The minimum variance of a random set on a Euclidean space

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.

Download Full-text

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

Scientific Research Journal ◽

10.24191/srj.v11i1.5416 ◽

2014 ◽

Vol 11 (1) ◽

pp. 15

Author(s):

Set Foong Ng ◽

Pei Eng Ch’ng ◽

Yee Ming Chew ◽

Kok Shien Ng

Keyword(s):

Soil Properties ◽

Lagrange Multipliers ◽

Unbiased Estimator ◽

Soil Property ◽

Minimum Variance ◽

Distance Method ◽

True Value ◽

A Site ◽

Method Of Lagrange Multipliers ◽

Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

Download Full-text

Compactification of Submanifolds in Euclidean Space by the Inversion

Progress in Differential Geometry ◽

10.2969/aspm/02210001 ◽

2018 ◽

Author(s):

Kazuyuki Enomoto

Keyword(s):

Euclidean Space

Download Full-text

ANALISIS PORTOFOLIO INVESTASI PADA SAHAM LQ45 DENGAN METODE MEAN VARIAN SATU KONSTRAIN

Jurnal Varian ◽

10.30812/varian.v1i2.68 ◽

2018 ◽

Vol 1 (2) ◽

pp. 22-29

Author(s):

Gilang Primajati

Keyword(s):

Capital Markets ◽

Minimum Variance ◽

Return Rate ◽

Optimal Portfolio ◽

Portfolio Diversification ◽

Portfolio Risk ◽

Expected Return ◽

Positive Weight ◽

The Mean

In the capital markets, especially the investment market, the establishment of a portfolio is something that must be understood by investors. Portfolio formation by investors to maximize profits as much as possible by minimizing the risk of losses that may occur. Portfolio diversification is defined as portfolio formation in such a way that it can reduce portfolio risk without sacrificing returns. Optimal portfolio with efficient-portfolio mean criteria, investors only invest in risk assets only. Investors do not include risk free assets in their portfolios. The efficient variance portfolio is defined as a portfolio that has minimum variance among the overall possible portfolio that can be formed, at the same expected return rate. The mean method of one constraint variant can be used as the basis for optimal portfolio determination. The shares of LQ-45 used are shares of AALI, BBCA, UNVR, TLKM and ADHI. AALI shares received a positive weight of 7%, BBCA 48%, UNVR 16%, TLKM 26% and ADHI 3%

Download Full-text

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.39 ◽

2020 ◽

pp. 507-522

Author(s):

Parisa Torkaman

Keyword(s):

Least Squares ◽

Exponential Distribution ◽

Mean Squared Error ◽

Weighted Least Squares ◽

Real Data ◽

Minimum Variance ◽

Cumulative Distribution ◽

Estimation Methods ◽

Data Set ◽

Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

Download Full-text