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On exact inference in linear models with two variance-covariance components

References [1] CHRISTENSEN, R.: Plane Answers to Complex Questions: The Theory of Linear Models. Springer-Verlag, New York, 1987. [2] CRAINICEANU, C. M.-RUPPERT, D.: Likelihood ratio tests in linear mixed models with one variance component , J. R. Stat. Soc. Ser. B Stat. Methodol. 66 (2004), 165-185. [3] HARTLEY, H. O.-RAO, J. N. K.: Maximum-likelihood estimation for the mixed alysis of variance model , Biometrika 54 (1967), 93-108. [4] HARVILLE, D. A.: Matrix Algebra from a Statistician

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Effects of Cluster Sizes on Variance Components in Two-Stage Sampling

.cdc.gov/nchs/data/nhanes/survey_content_99_10.pdf . Center for Disease Control and Prevention. 2012. National Health Interview Survey . Retrieved from National Center for Health Statistics: http://www.cdc.gov/nchs/nhis.htm . Chromy, J. and L. Myers. 2001. “Variance Models Applicable to the NHSDA.” In Proceedings of the Survey Research Methods Section: American Statistical Association, August 5–9, 2001. Alexandria, VA: American Statistical Association. Available at: http://www.amstat.org/sections/SRMS/Proceedings/ . (accessed October 12, 2015). Cochran, W. 1977. Sampling Techniques

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Regression Function and Noise Variance Tracking Methods for Data Streams with Concept Drift

analysis, Journal of Machine Learning Research 11: 1601-1604. Brown, L.D. and Levine, M. (2007). Variance estimation in nonparametric regression via the difference sequence method, Annals of Statistics 35(5): 2219-2232. Carroll, R.J. and Ruppert, D. (1988). Transformation and Weighting in Regression, CRC Press, Boca Raton, FL. Dai, W., Ma, Y., Tong, T. and Zhu, L. (2015). Difference-based variance estimation in nonparametric regression with repeated measurement data, Journal of Statistical Planning and Inference 163: 1

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Within-Laboratory Variance Outlier Detection: An Alternative to Cochran’s Test

, and Interpretation of Method-Performance Studies; Pure Appl. Chem. 67 (1995) 331–343. 4. Box, G.E.P.: Non-Normality and Tests on Variances; Biometrika 40 (1953) 318–335. DOI: 10.2307/2333350 5. Conover, W.J., M.E. Johnson, and M.M. Johnson: A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data; Technometrics 23 (1981) 351–361. DOI: 10.2307/1268225 6. Levene, H.: Robust Tests for Equality of Variances; in: Contributions to Probability and Statistics, edited by I. Olkin, Stanford

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On a new approach to the analysis of variance for experiments with orthogonal block structure.
II. Experiments in nested block designs

., Łacka A. (2014): On combining information in generally balanced nested block designs. Communications in Statistics − Theory and Methods 43: 954-974. Caliński T., Siatkowski I. (2017): On a new approach to the analysis of variance for experiments with orthogonal block structure. I. Experiments in proper block designs. Biometrical Letters 54: 91-122. Ceranka B. (1983): Planning of experiments in C -designs. Scientific Dissertations 136, Annals of Poznań Agricultural University, Poland. Houtman A.M., Speed T.P. (1983): Balance in designed experiments

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Evaluation of Generalized Variance Functions in the Analysis of Complex Survey Data

References Abramowitz, M. and Stegun, I.A. (1972). Handbook of Mathematical Functions. New York: Dover Publications, INC. Binder, D.A. (1983). On the Variances of Asymptotically Normal Estimators from Complex Surveys. International Statistical Review, 51, 279-292. Bureau Of Labor Statistics (1997). Employment, Hours, and Earnings from the Establishment Survey, Chapter 2 of BLS Handbook of Methods, U.S. Department of Labor. Butani, S., Stamas, G., and Brick, M. (1997). Sample Redesign for the

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On a New Approach to the Analysis of Variance for Experiments with Orthogonal Block Structure.
I. Experiments in proper block designs

-27 (in Polish). Houtman A.M., Speed T.P. (1983): Balance in designed experiments with orthogonal block structure. Annals of Statistics 11: 1069-1085. Kala R. (2017): A new look at combining information in experiments with orthogonal block structure. Matrices, Statistics and Big Data: Proceedings of the IWMS-2016 (in press). Mardia K.V., Kent J.T., Bibby J.M. (1979): Multivariate Analysis. Academic Press, London. Nelder J.A. (1954): The interpretation of negative components of variance. Biometrika 41: 544

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Neural Network Approach in Forecasting Realized Variance Using High-Frequency Data

), “GARCH based artificial neural networks in forecasting conditional variance of stock returns”, Croatian Operational Research Review, Vol. 5, No. 2, pp. 329-343. 12. Bandi, F. M., Russell, J. R. (2008), “Microstructure Noise, Realized Variance, and Optimal Sampling”, The Review of Economic Studies, Vol. 75, No. 1, pp. 339-369. 13. Bandi, F. M., Russell, J. R. (2011), “Market Microstructure Noise, Integrated Variance Estimators, and the Accuracy of Asymptotic Approximations”, Journal of Econometrics, Vol. 160, No. 1, pp. 145

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On a new approach to the analysis of variance for experiments with orthogonal block structure. III. Experiments in row-column designs

References Caliński T., Siatkowski I. (2017): On a new approach to the analysis of variance for experiments with orthogonal block structure. I. Experiments in proper block designs. Biometrical Letters 54: 91-122. Caliński T., Siatkowski I. (2018): On a new approach to the analysis of variance for experiments with orthogonal block structure. II. Experiments in nested block designs. Biometrical Letters 55: 147-178. Euler L. (1782): Recherches sur une nouvelle espèce de quarrés magiques. Verh. Zeeuwach Genootschap Wetenschappen Vlissengen 9: 85

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On Robust Estimation of Error Variance in (Highly) Robust Regression

Abstract

The linear regression model requires robust estimation of parameters, if the measured data are contaminated by outlying measurements (outliers). While a number of robust estimators (i.e. resistant to outliers) have been proposed, this paper is focused on estimating the variance of the random regression errors. We particularly focus on the least weighted squares estimator, for which we review its properties and propose new weighting schemes together with corresponding estimates for the variance of disturbances. An illustrative example revealing the idea of the estimator to down-weight individual measurements is presented. Further, two numerical simulations presented here allow to compare various estimators. They verify the theoretical results for the least weighted squares to be meaningful. MM-estimators turn out to yield the best results in the simulations in terms of both accuracy and precision. The least weighted squares (with suitable weights) remain only slightly behind in terms of the mean square error and are able to outperform the much more popular least trimmed squares estimator, especially for smaller sample sizes.

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