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Mean Square Error in ML Estimation of Two-Level Time Series Models

Olasunkanmi Isiaka Azeez, Kunle Bayo Adewoye. Published in Information Sciences.

Communications on Applied Electronics
Year of Publication: 2022
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors: Olasunkanmi Isiaka Azeez, Kunle Bayo Adewoye

Olasunkanmi Isiaka Azeez and Kunle Bayo Adewoye. Mean Square Error in ML Estimation of Two-Level Time Series Models. Communications on Applied Electronics 7(38):1-10, February 2022. BibTeX

	author = {Olasunkanmi Isiaka Azeez and Kunle Bayo Adewoye},
	title = {Mean Square Error in ML Estimation of Two-Level Time Series Models},
	journal = {Communications on Applied Electronics},
	issue_date = {February 2022},
	volume = {7},
	number = {38},
	month = {Feb},
	year = {2022},
	issn = {2394-4714},
	pages = {1-10},
	numpages = {10},
	url = {},
	doi = {10.5120/cae2022652890},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


Two-level time series models are commonly used to analyze longitudinal and correlated data with the standard and parametric assumption that the within-individual (level-1) residuals are uncorrelated rarely checked. There is marked disagreement in the literature as to whether such parametric assumption is important or innocuous. Monte Carlo methods were used to examine the conditions in which the level-1 independence of observations assumption on the parameter estimates of fixed effects was violated and the associated errors due to mean square were investigated. Conditions also varied the series lengths, the numbers of participants per study, and the strength of the autocorrelation coefficient. The simulation results, under the finite sampling properties of Mean Squared Error (MSE), Shown that in finite data, the maximum likelihood estimates may be substantially biased and possess mean square errors substantially higher than Cramer-Rao bounds.


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Longitudinal, Autocorrelation & Monte Carlo