In this paper we prove the asymptotic normality and rates of strong convergence of some types of estimators for the regression function in a xed-design regression model. We consider the Gasser-MMller estimator and the Priestley-Chao estimator (univariate and multivariate). The proofs of asymptotic normality are based on a central limit theorem from an earlier paper by the author (1996, Stochast...

In this paper, we introduce a new iterative procedure which is constructed by the modified block hybrid projection method for solving a common solution of fixed point problems for two countable families of uniformly total quasi-φ-asymptotically nonexpansive and uniformly Lipschitz continuous mappings. Under suitable conditions, some strong convergence theorems are established in a uniformly smo...

The purpose of this paper is to study a strong convergence of multi-step iterative scheme to a common solution for a finite family of strongly accretive operator equations in a reflexive Banach space with weakly continuous duality map. As a consequence, the strong convergence theorem for the multi-step iterative sequence to a common fixed point for finite family of strongly pseudocontractive ma...

We prove strong convergence and asymptotic normality for the record and the weak record rate of observations of the form Yn = Xn + Tn, n ≥ 1, where (Xn)n∈Z is a stationary ergodic sequence of random variables and (Tn)n≥1 is a stochastic trend process, with stationary ergodic increments. The strong convergence result follows from the Dubins-Freedman law of large numbers and Birkhoff’s ergodic th...

Abstract. We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes to Wiener process in the Skorohod space endowed by the topology of uniform convergence. An integral type almost sure version of this limit theorem i...

We study almost sure convergence for ρ̃-mixing sequences of random variables. Many of the previous results are our special cases. For example, the authors extend and improve the corresponding results of Chen et al. 1996 and Wu and Jiang 2008 . We extend the classical Jamison convergence theorem and theMarcinkiewicz strong law of large numbers for independent sequences of random variables to ρ̃-mi...

* Correspondence: [email protected] Faculty of Science, Jiangsu University, Zhenjiang, 212013, China Full list of author information is available at the end of the article Abstract In this paper, we study a convergence theorem for a finite second-order Markov chain indexed by a general infinite tree with uniformly bounded degree. Meanwhile, the strong law of large numbers (LLN) and Shannon-...

The aim of this article is to establish some strong convergence theorems of three-step iteration process with errors for approximating common fixed point for generalized asymptotically quasi-nonexpansive mappings and also establish a weak convergence theorem by using Opial’s [11] condition for said iteration scheme and mappings in the framework of Banach spaces. The results presented in this pa...

In this paper, we introduce and investigate two new generalized mixed equilibrium problems and explore the relationship between them and the properties of their solutions in Banach spaces. Based on the generalized f -projection, we construct hybrid algorithms to find common fixed points of a countable family of quasi-φnonexpansive mappings in Banach spaces, a common element of the set of soluti...