Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series

2016 ◽  
Vol 11 (2) ◽  
pp. 179-203
Author(s):  
Rita Giuliano
Keyword(s):  
Convergence In Probability ◽  
Convergence In Distribution ◽  
Asymptotic Results ◽  
Arithmetic Means ◽  
Convergence Results ◽  
Weighted Means

Abstract In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

Stochastics ◽  
2019 ◽  
Vol 92 (4) ◽  
pp. 497-518
Author(s):  
Rita Giuliano ◽  
Claudio Macci ◽  
Barbara Pacchiarotti
Keyword(s):  
Random Variables ◽  
Asymptotic Results ◽  
Linear Combinations ◽  
Weighted Means

scholarly journals Generic Uniform Convergence

1992 ◽  
Vol 8 (2) ◽  
pp. 241-257 ◽  
Author(s):  
Donald W.K. Andrews
Keyword(s):  
Uniform Convergence ◽  
Asymptotic Properties ◽  
Convergence In Probability ◽  
Test Statistics ◽  
Parameter Spaces ◽  
Totally Bounded ◽  
Convergence Results ◽  
Large Numbers ◽  
Uniform Law ◽  
Convergence Almost Surely

This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics.The results given here have the following attributes, (1) they extendresults of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for i.i.d. contexts, but which apply in some dependent nonidentically distributed contexts as well, and (4) they incorporate and extend themain results in the literature in a parsimonious fashion.

ASYMPTOTIC THEORY FOR SPECTRAL DENSITY ESTIMATES OF GENERAL MULTIVARIATE TIME SERIES

2017 ◽  
Vol 34 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Wei Biao Wu ◽  
Paolo Zaffaroni
Keyword(s):  
Time Series ◽  
Spectral Density ◽  
Multivariate Time Series ◽  
Rates Of Convergence ◽  
Stationary Time Series ◽  
Regularity Conditions ◽  
Dynamic Factor ◽  
Asymptotic Results ◽  
Density Estimates ◽  
Convergence Results

We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability, weak or distributional convergence, yet under a much stronger set of regularity conditions, such as linearity in iid innovations. Based on cross spectral density functions, we then propose a new test for independence between two stationary time series. We also explain the extent to which our results provide the foundation to derive the double asymptotic results for estimation of generalized dynamic factor models.

scholarly journals HUBUNGAN ANTARA KONVERGEN HAMPIR PASTI, KONVERGEN DALAM PELUANG, DAN KONVERGEN DALAM SEBARAN

2013 ◽  
Vol 2 (2) ◽  
pp. 10
Author(s):  
Vira Agusta ◽  
Dodi Devianto ◽  
Hazmira Yozza
Keyword(s):  
Probability Space ◽  
Random Variable ◽  
Convergence In Probability ◽  
Convergence In Distribution ◽  
Convergence Almost Surely ◽  
The Relationship

Let fXng be a sequence of random variable dened on a probability space ( ; F; P). In this paper, we studied about the relationship between the convergence almost surely, convergence in probability, and convergence in distribution. If the sequenceof random variable convergence almost surely to a random variable X then fXng convergence in probability to X. If the sequence of random variable fXng convergence in probability to a random variable X then fXng convergence in distribution to X.

scholarly journals On Some Series Dependent on a Parameter Which Generalize Euler’s Constant

2019 ◽  
Vol 12 (1) ◽  
pp. 1-13
Author(s):  
Paul Bracken
Keyword(s):  
Series Expansion ◽  
Infinite Series ◽  
Asymptotic Results ◽  
Euler’S Constant ◽  
Convergence Results ◽  
Special Case ◽  
Euler's Constant

Series which depend on a parameter and generalize the constant discovered by Euler are introduced and studied. Convergence results are established. An infinite series expansion is obtained from these generalized formulas which can be used to evaluate the generalized constant. Euler’s constant can be obtained as a special case. Some asymptotic results are formulated and limits of some closely related sequences are given at the end.

scholarly journals Asymptotic limits for a nonlinear integro-differential equation modelling leukocytes’ rolling on arterial walls

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 843-869
Author(s):  
Vuk Milišić ◽  
Christian Schmeiser
Keyword(s):  
Mathematical Framework ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Asymptotic Results ◽  
Differential Model ◽  
Absolute Value ◽  
Arterial Walls ◽  
Equation Modelling ◽  
Convergence Results ◽  
Long Time

