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We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine.…
Optimal pointwise estimates are derived for the biharmonic Green function under Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green…
The multinomial and related distributions have long been used to model categorical, count-based data in fields ranging from bioinformatics to natural language processing. Commonly utilized variants include the standard multinomial and the…
Standard ordinal allocation methods ignore how strongly agents value different improvements, while cardinal methods require additional assumptions that are often considered too demanding. This paper studies assignment problems in the middle…
We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum…
Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for…
We study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…
Suppose $\{\widehat\theta_n\colon n\ge1\}$ is a strongly consistent sequence of estimators for a parameter $\theta$, where $\widehat\theta_n$ is based on the first $n$ observations. Consider $Q_\varepsilon$, the number of times…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers
In this article, we revisit the problem of estimating the unknown zero-symmetric distribution in a two-component location mixture model, considered in previous works, now under the assumption that the zero-symmetric distribution has a…
In this paper, we focus on efficient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson [25], that efficiency is characterized by a…
We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method.…
In this paper, we consider estimators for an additive functional of $\phi$, which is defined as $\theta(P;\phi)=\sum_{i=1}^k\phi(p_i)$, from $n$ i.i.d. random samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires…
The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is to compare the…
In this paper, we introduce SCALE, a collaborative framework that connects compact Specialized Translation Models (STMs) and general-purpose Large Language Models (LLMs) as one unified translation engine. By introducing translation from STM…
Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…
Use of machine learning to estimate nuisance functions (e.g. outcomes models, propensity score models) in estimators used in causal inference is increasingly common, as it can mitigate bias due to model misspecification. However, it can be…