On Asymptotic Distributions of Arithmetical Functions

1988 ◽  
pp. 43-58
Author(s):  
I. J. Schoenberg
Keyword(s):  
Asymptotic Distributions ◽  
Arithmetical Functions

Arithmetical Functions

1994 ◽  
Author(s):  
Wolfgang Schwarz ◽  
Jürgen Spilker
Keyword(s):  
Arithmetical Functions

On Some Rings of Arithmetical Functions

1999 ◽  
Vol 6 (4) ◽  
pp. 299-306
Author(s):  
D. Bhattacharjee
Keyword(s):  
Arithmetical Functions ◽  
Algebraic Properties

Abstract In this paper we consider several constructions which from a given 𝐵-product *𝐵 lead to another one . We shall be interested in finding what algebraic properties of the ring 𝑅𝐵 = 〈𝐶ℕ, +, *𝐵〉 are shared also by the ring . In particular, for some constructions the rings 𝑅𝐵 and will be isomorphic and therefore have the same algebraic properties.

scholarly journals Small-sample asymptotic distributions of M-estimators of location

Biometrika ◽  
1982 ◽  
Vol 69 (1) ◽  
pp. 29-46 ◽  
Author(s):  
CHRISTOPHER A. FIELD ◽  
FRANK R. HAMPEL
Keyword(s):  
Small Sample ◽  
Asymptotic Distributions

scholarly journals Statistical Inference for the Beta Coefficient

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 56 ◽  
Author(s):  
Taras Bodnar ◽  
Arjun K. Gupta ◽  
Valdemar Vitlinskyi ◽  
Taras Zabolotskyy
Keyword(s):  
Confidence Interval ◽  
Empirical Study ◽  
Crucial Role ◽  
Risk Measure ◽  
Statistical Test ◽  
Asymptotic Distributions ◽  
Finite Sample ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Theoretical Results

The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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