Edgeworth expansion of the Studentized product-limit estimator for truncated and censored data

Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).     

An Edgeworth Expansion for Studentized Finite Population Statistics

We show the validity of the one-term Edgeworth expansion for Studentized asymptotically linear statistics based on samples drawn without replacement from finite populations. Replacing the moments defining the expansion by their estimators we obtain an empirical Edgeworth expansion. We show the validity of the empirical Edgeworth expansion in probability.     

Edgeworth Expansions for Studentized Versions of Symmetric Finite Population Statistics

We show the validity of the one-term Edgeworth expansion for Studentized asymptotically linear statistics based on samples drawn without replacement from finite populations. Replacing the moments defining the expansion by their estimators, we obtain an empirical Edgeworth expansion. We show the validity of the empirical Edgeworth expansion in probability.     

RANDOM WEIGHTING APPROXIMATION IN LINEAR REGRESSION MODELS

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Edgeworth expansion for the survival function estimator in the Koziol-Green model

In the Koziol-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studentized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.     

An edgeworth expansion for finite-population L-statistics

We consider the one-term Edgeworth expansion for finite-population L-statistics. We provide an explicit formula for the Edgeworth correction term and give sufficient conditions for the validity of the expansion that are expressed in terms of the weight function defining the statistics and moment conditions.     

Empirical Edgeworth Expansion for Finite Population Statistics. I

For symmetric asymptotically linear statistics based on simple random samples, we construct the one-term empirical Edgeworth expansion, where the moments defining the true Edgeworth expansion are replaced by their jackknife estimators. In order to establish the validity of the empirical Edgeworth expansion (in probability), we prove the consistency of the jackknife estimators.     

关于Jacobi函数的渐近性态研究

采取改进取点x(t)的做法,提高了Jacobi函数的一项近似精确度.我们分别取x(t)的两项和三项,做出了Jacobi函数φ(α,β)μ(t) (α>-1 )当μ→+∞渐近近似,并给出了相应的误差限.随着x(t)取的项数增加,即点x(t)取的更“精确”,Jacobi函数φ(α,β)μ(t)渐近近似的精确度也随之提高.     

Edgeworth expansion for the bivariate product-limit estimator

LetS(s,t) be the bivariate survival function. LetS _π(s,t) be the bivariate product limit estimator proposed by Campbell and Földes. The one-term Edgeworth expansion forS _π(s,t) is established by expressing logS _π(s,t)-logS(s,t) as U-statistics, which admits one-term Edgeworth expansion plus some remainders with sufficient accuracy.     

One-Term Edgeworth Expansion for Finite Population U-Statistics of Degree Two

By means of Hoeffding"s decomposition, we represent a finite population U-statistic of degree two by the sum of a linear and a quadratic part. Assuming that the linear part is nondegenerate, we prove the validity of one-term Edgeworth expansion for the distribution function of the statistic under the optimal (minimal) conditions on the linear part and 2 + moment condition on the quadratic part. No condition is imposed on the ratio N / n, where N, respectively n, denotes the sample size respectively the population size.     

On a tropical dual Nullstellensatz

Since a tropical Nullstellensatz fails even for tropical univariate polynomials we study a conjecture on a tropical dual Nullstellensatz for tropical polynomial systems in terms of solvability of a tropical linear system with the Cayley matrix associated to the tropical polynomial system. The conjecture on a tropical effective dual Nullstellensatz is proved for tropical univariate polynomials.     

Bifurcation and chaos of thin circular functionally graded plate in thermal environment

A ceramic/metal functionally graded circular plate under one-term and two-term transversal excitations in the thermal environment is investigated, respectively. The effects of geometric nonlinearity and temperature-dependent material properties are both taken into account. The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power law distribution of the volume fraction of the constituents. Using the principle of virtual work, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic forcing excitation and thermal load are derived. For the circular plate with clamped immovable edge, the Duffing nonlinear forced vibration equation is deduced using Galerkin method. The criteria for existence of chaos under one-term and two-term periodic perturbations are given with Melnikov method. Numerical simulations are carried out to plot the bifurcation curves for the homolinic orbits. Effects of the material volume fraction index and temperature on the criterions are discussed and the existences of chaos are validated by plotting phase portraits, Poincare maps. Also, the bifurcation diagrams and corresponding maximum Lyapunov exponents are plotted. It was found that periodic, multiple periodic solutions and chaotic motions exist for the FGM plate under certain conditions.     

EDGEWORTH EXPANSION AND BOOTSTRAP APPROXIMATION FOR THE STUDENTIZED MLE FROM RANDOMLY CENSORED EXPONENTIAL SAMPLES

In this paper,the author studies the asymptotic accuracies of the one-term Edgeworth expansions and the bootstrap approximation for the studentized MLE from randomly censored exponential population.It is shown that the Edgeworth expansions and the bootstrap approximation are asymptotically close to the exact distribution of the studentized MLE with a rate.     

Kronecker type theorems,normality and continuity of the multivariate Padé operator

Summary. For univariate functions the Kronecker theorem, stating the equivalence between the existence of an infinite block in the table of Padé approximants and the approximated function being rational, is well-known. In [Lubi88] Lubinsky proved that if is not rational, then its Padé table is normal almost everywhere: for an at most countable set of points the Taylor series expansion of is such that it generates a non-normal Padé table. This implies that the Padé operator is an almost always continuous operator because it is continuous when computing a normal Padé approximant [Wuyt81]. In this paper we generalize the above results to the case of multivariate Padé approximation. We distinguish between two different approaches for the definition of multivariate Padé approximants: the general order one introduced in [Levi76, CuVe84] and the so-called homogeneous one discussed in [Cuyt84]. Received December 19, 1994     

Edgeworth expansions for compound Poisson processes and the bootstrap

One-term Edgeworth Expansions for the studentized version of compound Poisson processes are developed. For a suitably defined bootstrap in this context, the so called one-term Edgeworth correction by bootstrap is also established. The results are applicable for constructing second-order correct confidence intervals (which make correction for skewness) for the parameter “mean reward per unit time”. Research work of Gutti Jogesh Babu was supported in part by NSF grants DMS-9626189 and DMS-0101360.     

Trivariate near-best blending spline quasi-interpolation operators

A method to define trivariate spline quasi-interpolation operators (QIOs) is developed by blending univariate and bivariate operators whose linear functionals allow oversampling. In this paper, we construct new operators based on univariate B-splines and bivariate box splines, exact on appropriate spaces of polynomials and having small infinity norms. An upper bound of the infinity norm for a general blending trivariate spline QIO is derived from the Bernstein-Bézier coefficients of the fundamental functions associated with the operators involved in the construction. The minimization of the resulting upper bound is then proposed and the existence of a solution is proved. The quadratic and quartic cases are completely worked out and their exact solutions are explicitly calculated.     

Invariants of trace forms in odd characteristic and authentication codes

We complete A. Klapper's work on the invariant of a one-term trace form over a finite field of odd characteristic. We apply this to computing the probability of a successful impersonation attack on an authentication code proposed by C. Ding et al. (2005).     

ON THE GENERALIZED INVERSE NEVILLE—TYPE MATRIX—VALUED RATIONAL INTERPOLANTS

A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson iverse for matrices,with scalar numerator and matrix-valued denominatror.In this respect,it is essentially different form that of the previous works [7,9],where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator.For both univariate and bivariate cases,sufficient conditions for existence,characterisation and univquenese in some sense are proved respectively,and an error formula for the univariate interpolating function is also given.The results obtained in this paper are illustrated with some numerical examples.     

A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)

An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.      

Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions

We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L₁-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.