In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence, we prove a Korovkin type approximation theorem for sequences of positive linear operator defined on C∗(R) which is the space of all 2π-periodic and continuous functions on R, the set of all real numbers. We also compute the rates of statistical A-summability of sequence of positiv...

In this paper, we develop a family of algorithms for optimizing “superpositionstructured” or “dirty” statistical estimators for high-dimensional problems involving the minimization of the sum of a smooth loss function with a hybrid regularization. Most of the current approaches are first-order methods, including proximal gradient or Alternating Direction Method of Multipliers (ADMM). We propose...

These operators were generalized by Dog̃ru in [6]. A Stancu type generalization of these operators has been studied by Agratini [1] and Kantorovich type generalization of Agratini’s operators were constructed and statistical approximation properties were examined by Dog̃ru, Duman and Orhan in [8]. A Kantorovich type generalization of MKZ operators can also be found in [7]. In 2000, Trif [18] intr...

The statistical leverage scores of a matrix A are the squared row-norms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities have been of interest in recently-popular problems such as matrix completion and Nyström-based low-rank matrix approximation; in large-scale statistical data analysis applications more generally; and si...

The verification of probabilistic timed automata involves finding schedulers that optimise their nondeterministic choices with respect to the probability of a property. In practice, approaches based on model checking fail due to state-space explosion, while simulation-based techniques like statistical model checking are not applicable due to the nondeterminism. We present a new lightweight on-t...

This paper presents new algorithms for distributed statistical estimation that can take advantage of the divide-and-conquer approach. We show that one of the key benefits attained by an appropriate divide-and-conquer strategy is robustness, an important characteristic of large distributed systems. We introduce a class of algorithms that are based on the properties of the geometric median, estab...

Inventory levels are critical to the operations, management, and capacity decisions of inventory systems but can be difficult to model in heterogeneous, non-stationary throughput systems. The inpatient hospital is a complicated throughput system and, like most inventory systems, hospitals dynamically make managerial decisions based on short term subjective demand predictions. Specifically, shor...

Ever since the introduction of the path-integrals by R. Feynman, the path-integral formulas with a complex \temperature" have presented an elusive mathematical problem|for instance, the Wiener measure, which is so useful for positive temperature statistics, cannot be extended to the complex case. In fact, since real time processes and real temperature statistics can be identi ed with each other...

In this study, using the concept of statistical σ−convergence which is stronger than convergence and statistical convergence we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on C∗ which is the space of all 2π-periodic and continuous functions on R, the set of all real numbers. We also study the rates of statistical σ−convergence of approximating ...

The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, we provide various approximation results concerning the classical Korovkin theorem via Fibonacci type statistical convergence.