Related papers: Rejoinder: The Dantzig selector: Statistical estim…
Let $(X,Y)$ be a random vector whose conditional excess probability $\theta(x,y):=P(Y\leq y | X>x)$ is of interest. Estimating this kind of probability is a delicate problem as soon as $x$ tends to be large, since the conditioning event…
Let $N$ denotes a sufficiently large even integer, $p$ denotes a prime and $P_{r}$ denotes an integer with at most $r$ prime factors. In this paper, we study the solutions of the equation $N-p=P_3$ and consider two special cases where $p$…
We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.
In the preceding articles we considered fractional integral transforms involving one real scalar variable, one real matrix variable and real scalar multivariable case. In the present paper we consider the multivariable case when the…
Rejoinder of "Treelets--An adaptive multi-scale basis for spare unordered data" [arXiv:0707.0481]
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…
Rejoinder to "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet [arXiv:1208.3378].
Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t) $ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional…
The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness…
An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
The statistically unbounded $p$-convergence is an abstraction of the statistical order, unbounded order, and $p$-convergences. We investigate the concept of the statistically unbounded convergence on lattice-normed Riesz spaces with respect…
As large and powerful neural language models are developed, researchers have been increasingly interested in developing diagnostic tools to probe them. There are many papers with conclusions of the form "observation X is found in model Y",…
Rejoinder to "Likelihood Inference for Models with Unobservables: Another View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
New cases of the multiplicity conjecture are considered.
Let $d\ge 3$ be a fixed integer, $p\in (0,1)$, and let $n\geq 1$ be a positive integer such that $dn$ is even. Let $\mathbb{G}(n, d, p)$ be a (random) graph on $n$ vertices obtained by drawing uniformly at random a $d$-regular (simple)…
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…
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…
This paper offers a commentary on the use of notions of statistical significance in choice modelling. We review the reasons for uncertainty in parameter estimates, provide a precise discussion on the computation of measures of uncertainty…
We introduce a variant of the large sieve and give an example of its use in a sieving problem. Take the interval [N] = {1,...,N} and, for each odd prime p <= N^{1/2}, remove or ``sieve out'' by all n whose reduction mod p lies in some…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…