Asymptotic properties of the least squares estimators of the parameters of the chirp signals

Chirp signals are quite common in different areas of science and engineering. In this paper we consider the asymptotic properties of the least squares estimators of the parameters of the chirp signals. We obtain the consistency property of the least squares estimators and also obtain the asymptotic distribution under the assumptions that the errors are independent and identically distributed. We also consider the generalized chirp signals and obtain the asymptotic properties of the least squares estimators of the unknown parameters. Finally we perform some simulations experiments to see how the asymptotic results behave for small sample and the performances are quite satisfactory.     

Asymptotic Properties of the Electromagnetic Field in the External Schwarzschild Spacetime

. We study the asymptotic behaviour of the solutions to the vacuum Maxwell equations in the external Schwarzschild spacetime. The results are based on the extensive use of geometric considerations and the introduction of generalized energy estimates. We obtain the asymptotic behaviour along the null outgoing directions and we prove also some partial results concerning the behaviour along the timelike curves. Our techniques can be also used to control the asymptotic behaviour of the various derivatives of the Maxwell field and to obtain the asymptotic behaviour of the Weyl tensor fields, solutions of the "spin 2" equations.     

Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection

For a singularly perturbed parabolic equation termed in applications as the reaction-diffusion-advection equation, stationary solutions with internal transition layers (contrast structures) are studied. An arbitrary-order asymptotic approximation of such solutions is constructed, and an existence theorem is proved. An efficient algorithm for constructing an asymptotic approximation of the transition point is proposed. The constructed asymptotic approximation is justified by applying the asymptotic method of differential inequalities, which is extended to the class of problems under study. This method is also used to establish the Lyapunov stability of such stationary solutions.     

强混合样本下最近邻密度估计的渐近正态性

研究了α-混合样本下最近邻密度估计的渐近性质,证明了估计的渐近正态性并且给出了其渐近方差的显式表达式,由此构造了α-混合样本下概率密度的渐近置信区间.     

On the cubic convergence of the Paardekooper method

We show a simple way how asymptotic convergence results can be conveyed from a simple Jacobi method to a block Jacobi method. Our pilot methods are the well known symmetric Jacobi method and the Paardekooper method for reducing a skew-symmetric matrix to the real Schur form. We show resemblance in the quadratic and cubic convergence estimates, but also discrepances in the asymptotic assumptions. By numerical tests we confirm that our asymptotic assumptions for the Paardekooper method are most general.     

On the asymptotic spectra of the bounded solutions of a nonlinear Volterra equation

We consider the asymptotic behavior of the bounded solutions of a nonlinear Volterra integrodifferential equation with a positive definite convolution kernel. Our main result states that (under appropriate assumptions) the asymptotic spectra of the solutions are contained in the set where the real part of the Fourier transform of the kernel vanishes. We also give a new asymptotic stability theorem, and present a new proof of a known result on the asymptotic behavior of the bounded solutions of a nonlinear, nondifferentiated Volterra equation.     

Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.     

Computing the asymptotic worst-case of bin packing lower bounds

This paper addresses the issue of computing the asymptotic worst-case of lower bounds for the Bin Packing Problem. We introduce a general result that allows to bound the asymptotic worst-case performance of any lower bound for the problem and to derive for the first time the asymptotic worst-case of the well-known bound L₃ by Martello and Toth. We also show that the general result allows to easily derive the asymptotic worst-case of several lower bounds proposed in the literature.     

A note on the asymptotic distribution of the maximum likelihood estimator in a non-regular case

We consider the asymptotic distribution of the maximum likelihood estimator (MLE), when the log-likelihood ratio statistic weakly converges to the non-degenerated Gaussian process. We provide a simple expression for the density function of the asymptotic distribution by fundamental stochastic results. This note is helpful to investigate asymptotic properties of the MLE in a certain non-regular case.     

On the asymptotic distribution of multivariate M-estimates

The asymptotic distribution of multivariate M-estimates is studied. It is shown that, in general, consistency leads to asymptotic normality and a Law of the Iterated Logarithm. The results are used to compute via matrix derivatives the asymptotic distribution of a class of estimates due to Maronna.     

