scholarly journals Asymptotic distribution of the zeros of recursively defined non-orthogonal polynomials

2022 ◽  
pp. 105700
Author(s):  
Bernhard Heim ◽  
Markus Neuhauser
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Distribution

scholarly journals A new proof of a theorem about generalized orthogonal polynomials

1991 ◽  
Vol 14 (2) ◽  
pp. 393-397
Author(s):  
A. McD. Mercer
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Recent Result ◽  
Asymptotic Distribution ◽  
Generalized Polynomials ◽  
Generalized Orthogonal Polynomials ◽  
Generalized Orthogonal ◽  
Polynomial Theory

In this note it is shown that a fairly recent result on the asymptotic distribution of the zeros of generalized polynomials can be deduced from an old theorem ofG. Polya, using a minimum of orthogonal polynomial theory.

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

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