Asymptotic properties of some functions of nonparametric estimates of a density function

Let be a nonparametric estimate of a two-dimensional density f(x,y) constructed with the help of two-dimensional “window.” The main purpose of the paper is to study the asymptotic properties of the marginal moments estimates and differentiable functions , of these moments.     

Asymptotic properties of nonparametric curve estimates

We consider a class of nonparametric estimators for the regression functionm(t) in the model:y _i =m(t _i ) + _i , 1 i n, t _i [0, 1], which are linear in the observationsy _i . Several limit theorems concerning local and global stochastic and a.s. convergence and limit distributions are given.     

Asymptotic theory of nonparametric regression estimates with censored data

For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right_censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, Cp and FPE criteria in the process of selecting the parameters.     

Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

Consider the nonparametric regression model Y_ni=g(x_ni)+ε_ni for i=1,…,n, where g is unknown, x_ni are fixed design points, and ε_ni are negatively associated random errors. Nonparametric estimator g_n(x) of g(x) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of g_n(x) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).     

Asymptotic estimates of integral functions defined by canonical products

The principal part of an asymptotic expansion at infinity of the logarithm of integral functions of finite order with simple positive zeros is determined. The asymptotic form is obtained with the aid of a Cauchy-type integral with smooth density.Translated from Matematicheskie Zametki, Vol. 10, No. 6, pp. 641–648, December, 1971.The author is indebted to the reviewer for valuable comments.     

Asymptotic estimates for the coefficients of bounded univalent functions

In the class of univalent bounded normalized holomorphic functions in the unit disk, we give an asymptotic estimate for the coefficients when the uniform norm of the modulus of the function tends to infinity.     

Asymptotic distribution of the nonparametric distribution estimator based on a martingale approach in doubly censored data

For analysis of time-to-event data with incomplete information beyond right-censoring, many generalizations of the inference of the distribution and regression model have been proposed. However, the development of martingale approaches in this area has not progressed greatly, while for right-censored data such an approach has spread widely to study the asymptotic properties of estimators and to derive regression diagnosis methods. In this paper, focusing on doubly censored data, we discuss a martingale approach for inference of the nonparametric maximum likelihood estimator (NPMLE). We formulate a martingale structure of the NPMLE using a score function of the semiparametric profile likelihood. Finally, an expression of the asymptotic distribution of the NPMLE is derived more conveniently without depending on an infinite matrix expression as in previous research. A further useful point is that a variance-covariance formula of the NPMLE computable in a larger sample is obtained as an empirical version of the limit form presented here.     

Asymptotic behavior of nonparametric estimators of the two-dimensional and bivariate renewal functions

Statistical Inference for Stochastic Processes - We study the asymptotic behavior of the two-dimensional or bivariate nonparametric estimators of the renewal function associated to a sequence of...     

Asymptotic behavior of Mean-CVaR portfolio selection model under nonparametric framework

Portfolio selection is an important issue in finance and it involves the balance between risk and return. This paper investigates portfolio selection under Mean-CVa R model in a nonparametric framework with α-mixing data as financial data tends to be dependent. Many works have provided some insight into the performance of portfolio selection from the aspects of data and simulation while in this paper we concentrate on the asymptotic behaviors of the optimal solutions and risk estimation in theory.     

Asymptotic distribution of simple linear rank statistics for testing symmetry

Summary The object of the present paper is to derive asymptotic distributions of simple linear rank statistics used for testing symmetry under various systems of conditions. The main result is stated in Theorem 3 (Section 2) and in Theorem 6 (Section 3). The assertions have been derived by the method worked out in [1]. Similar assertions concerning the multivariate case (the other part of the author's thesis) will be published in a next paper.     

Asymptotic estimates of wave functions and the existence of wave operators

The existence of wave operators is proved for the case, where the unperturbed operator is the operator of multiplication by a smooth function in momentum space and the perturbation is an arbitrary operator satisfying a fall off condition near infinity or a weighted L_p-estimate in configuration space. Under somewhat more restrictive conditions the invariance principle is also proved.     

Asymptotic estimates of approximation of continuous periodic functions by Fourier sums

Asymptotic estimates, expressed in terms of the value of the modulus of continuity of r-th order (r2) at the point t=/n of a functionf C ₂ or of the (, )-derivative of a functionf C _B C, are established for the deviations of continuous periodic functions from their Fourier sums.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 747–755, June, 1990.     

Asymptotic estimates of certain integral means for meromorphic functions. II

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 844–847, June, 1989.     

Asymptotic ordering of distribution functions and convolution semigroups

It is well-known that the setH of distribution functions on [0,∞] supplied with the convolution product * is a semigroup. We introduce a preorder on (H,*) with attractive algebraic properties. The corresponding equivalence relation ≈^W extends the concept of tail-equivalence of distribution functions. We show that the idempotents of the factorsemigroupH _W form a subsemigroup ofH _W.     

Asymptotic distribution of functions on compact homogeneous spaces

Summary Some distribution properties of continuous functions on compact, connected, homogeneous Riemannian manifolds are investigated. It is proved that almost all functions are uniformly distributed and almost no functions are well distributed. Furthermore similar results for sequences are established.