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"**Authors:** Andrej Gajdoš, Jozef Hanč, Martina Hančová
*[Faculty of Science](https://www.upjs.sk/en/faculty-of-science/?prefferedLang=EN), P. J. Šafárik University in Košice, Slovakia*
email: [andrej.gajdos@student.upjs.sk](mailto:andrej.gajdos@student.upjs.sk), [martina.hancova@upjs.sk](mailto:martina.hancova@upjs.sk)\n",
"***\n",
"** Binder for EBLUP-NE using standard R tools and CVXR ** \n",
"\n",
"Interactive execution of Jupyter Notebooks. Use SHIFT-Enter or menu for executing cells in open notebooks.\n",
"\n",
"***\n",
"## Index \n",
"\n",
"### Electricity consumption - toy model 1 \n",
" * [R-estimation-electricity1-standardRtools.ipynb](Rnotebooks/R-estimation-electricity1-standardRtools.ipynb), EBLUP-NE in *nlme, MMEinR, sommer, fdslrm* \n",
" * [R-estimation-electricity1-CVXR.ipynb](Rnotebooks/R-estimation-electricity1-CVXR.ipynb), EBLUP-NE in *CVXR* \n",
" \n",
"### Electricity consumption - toy model 2 \n",
" * [R-estimation-electricity2-standardRtools.ipynb](Rnotebooks/R-estimation-electricity2-standardRtools.ipynb), EBLUP-NE in *nlme, MMEinR, sommer, fdslrm* \n",
" * [R-estimation-electricity2-CVXR.ipynb](Rnotebooks/R-estimation-electricity2-CVXR.ipynb), EBLUP-NE in *CVXR* \n",
"\n",
"### Tourism \n",
" * [tourism.ipynb](Modeling/tourism.ipynb), FDSLRM modeling in *R* \n",
" * [R-estimation-tourism-standardRtools.ipynb](Rnotebooks/R-estimation-tourism-standardRtools.ipynb), EBLUP-NE in *nlme, MMEinR, sommer, fdslrm*\n",
" * [R-estimation-tourism-CVXR.ipynb](Rnotebooks/R-estimation-tourism-CVXR.ipynb), EBLUP-NE in *CVXR*\n",
"\n",
"### Cyber attacks \n",
" * [cyberattacks.ipynb](Modeling/cyberattacks.ipynb), FDSLRM modeling in *R* \n",
" * [R-estimation-cyberattacks-standardRtools.ipynb](Rnotebooks/R-estimation-cyberattacks-standardRtools.ipynb), EBLUP-NE in *nlme, MMEinR, sommer, fdslrm*\n",
" * [R-estimation-cyberattacks-CVXR.ipynb](Rnotebooks/R-estimation-cyberattacks-CVXR.ipynb), EBLUP-NE in *CVXR*"
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"***\n",
"\n",
"# References \n",
"This notebook belongs to suplementary materials of the paper submitted to Statistical Papers and available at .\n",
"\n",
"* Hančová, M., Vozáriková, G., Gajdoš, A., Hanč, J. (2019). [Estimating variance components in time series\n",
"\tlinear regression models using empirical BLUPs and convex optimization](https://arxiv.org/abs/1905.07771), https://arxiv.org/, 2019.\n",
"\n",
"### Abstract of the paper\n",
"\n",
"We propose a two-stage estimation method of variance components in time series models known as FDSLRMs, whose observations can be described by a linear mixed model (LMM). We based estimating variances, fundamental quantities in a time series forecasting approach called kriging, on the empirical (plug-in) best linear unbiased predictions of unobservable random components in FDSLRM. \n",
"\n",
"The method, providing invariant non-negative quadratic estimators, can be used for any absolutely continuous probability distribution of time series data. As a result of applying the convex optimization and the LMM methodology, we resolved two problems $-$ theoretical existence and equivalence between least squares estimators, non-negative (M)DOOLSE, and maximum likelihood estimators, (RE)MLE, as possible starting points of our method and a \n",
"practical lack of computational implementation for FDSLRM. As for computing (RE)MLE in the case of $ n $ observed time series values, we also discovered a new algorithm of order $\\mathcal{O}(n)$, which at the default precision is $10^7$ times more accurate and $n^2$ times faster than the best current Python(or R)-based computational packages, namely CVXPY, CVXR, nlme, sommer and mixed. \n",
"\n",
"We illustrate our results on three real data sets $-$ electricity consumption, tourism and cyber security $-$ which are easily available, reproducible, sharable and modifiable in the form of interactive Jupyter notebooks."
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"* Gajdoš A., Hanč J., and Hančová M. (2019). _fdslrm EBLUP-NE_. GitHub repository, P.J. Šafárik University in Košice, Slovakia. https://github.com/fdslrm/EBLUP-NE"
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