微分方程零解的弱渐近稳定与不稳定的判定定理

给出了平凡解弱渐近稳定定义及在已知导函数 d Vdt负定的情况下 ,通过 V( t,x)函数的符号性质来判定微分方程平凡解的弱渐近稳定性与不稳定性 ,并举例说明定理的应用 .     

Asymptotic models for the topological sensitivity of the energy functional

The refined method of matched asymptotic expansions is used for constructing asymptotic models for the topological sensitivity of the energy functional with respect to the creation of several small holes in the geometrical domain.     

On the asymptotic behaviour of capillary surfaces in cusps

Concus and Finn [2] discovered that capillary surfaces rise to infinity in corners with sufficiently small opening angle. They also found the leading term of an asymptotic expansion. Miersemann [5] improved this result to obtain a complete asymptotic expansion. In the present paper we will apply the methods of the above authors to discuss asymptotic behaviour of capillarities in cusps, which is a corner with opening angle 0. A large variety of asymptotic formulas will be provided. The general comparison theorem from Concus and Finn will play an important role in the proofs.     

Boundary-value problems of the asymmetric theory of elasticity for thin plates

Boundary-value problems of the three-dimensional asymmetric micropolar, moment theory of elasticity with free rotation are considered for thin plates. It is assumed that the total stress-strain state is the sum of the internal stress-strain state and the boundary layers, which are determined in an approximation using asymptotic analysis. Three different asymptotic forms are constructed for the three-dimensional boundary-value problem posed, depending on the values of dimensionless physical constants of the plate material. The initial approximation for the first asymptotic form leads to a theory of micropolar plates with free rotation, the initial approximation for the second asymptotic form leads to a theory of micropolar plates with constrained rotation, and the initial approximation for the third asymptotic form leads to a theory of micropolar plates with “small shear stiffness.” The corresponding micropolar boundary layers are constructed and studied. The regions of applicability of each of the theories of micropolar plates constructed are indicated.     

Asymptotic behavior of the resolvent of an unstable volterra equation with kernel depending on the difference of the arguments

We present the structure of the resolvent of a difference kernel, which allows us to study the asymptotic behavior of the solution of the renewal equation for a given asymptotic behavior of the constant term. An asymptotic representation for the resolvent is obtained under minimal requirements on the moments of the kernel. Similar results are given for integro-differential equations. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 88–94, July, 1997. Translated by M. A. Shishkova     

Asymptotics for the ratio and the zeros of multiple Charlier polynomials

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depends on the degree of the polynomial, in which case we obtain another asymptotic distribution of the zeros.     

Unified treatment of several asymptotic formulas for the gamma function

We consider a class of the asymptotic expansions for the gamma function, and derive a formula for determining the coefficients of the asymptotic expansions. Thus, we give a unified treatment of several asymptotic expansions for the gamma function due to Laplace, Ramanujan–Karatsuba, Gosper, Mortici and Batir.     

Asymptotic solution of the first boundary-value problem of the theory of elasticity of the forced vibrations of an isotropic strip

The first boundary-value problem of the theory of elasticity of the forced vibrations of an isotropic strip is solved by an asymptotic method. The asymptotic form of the components of the stress tensor and the displacement vector, which differ in principle from the asymptotic form in the corresponding static problem, is established. All the required quantities in the inner problem are determined and the conditions for resonance to occur are established. The solution in the dynamic boundary layer is constructed and the fundamental (inner) and boundary solutions are matched.     

Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters

We consider an eigenvalue problem for the two-dimensional Hartree operator with a small parameter at the nonlinearity. We obtain the asymptotic eigenvalues and the asymptotic eigenfunctions near the upper boundaries of the spectral clusters formed near the energy levels of the unperturbed operator and construct an asymptotic expansion around the circle where the solution is localized.     

第五类Painlevé方程解的渐近性态分析

本文用比较直接的方法研究Painleve方程的渐近解和连同公式:(1)先求出数值解,然后用最小二乘法拟合出最佳渐近解;(2)根据最佳渐近解的表达形式,用谐波平衡法得到振荡渐近解与参数之间的依赖关系,即连同公式．当参数α,β,γ和δ满足一些条件时,对一般实的第五类Painleve方程,我们找出了振荡渐近解和连同公式．