Abstract
Rounding errors have a considerable impact on statistical inferences, especially when the data size is large and the finite normal mixture model is very important in many applied statistical problems, such as bioinformatics. In this article, we investigate the statistical impacts of rounding errors to the finite normal mixture model with a known number of components, and develop a new estimation method to obtain consistent and asymptotically normal estimates for the unknown parameters based on rounded data drawn from this kind of models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bai ZD, Zheng SR, Zhang BX, Hu GR (2009) Statistical analysis for rounded data. J Stat Plan Inference 139(8): 2526–2542
Basford KE, McLachlanSource GJ (1985) Likelihood estimation with normal mixture models. J R Stat Soc C 34: 282–289
Beaton AE, Rubin DB, Baxone JL (1976) The acceptability of regression solutions: another look at computational accuracy. J Am Stat Assoc 71: 158–168
Cuesta-Albertos JA, Matrán C, Mayo-Iscar A (2008) Robust estimation in the normal mixture model based on robust clustering. J R Stat Soc B 70: 779–802
Dempster AP, Rubin DB (1983) Rounding error in regression: the appropriateness of Sheppard’s corrections. J R Stat Soc B 45: 51–59
Fisher RA (1922) On the mathematical foundations of theoretical statistics. Philos Trans R Soc A 222: 309–368
Hasselblad V (1966) Estimation of parameters for a mixture of normal distributions. Technometrics 8(3): 431–444
Lee CS, Vardeman SB (2001) Interval estimation of a normal process mean from rounded data. J Qual Technol 33: 335–348
Lee CS, Vardeman SB (2002) Interval estimation of a normal process standard deviation from rounded data. Commun Stat B 31: 13–34
Lee CS, Vardeman SB (2003) Confidence interval based on rounded data from the balanced one-way normal random effects model. Commun Stat B 32: 835–856
Lindley DV (1950) Grouping correction and maximum likelihood equations. Proc Camb Philos Soc 46: 106–110
Mullet GM, Murray TW (1971) A new method for examining rounding error in least-squares regression computer programs. J Am Stat Assoc 66: 496–498
Murray A, Donald BR (1985) Estimation and hypothesis testing in finite mixture models. J R Stat Soc B 47: 67–75
Richard JH (1985) A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Ann Stat 13(2): 795–800
Sheppard WF (1898) On the calculation of the most probable values of frequency constants for data arranged according to equidistant divisions of a scale. Proc Lond Math Soc 29: 353–380
Tricker A (1984) The effect of rounding data sampled from the exponential distribution. J Appl Stat 11: 54–87
Tricker A (1990a) Estimation of parameters for rounded data from non-normal distributions. J Appl Stat 17: 219–228
Tricker A (1990b) The effect of rounding on the significance level of certain normal test statistics. J Appl Stat 17: 31–38
Tricker A, Coates E, Okell E (1998) The effect on the R chart of precision of measurement. J Qual Technol 30: 232–239
Vardeman SB (2005) Sheppard’s correction for variances and the quantization noise model. IEEE Trans Instrum Meas 54: 2117–2119
Zhang BX, Liu TQ, Bai ZD (2010) Analysis of rounded data from dependent sequences. Ann Inst Stat Math 62(6): 1143–1173
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, N., Bai, Z. Analysis of rounded data in mixture normal model. Stat Papers 53, 895–914 (2012). https://doi.org/10.1007/s00362-011-0395-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-011-0395-0