Abstract We consider a nonlinear integro-differential model describing z, the position of the cell center on the real line presented in Grec et al (2018 J. Theor. Biol. 452 35–46). We introduce a new ɛ-scaling and we prove rigorously the asymptotics when ɛ goes to zero. We show that this scaling characterizes the long-time behavior of the solutions of our problem in the cinematic regime (i.e. the velocity z ˙ tends to a limit). The convergence results are first given when ψ, the elastic energy associated to linkages, is convex and regular (the second order derivative of ψ is bounded). In the absence of blood flow, when ψ, is quadratic, we compute the final position z ∞ to which we prove that z tends. We then build a rigorous mathematical framework for ψ being convex but only Lipschitz. We extend convergence results with respect to ɛ to the case when ψ′ admits a finite number of jumps. In the last part, we show that in the constant force case [see model 3 in Grec et al (2018 J. Theor. Biol. 452 35–46), i.e. ψ is the absolute value)] we solve explicitly the problem and recover the above asymptotic results.

scholarly journals Linear Processes for Functional Data

2018 ◽  
Author(s):  
André Mas ◽  
Besnik Pumo
Keyword(s):  
Hilbert Space ◽  
Functional Data ◽  
Statistical Models ◽  
Autoregressive Processes ◽  
Asymptotic Results ◽  
Linear Processes ◽  
Finite Dimensional ◽  
Convergence Results ◽  
General Estimation ◽  
General Method

This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressive processes as well as two issues related to the general estimation problem, namely: identifiability and the inverse problem. Finally, it examines convergence results for the autocorrelation operator and the predictor, extensions for the autoregressive Hilbertian (ARH) model, and some numerical aspects of prediction when the data are curves observed at discrete points.

Which Mean Do You Mean?

1991 ◽  
Vol 84 (1) ◽  
pp. 24-28
Author(s):  
Andre Michelle Lubecke
Keyword(s):  
Arithmetic Means ◽  
Geometric Means ◽  
Weighted Means ◽  
Statistics Courses ◽  
Elementary Statistics ◽  
Classroom Presentation

This article can be viewed as a script for a classroom presentation introducing weighted means and geometric means to students who are already familiar with arithmetic means. It is written in the style and language I actually use in the classroom, illustrating a method of teaching I have found to be effective with students in elementary statistics courses. The frequent questioning is designed to keep the students mentally active and involved in the development of a new idea, and typical student or class responses have been indicated in parenthetical statements throughout the text.

WEIGHTED MEANS BASED ON TRIANGULAR CONORMS

2001 ◽  
Vol 09 (02) ◽  
pp. 183-196 ◽  
Author(s):  
TOMASA CALVO ◽  
RADKO MESIAR
Keyword(s):  
Arithmetic Means ◽  
New Class ◽  
Weighted Means ◽  
Ordinal Scales

Generalizing the construction of weighted quasi–arithmetic means from generated t–conorms, we propose a new class of weighted means related to continuous t–conorms. By duality, t–norm based weighted means can be obtained, too. Our method fits also in the case of finite ordinal scales. Several examples are given.

QuickSelect Tree Process Convergence, With an Application to Distributional Convergence for the Number of Symbol Comparisons Used by Worst-Case Find

2014 ◽  
Vol 23 (5) ◽  
pp. 805-828 ◽  
Author(s):  
JAMES ALLEN FILL ◽  
JASON MATTERER
Keyword(s):  
Banach Space ◽  
Search Algorithm ◽  
Key Comparisons ◽  
List Type ◽  
Convergence In Distribution ◽  
Type Number ◽  
Worst Case ◽  
Convergence Results ◽  
Process Convergence ◽  
Master Theorem

We define a sequence of tree-indexed processes closely related to the operation of the QuickSelect search algorithm (also known as Find) for all the various values of n (the number of input keys) and m (the rank of the desired order statistic among the keys). As a ‘master theorem’ we establish convergence of these processes in a certain Banach space, from which known distributional convergence results as n → ∞ about (1)the number of key comparisons requiredare easily recovered (a)when m/n → α ∈ [0, 1], and(b)in the worst case over the choice of m. From the master theorem it is also easy, for distributional convergence of(2)the number of symbol comparisons required, both to recover the known result in the case (a) of fixed quantile α and to establish our main new result in the case (b) of worst-case Find.Our techniques allow us to unify the treatment of cases (1) and (2) and indeed to consider many other cost functions as well. Further, all our results provide a stronger mode of convergence (namely, convergence in Lp or almost surely) than convergence in distribution. Extensions to MultipleQuickSelect are discussed briefly.

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