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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strichartz estimates for wave equations with a potential in non-trapping exterior domains
斯特里查茨估计 非陷阱外域 波动方程
2023/4/14
Consider the linear wave equations with a potential outside a compact set with a non-trapping boundary condition. Assuming that the potential satisfies an appropriate decreasing condition and that zer...
STRONG CONSISTENCY OF M-ESTIMATES OF MULTIPLE REGRESSION COEFFICIENTS
Linear regression M-estimate strong co
2007/12/17
In the case where ρ is convex we give a set of sufficient conditions for the strong consistency of M-estimate of multiple regression coefficients.
OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION
Nonparametric regression optimal rate o
2007/12/17
Let (X, Y) be a pair of random variables such that X ranges over [0, 1] and Y is real-valued and let go(X) be the conditional expectation of Y given X. Based on a training sample, the piecewise polyno...
EXISTENCE OF CONSISTENT ESTIMATES OF LINEAR REGRESSION COEFFICIENTS WHEN THE ERROR VARIANCES ARE UNEQUAL
Linear regression model consistency
2007/12/10
摘要 Consider the linear regression model Y_i=x_i′β+σ_ie_i,i=1,…,n,…, where E(e_i)=0, E(e_ie_j)=δ_(ij), 00. This paper shows that (i) if σ_i~2,i=1,2…, are known, then the necessary and sufficient condit...
In this paper, we use the virtual system method to estimate the parametersin a system tree and obtain a series of asymptotically efficient estimates of the interesting parameters. Section 1 is an intr...
The M-estimate of parameters in the errors-in-variables (EV) model Y =x^τβ_0+∈, X =x+u ((∈,u^τ)^τ is a (p+1)-dimensional spherical error, Coy[(∈, u^τ)^τ] =σ^2I_{p+1})being considered. The M-estimate \...
CONVERGENCE PROPERTIES OF MULTI-DIMENSIONAL NEAREST NEIGHBOR DENSITY ESTIMATES FOR THE CASE OF GENERAL KERNEL
N.N. estimate convergence rate bounded s
2007/8/7
In this paper we give weaker conditions to ensure the strong uniform consis-tency of multi-dimensional nearest neighbor (N.N.) estimates with non-uniform kernel and obtain the convergence rates of the...
This paper is concerned with the L1-norm estimators for the partly linear modelwhere (T_1,X_1, Y_1),…(T_n, X_n, Y_n) are independent random(d +2)-vectors such that K_i is real-valued, X_i is a d-vecto...
ASYMPTOTIC BEHAVIOR OF THE ESTIMATES OF HIGHER ORDER SPECTRA UNDER TRUNCATED WINDOW
Higher order spectra higher order perio
2007/8/7
This paper is concerned with the asymptotic behavior of the estimation of higher order spectra of stationary processes. Under suitable conditions, the L_2-consistency, the bias of the estimation and t...
ALL ADMISSIBLE LINEAR ESTIMATES OF REGRESSION COEFFICIENTS UNDER MATRIX LOSS
Admissibility matrix loss function lin
2007/8/7
The necessary and sufficient conditions for a linear estimator of a linear estimable function of regression coefficients in a general fixed effects linear model with the assumptions of normality to be...
ITERATIVE METHODS OF OBTAINING ESTIMATES FOR INCOMPLETE CONTINGENCY TABLES
Incomplete contingency tables maximum l
2007/8/7
An iterative method of De Jong, Greig and Madan(1985)for obtaining maximum likelihood estimates for contingency tables derived from a Mover-Stayer model is considered. It is shown that this method wor...
A PRIORI L~2 ERROR ESTIMATES FOR GALERKIN METHODS FOR NONLINEAR SOBOLEV EQUATIONS
Error estimates Galerkin method Sobole
2007/8/7
In this paper we study Galerkin approximations to the solution of the nonlinear Sobolev equation c(u)u_t=▽·{a(u)▽u_t+b(u)▽u}+f(u) in two spatial dimensions and derive optimal L~2 error estimates for t...