Related papers: Discussion: The Dantzig selector: Statistical esti…
We report on the results of a computer search for primes $p$ which divide an Harmonic number $H_{\lfloor p/N \rfloor}$ with small $N > 1$.
We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has…
Estimation of the population size $n$ from $k$ i.i.d.\ binomial observations with unknown success probability $p$ is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously…
We point out that the traditional notion of test statistic is too narrow, and we propose a natural generalization that is arguably maximal. The study is restricted to simple statistical hypotheses.
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
Pausinger recently investigated a special determinant involving prime numbers. In this short note we point out that this type of determinants was already known in linear algebra and its computation is unrelated to prime numbers.
Some question about representations of $p$-adic groups are discussed.
Shafer (2021) offers a betting perspective on statistical testing which may be useful for foundational debates, given that disputes over such testing continue to be intense. To be helpful for researchers, however, this perspective will need…
We survey large value problems, including the large value problem for Dirichlet polynomials, the restriction problem, and problems from computer science. We describe known techniques and open problems, drawing on perspectives from all three…
This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of treatment rules. The specific new contribution is to study as-if optimization…
This paper deals with the proportional hazards model proposed by D. R. Cox in a high-dimensional and sparse setting for a regression parameter. To estimate the regression parameter, the Dantzig selector is applied. The variable selection…
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to…
In this paper, we consider statistical inference with generalized linear models in high dimensions under a longitudinal clustered data framework. Specifically, we propose a de-sparsified version of an initial Dantzig-type regularized…
Differentially private statistical estimation has seen a flurry of developments over the last several years. Study has been divided into two schools of thought, focusing on empirical statistics versus population statistics. We suggest that…
Let $V \subset \mathbb{R}$ be a finite set with $|V| = n $ and suppose we are given each pairwise distance independently with probability $p$. We show that if $p = (1+\epsilon)/n$, for some fixed $\epsilon >0$, then we can reconstruct a…
We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of…
The distcomp command is introduced and illustrated. The command assesses whether or not two distributions differ at each possible value while controlling the probability of any false positive, even in finite samples. Syntax and the…
The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets…
Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]