Consistent deconvolution in density estimation

Suppose we have n observations from X = Y + Z, where Z is a noise component with known distribution, and Y has an unknown density f. When the characteristic function of Z is nonzero almost everywhere, we show that it is possible to construct a density estimate f_n such that for all f, Iim_n| |=0.     

Institutionalizing Counter‐Memories of the U.S. Civil Rights Movement: The National Civil Rights Museum and an Application of the Interest‐Convergence Principle

During the post–Reconstruction era in the United States, white southerners marked the cultural landscape with monuments and memorials honoring the Confederate cause and its heroes. These racialized symbols enjoyed an undisputed claim to public squares and parks throughout the South. It was not until the late twentieth century that commemorations to the black freedom struggle were publicly supported. This analysis examines the institutionalization of counter‐memories of the civil rights movement in Memphis, Tennessee at the Lorraine Motel, the site of the assassination of Reverend Dr. Martin Luther King, Jr. The author draws on collective memory, cultural trauma, and social movements research as well as critical race theory to explain the creation of the National Civil Rights Museum. Using primary and secondary data sources the author examines how social memory agents, a changing political culture, and the passage of time mediated the cultural trauma of King's assassination and influenced the institutionalization of oppositional collective memories. Relying on Derrick Bell's interest‐convergence principle, the author concludes that the creation of this major memorial museum was a result of the convergence of white and black interests, specifically the economic and political interests of white elites and the cultural and political interests of black symbolic entrepreneurs.     

Approximating moments of continuous functions of random variables using Bernstein polynomials

Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function $g\left(X\right)$ of a random variable $X$, and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of $g\left(X\right)$ with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).     

Local Estimation of the Conditional Stable Tail Dependence Function

We consider the local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centred Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study and on a dataset of air pollution measurements.     

Complete convergence and the strong laws of large numbers for pairwise NQD random variables

The authors study the strong convergence for sequences of pairwise negatively quadrant dependent (NQD) random variables under some wide conditions, and present some new theorems on the complete convergence and the strong laws of large numbers. The obtained results extend and improve some theorems in existing literature.     

FDA: strong consistency of the kNN local linear estimation of the functional conditional density and mode

In this paper we present a new estimator of the conditional density and mode when the co-variables are of functional kind. This estimator is a combination of both, the k-Nearest Neighbours procedure and the functional local linear estimation. Then, for each statistical parameter (conditional density or mode), results concerning the strong consistency and rate of convergence of the estimators are presented. Finally, their performances, for finite sample sizes, are illustrated by using simulated data.     

Uniform Convergence of Compactly Supported Wavelet Expansions of Gaussian Random Processes

New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of non stationary processes. An application of the obtained results to stationary processes is also presented. It is shown that the convergence rate of the expansions is exponential.     

基于潜类别随机前沿的区域创新效率及其影响因素分析

运用可根据研究对象的潜在属性内生分组的潜类别随机前沿模型,采用1999-2012年中国各省区数据,研究各省区的创新效率及影响因素。结果表明:以人力资本水平和基础设施状况为条件变量,将全国各省区分成两个技术类别,分别有各自的技术前沿和函数形式,A类别中上海市的创新效率最高,B类别中河北省的创新效率最高;平均来看,各类的创新效率均呈上升趋势,贸易开放、产业结构和金融发展对创新效率均有显著的正向作用,同时创新效率在各类内部均存在俱乐部收敛。     

Global convergence of the log-concave MLE when the true distribution is geometric

Let X₁, …, X_n be i.i.d. from a discrete probability mass function (pmf) p. In Balabdaoui et al. [(2013), ‘Asymptotic Distribution of the Discrete Log-Concave mle and Some Applications’, JRSS-B, in press], the pointwise limit distribution of the log-concave maximum-likelihood estimator (MLE) was derived in both the well- and misspecified settings. In the well-specified setting, the geometric distribution was excluded, classified as being degenerate. In this article, we establish the global asymptotic theory of the log-concave MLE of a geometric pmf in all ?_q distances for q∈{1, 2, …}∪{∞}. We also show how these asymptotic results could be used in testing whether a pmf is geometric.     

Optimal scaling of Metropolis algorithms: Heading toward general target distributions

The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.