterintuitive negative amplification effect. We…
In this paper we analyse the behaviour of adaptive filters or detectors when they are trained with $t$-distributed samples rather than Gaussian distributed samples. More precisely we investigate the impact on the distribution of some…
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The…
Time-to-event endpoints show an increasing popularity in phase II cancer trials. The standard statistical tool for such one-armed survival trials is the one-sample log-rank test. Its distributional properties are commonly derived in the…
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change…
Two-stage least squares (TSLS) estimators and variants thereof are widely used to infer the effect of an exposure on an outcome using instrumental variables (IVs). They belong to a wider class of two-stage IV estimators, which are based on…
Suppose that a data analyst wishes to report the results of a least squares linear regression only if the overall null hypothesis, $H_0^{1:p}: \beta_1= \beta_2 = \ldots = \beta_p=0$, is rejected. This practice, which we refer to as…
Measurement uncertainty is a non trivial aspect of the laboratory component of most undergraduate physics courses. Confusion about the application of statistical tools calls for the elaboration of guidelines and the elimination of…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
The F-measure or F-score is one of the most commonly used single number measures in Information Retrieval, Natural Language Processing and Machine Learning, but it is based on a mistake, and the flawed assumptions render it unsuitable for…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
Experimentation platforms in industry must often deal with customer trust issues. Platforms must prove the validity of their claims as well as catch issues that arise. As a central quantity estimated by experimentation platforms, the…
The Friedman test has been extensively applied as a nonparametric alternative to the conventional F procedure for comparing treatment effects in randomized complete block designs. A chi-square distribution provides a convenient…
We introduce a first-order quantum-phase-transition model, which exhibits giant sensitivity $\chi \propto N^2$ at the critical point. Exploiting this effect, we propose a quantum critical detector (QCD) to amplify weak input signals. The…