关于非中心Laplace分布的密度函数

在本文中,对文[1]提出的广义Laplace分布进行了讨论,给出了广义Laplace分布的密度函数的解析表达式,同时进一步推导了非中心Laplace分布的密度函数表达式,最后对这类分布重要的数字特征在文中也被给出.     

等热流热绕流运动密度场的加权残数解

本文给出了等热流条件下热绕流运动密度场的加权残数解，并且在一给定的工况下计算了相应的密度场，所得结果与数值解及实验情况相吻合．该解法具有解析结构清楚、计算工作量小的特点．     

康有为1888年上书的文化渊源

康有为1888年上书与他的早期大同思想有直接的联系。"内圣外王"是康有为的思想体系,其渊源来自朱熹理学。他依循朱熹的伦理哲学,"修养"分为内外两个方面:其内的心性修养,产生了救国献身的精神力量;其外的穷究义理,得到了"治国平天下"的公理,为今后的变法行动作好了理论准备。由"内圣"走向"外王",第一步就是《第一次上清皇帝书》。     

酶催化乙酰基转移反应的密度泛函研究(Ⅱ)

用密度泛函方法的B3LYP在6-31 g(d,p)基组水平上,研究了底物对-氨基苯甲酸与芳基胺-N-乙酰基转移酶之间的乙酰化反应.该反应共有两种可能的反应机理:协同反应和分步反应.计算结果表明,协同反应机制在竞争中占优势,是势能面上的最低能量反应通道.     

Penalized contrast estimator for adaptive density deconvolution

The authors consider the problem of estimating the density g of independent and identically distributed variables X_I, from a sample Z₁,… Z_n such that Z_I = X_I + σ? for i = 1,…, n, and E is noise independent of X, with σ? having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.     

Integrated Square Error Asymptotics for Supersmooth Deconvolution

Abstract.  We derive the asymptotic distribution of the integrated square error of a deconvolution kernel density estimator in supersmooth deconvolution problems. Surprisingly, in contrast to direct density estimation as well as ordinary smooth deconvolution density estimation, the asymptotic distribution is no longer a normal distribution but is given by a normalized chi-squared distribution with 2 d.f. A simulation study shows that the speed of convergence to the asymptotic law is reasonably fast.     

Rate of strong uniform convergence of k-NN density estimates

Let f_n(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f_n(x) on some suitably chosen interval J_δ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.     

Non-parametric recursive estimates of a probability density function and its derivatives

Recursive estimates of a probability density function (pdf) are known. This paper presents recursive estimates of a derivative of any desired order of a pdf. Let f be a pdf on the real line and p?0 be any desired integer. Based on a random sample of size n from f, estimators f^(p)_n of f^(p), the pth order derivatives of f, are exhibited. These estimators are of the form $\text{n}{}^{\mathrm{?1}}\text{∑n}\text{j=1}\text{δ}{}_{\mathrm{jp}}$, where δ_jp depends only on p and the jth observation in the sample, and hence can be computed recursively as the sample size increases. These estimators are shown to be asymptotically unbiased, mean square consistent and strongly consistent, both at a point and uniformly on the real line. For pointwise properties, the conditions on f^(p) have been weakened with a little stronger assumption on the kernel function.     

Density estimation for samples satisfying a certain absolute regularity condition

Let {ξ_i} be an absolutely regular sequence of identically distributed random variables having common density function f(x). Let H_k(x,y) (k=1, 2,…) be a sequence of Borel-measurable functions and f_n(x)=n^?1(H_n(x,ξ₁)+…+H_n(x,ξ_n)) the empirical density function. In this paper, the asymptotic property of the probability P(sup_x|f_n(x)?f(x)|>ε) (n→∞) is studied.     

The strong uniform convergence of multivariate variable kernel estimates

We show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f, and f_n is the variable kernel estimate Here H_ni is the distance between X_i and its kth nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn