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1.
条件密度近邻-核估计的强相合性 总被引:1,自引:0,他引:1
Let (X, Y), (X_1, Y_1), …, (X_n, Y_n) be R~p×R~q-valued i.i.d, random vectors, and f(y|x) the conditional density function of Y, given X=x. Note that the existence of the density of (X, Y) is not assumed here. In this paper, we introduce the nearest neighborkernel estimator f_n(y|x) of f(y|x), and establish the strong consistency of f_n(y|x) under some mild conditions. 相似文献
2.
《数学物理学报(B辑英文版)》2015,(6)
In this paper,we solve the quadratic p-functional inequalities‖f(x+y)+f(x-y)-2f(x)-2f(y)‖≤‖ρ(2f((x+y)/2)+2f((x-y)/2)-f(x)-f(y))‖,(0.1)where ρ is a fixed complex number with |ρ| 1,and‖2f((x+y)/2)+2f((x-y)/2)-f(x)-f(y)‖≤‖ρ(f(x+y)+f(x-y)-2f(x)-2f(y))‖,(0.2)where ρ is a fixed complex number with |ρ| 1/2.Using the direct method,we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities(0.1) and(0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities(0.1)and(0.2) in complex Banach spaces. 相似文献
3.
On the uniform strong approximation of Marcinkiewicz type for multivariable continuous functions 总被引:2,自引:0,他引:2
Yujun Zhang Xiaoyuan He 《分析论及其应用》2005,21(4):377-384
The rate of uniform strong approximation of Marcinkiewicz type for multivariable continuous func-tions is obtained in this paper as follows:‖1/k 1 k∑j=0|Sj(f)- f|q‖≤C/k 1 k∑j=0 Eqj(f),where Sj (f) denotes the square partial Fourier sum of f and Ej (f) denotes the square best approximation of f by trigonometric polynomials of degree (j, j, … ,j),j = 0,1, 2,…. 相似文献
4.
Lagrange插值逼近导数的平均收敛 总被引:1,自引:0,他引:1
<正>We consider the rate of mean convergence of derivatives by Lagrange interpolation operators L_n(f,x) based on the zeros of Chebyshev polynomials of the first kind.A sharp estimate of the derivative of L_n(f,x)—f(x) in terms of the error of best approximation by polynomials of degree n is derived. 相似文献
5.
施锡铨 《应用数学学报(英文版)》1985,2(2):112-117
Let U_n be a U-statistic with symmetric kernel h(x,y) such that Eh(X_1,X_2)=θ and Var E[h(X_1,X_2)-θ|X_j]>0.Let f(x) be a function defined on R and f″ be bounded.If f(θ) is the parameterof interest,a natural estimator is f(U_n).It is known that the distribution function of z_n=(n~(1/2){Jf(U_n)-f(θ)})/(S_n~*) converges to the standard normal distribution Φ(x) as n→∞,where Jf(U_n) isthe jackknife estimator of f(U_n),and S_n~(*2) is the jackknife estimator of the asymptotic variance ofn~(1/2) Jf(U_n).It is of theoretical value to study the rate of the normal approximation of the statistic.In this paper,assuming the existence of fourth moment of h(X_1,X_2),we show that(?)|P{z_n≤x}-Φ(x)|=O(n~(-1/2)log n).This improves the earlier results of Cheng(1981). 相似文献
6.
An L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)-f(y)|(?)2 if d(x, y)=1 and |f(x)-f(y)|(?)1 if d(x,y)=2. The L(2,1)-labeling numberλ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v) : v∈V(G)}=k. We study the L(3,2,1)-labeling which is a generalization of the L(2,1)-labeling on the graph formed by the (Cartesian) product and composition of 3 graphs and derive the upper bounds ofλs(G) of the graph. 相似文献
7.
