RT Journal Article T1 Robust analysis of variance with imprecise data: an ad hoc algorithm A1 Rivero, Carlos A1 Valdés Sánchez, Teófilo AB We present an easy to implement algorithm, which is valid to analyse the variance of data under several robust conditions. Firstly, the observations may be precise or imprecise. Secondly, the error distributions may vary within the wide class of the strongly unimodal distributions, symmetrical or not. Thirdly, the variance of the errors is unknown. The algorithm starts by estimating the parameters of the ANOVA linear model. Then, the asymptotic covariance matrix of the effects is estimated. Finally, the algorithm uses this matrix estimate to test ANOVA hypotheses posed in terms of linear combinations of the effects. PB Springer SN 1352-8505 YR 2011 FD 2011-12 LK https://hdl.handle.net/20.500.14352/43677 UL https://hdl.handle.net/20.500.14352/43677 LA eng NO AnMY (1998) Logconcavity versus logconvexity: a complete characterization. J Econ Theory 80:350–369Anido C, Rivero C, Valdes T (2000) Modal iterative estimation in linear models with unihumped errors and non-grouped and grouped data collected from different sources. Test 9(2):393–416Anido C, Rivero C, Valdes T (2008) Analysis of variance with general errors and grouped and non-grouped data: some iterative algorithms. J Multivar Anal 99:1544–1573Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Soc 39:1–22Fahrmeir L,KufmannH (1985) Consistency and asymptotic normality of themaximum likelihood estimator in generalized linear models. Ann Stat 13:342–368Healy MJR, Westmacott M (1956) Missing values in experiments analysed on automatic computers. Appl Stat 5:203–206James IR, Smith PJ (1984) Consistency results for linear regression with censored data. Ann Stat 12:590–600Little RJA, Rubin DB (2002) Statistical analysis with missing data. Wiley, New JerseyLouis TA (1982) Finding observed information using the EM algorithm. J Roy Stat Soc B 44:98–130McLachlan GJ, Krishnan T (1997) The EM algorithm and extensions. Wiley, New YorkMeilijson I (1989) A fast improvement of the EMalgorithm on its own terms. J Roy Stat Soc B 51:127–138Meng XL, Rubin DB (1991) Using EM to obtain asymptotic variance-covariance matrices. J Amer Stat Assoc 86:899–909Orchard T,WoodburyMA(1972)Amissing information principle: theory and applications. In: Proceedings of the 6th Berkeley Symposium on mathematical statistics and probability, Vol I. pp 697–715Ritov Y (1990) Estimation in linear regression model with censored data. Ann Stat 18:303–328TannerMA (1996) Tools for statistical inference. Methods for the exploration of posterior distributions and likelihood functions. Springer, New York NO MEC NO EUROSTAT DS Docta Complutense RD 28 abr 2024