Empirical likelihood estimation in multivariate mixture models with repeated measurements

Yuejiao Fua Department of Mathematics and Statistics, York University, Toronto, Canada

https://orcid.org/0000-0001-8606-570X View further author information

Yukun Liub School of Statistics, East China Normal University, Shanghai, ChinaCorrespondence[email protected]
View further author information

Hsiao-Hsuan Wanga Department of Mathematics and Statistics, York University, Toronto, CanadaView further author information

Xiaogang Wanga Department of Mathematics and Statistics, York University, Toronto, Canada;c Institute of Data Science, Tsinghua University, Beijing, ChinaView further author information

Figures & data

Table 1. Biases (%) and standard deviations (%) (in parentheses) of different estimators based on 1,000 simulations with n=400. Data were generated from the multivariate mixture model with $f_{1}$ and $f_{2}$ being $N (μ_{1}, 1)$ and $N (μ_{2}, 1)$ , respectively. Here $μ_{1} = 0$ , $μ_{2} = 1$ or 2 and d=3 or 6.

Display Table

Table 2. Biases (%) and standard deviations (%) (in parentheses) of different estimators based on 1,000 simulations with n=400. Data were generated from the multivariate mixture model with $f_{1}$ and $f_{2}$ being $t (4, μ_{1})$ and $t (4, μ_{2} / {\sqrt{2} Γ (3 / 2) / Γ (2)})$ , respectively. Here $μ_{1} = 0$ , $μ_{2} = 1.5$ or 2 and d=3 or 6.

Display Table

Table 3. Biases (%) and standard deviations (%) (in parentheses) of different estimators based on 1,000 simulations with n=400. Data were generated from the multivariate mixture model with $f_{1}$ and $f_{2}$ being $χ_{μ_{1}}^{2}$ and $χ_{μ_{2}}^{2}$ , respectively. Here $μ_{1} = 5$ , $μ_{2} = 10$ or 20 and d=3 or 6.

Display Table

Figure 1. Histogram of the first measurement of the RT data.

Table 4. Point and interval estimates of the EL, MN and ML methods for $π, μ_{1}$ and $μ_{2}$ . EL $_{0}$ : EL with $K = (\binom{6}{3}) = 20$ ; EL $_{1}$ , EL $_{2}$ , EL $_{3}$ : EL with K=8; MN $_{1}$ : MN with cut points $c_{1}, \dots, c_{10}$ being the deciles of the empirical distribution, which was suggested by Cruz-Medina et al. (Citation2004) for general use; MN $_{2}$ : MN with cut points $(c_{1}, \dots, c_{10}) = (0.5, 1, 1.2, 1.4, 1.6, 2, 2.5, 3, 4, 5)$ , which was used by Cruz-Medina et al. (Citation2004) when they analysed this dataset.

Display Table

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Empirical likelihood estimation in multivariate mixture models with repeated measurements

Information for

Open access

Opportunities

Help and information

Your download is now in progress and you may close this window

Login or register to access this feature

Empirical likelihood estimation in multivariate mixture models with repeated measurements

Figures & data

Table 1. Biases (%) and standard deviations (%) (in parentheses) of different estimators based on 1,000 simulations with n=400. Data were generated from the multivariate mixture model with f1 and f2 being N(μ1,1) and N(μ2,1), respectively. Here μ1=0, μ2=1 or 2 and d=3 or 6.

Table 2. Biases (%) and standard deviations (%) (in parentheses) of different estimators based on 1,000 simulations with n=400. Data were generated from the multivariate mixture model with f1 and f2 being t(4,μ1) and t(4,μ2/{2Γ(3/2)/Γ(2)}), respectively. Here μ1=0, μ2=1.5 or 2 and d=3 or 6.

Table 3. Biases (%) and standard deviations (%) (in parentheses) of different estimators based on 1,000 simulations with n=400. Data were generated from the multivariate mixture model with f1 and f2 being χμ12 and χμ22, respectively. Here μ1=5, μ2=10 or 20 and d=3 or 6.

Reprints and Corporate Permissions

Academic Permissions

Related research

To cite this article:

Download citation

Information for

Open access

Opportunities

Help and information

Keep up to date