We point out that the Meyer-Konig and Zeller operator M. (f;x) are unbounded in usual Jacobiweighted norm at first, and then we consider the weighted approximation by M.(f ;x) by a new norm andobtain the characterization of convergence rate in nonoptimal approximation by K-functional. 相似文献
8.
We point out that the Meyer-Konig and Zeller operator Mn(f;x) are unbounded in usual Jacobi weighted norm at first,and then we consider the weighted approximation by Mn(f;x) by a new norm and obtain the characterization of convergence rate in nonoptimal approximation by K-functional. 相似文献
9.
《分析论及其应用》2002,(3)
We point out that the Meyer-Konig and Zeller operator M(?) (f;x) are unbounded in usual Jacobi weighted norm at first, and then we consider the weighted approximation by M(?)(f;x) by a new norm and obtain the characterization of convergence rate in nonoptimal approximation by K-functional. 相似文献
10.
Vesselin Vatchev 《分析论及其应用》2011,27(2):187-200
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed. 相似文献
11.
Xue Liugen Cai GuoliangDept.of Appl.Math. Beijing Polytechnic Univ. Beijing . Faculty of Science Jiangsu Univ.of Science Technology Zhenjiang . 《高校应用数学学报(英文版)》2000,(4)
§ 1 IntroductionLet(X,Y) be a random vector taking values Rp×Rqand assume that with given X=x,f(y|x) is the conditional density of Y,the Borel-measurable function on(x,y) ,X has amarginal distribution function F(x) and a marginal density function f(x) .Let(X1 ,Y1 ) ,...,(Xn,Yn) be i.i.d.sample taking values in(X,Y) .A class of double kernel esti-mates of f(y|x) proposed by Zhao Linchang and Liu Zhijun[1 ] has the formfn(y|x) = ni=1K1Xi -xan K2Yi -ybn bqn nj=1K1Xj-xan ,(1 .1 )where… 相似文献
12.
We study the rate of uniform approximation by Nörlund means of the rectangular partial sums of double Fourier series of continuous functionsf(x, y), 2π-periodic in each variable. The results are given in terms of the modulus of symmetric smoothness defined by $$\begin{gathered} \omega _2 \left( {f,\delta _1 ,\delta _2 } \right) = \mathop {\sup }\limits_{x,y} \mathop {\sup }\limits_{\left| u \right| \leqslant \delta _1 ,\left| v \right| \leqslant \delta _2 } \left| {f\left( {x + u,y + v} \right)} \right. + f\left( {x + u,y - v} \right) + f\left( {x - u,y + v} \right) \hfill \\ + \left. {f\left( {x - u,y - v} \right) + 4f\left( {x,y} \right)} \right| for \delta _1 ,\delta _2 \geqslant 0. \hfill \\ \end{gathered} $$ As a special case we obtain the rate of uniform approximation to functionsf(x,y) in Lip({α, β}), the Lipschitz class, and inZ({α, β}), the Zygmund class of ordersα andβ, 0<α,β ≤ l, as well as the rate of uniform approximation to the conjugate functions \(\tilde f^{(1,0)} (x,y), \tilde f^{(0,1)} (x,y)\) and \(\tilde f^{(1,1)} (x,y)\) . 相似文献
13.
In this paper, solutions for two types of ultrametric kinetic equations of the form reaction-diffusion are obtained and properties
of these solutions are investigated. General method to find the solution of equation of the form
$
\tfrac{\partial }
{{\partial t}}f(x,t) = \int_{\mathbb{Q}_p } {W(|x - y|_p )(f(y,t) - f(x,t))dy + V(|x|_p )f(x,t),f(x,0) = \phi (|x|_p ),}
$
\tfrac{\partial }
{{\partial t}}f(x,t) = \int_{\mathbb{Q}_p } {W(|x - y|_p )(f(y,t) - f(x,t))dy + V(|x|_p )f(x,t),f(x,0) = \phi (|x|_p ),}
相似文献
14.
Ante Mimica 《Potential Analysis》2012,36(2):203-222
We consider the following non-local operator
|