Analysis of rounded data from dependent sequences

Zhang, Baoxue; Liu, Tianqing; Bai, Zhidong

doi:10.1007/s10463-009-0224-6

Cited by 15 publications

(16 citation statements)

References 34 publications

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“…In this case, the strong consistency and asymptotic normality of MLE have been established by Zhang et al (2009). In this section, we extend their results to a general RRSS case.…”

Section: The Maximum Likelihood Estimate and Its Asymptotic Propertiesmentioning

confidence: 61%

“…Notice the independence of RRSS, these two theorems can follow easily from Lemma 1, 2 and the main theorem of Zhang et al (2009). Details are omitted.…”

Section: Proof Of Theorems 3 Andmentioning

confidence: 93%

“…But they didn't obtain simultaneous interval estimation of the parameters μ and σ 2 as their method is based on an unjustified inversion of rounded data likelihood ratio statistic. For some recent references, one may turn to Tricker et al (1998);Vardeman (2005); Vardeman and Lee (2005); Zhang et al (2009).…”

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confidence: 99%

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Rounded data analysis based on ranked set sample

Liu

Bai

2010

Stat Papers

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In this paper we investigate the Fisher information matrix of a rounded ranked set sampling (RSS) sample and show that the sample is always more informative than a rounded simple random sampling (SRS) sample of the same size. On the other hand, we propose a new method to approximate maximum likelihood estimates (MLE) of unknown parameters for this model and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that the approximated MLE based on rounded RSS is always more efficient than those based on rounded SRS.

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“…In this case, the strong consistency and asymptotic normality of MLE have been established by Zhang et al (2009). In this section, we extend their results to a general RRSS case.…”

Section: The Maximum Likelihood Estimate and Its Asymptotic Propertiesmentioning

confidence: 61%

“…Notice the independence of RRSS, these two theorems can follow easily from Lemma 1, 2 and the main theorem of Zhang et al (2009). Details are omitted.…”

Section: Proof Of Theorems 3 Andmentioning

confidence: 93%

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Rounded data analysis based on ranked set sample

Liu

Bai

2010

Stat Papers

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“…ML estimation of stochastic processes, in particular ARMA processes, has been studied by Zhang et al (2010).…”

Section: Estimation When H Is Largementioning

confidence: 99%

Symmetric and asymmetric rounding: a review and some new results

Schneeweiß¹,

Komlos²,

Ahmad

2010

AStA Adv Stat Anal

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Using rounded data to estimate moments and regression coefficients typically biases the estimates. We explore the bias-inducing effects of rounding, thereby reviewing widely dispersed and often half forgotten results in the literature. Under appropriate conditions, these effects can be approximately rectified by versions of Sheppard's correction formula. We discuss the conditions under which these approximations are valid and also investigate the efficiency loss caused by rounding. The rounding error, which corresponds to the measurement error of a measurement error model, has a marginal distribution, which can be approximated by the uniform distribution, but is not independent of the true value. In order to take account of rounding preferences (heaping), we generalize the concept of simple rounding to that of asymmetric rounding and consider its effect on the mean and variance of a distribution.

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“…They analyzed a mixture model for rounded data by the Bayesian approach implemented by using the Gibbs sampler. Zhang, Liu and Bai [27] presented a new approach of the parameter estimation, named as "short, overlapping series" (SOS), to deal with the rounded data from an autoregressive moving average models (ARMA), and established the asymptotic properties of the SOS estimators when the innovations are normally distributed. The general issue of rounding continuous data has been indispensable for practical exercises.…”

Section: Introductionmentioning

confidence: 99%

Revisit of Sheppard corrections in linear regression

Liu

Zhang

et al. 2010

Sci. China Math.

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Dempster and Rubin (D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction, BRB correction and the ordinary LSE by simulations. Some asymptotic results when the rounding scale tends to 0 were also presented. In a previous research, we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding scale. In the light of these results, in this paper we further investigate the rounding errors in linear regressions. We notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is incorrect. Examples in which the Sheppard correction works worse than the BRB correction are also given. Furthermore, we propose a new approach to estimate the parameters, called "two-stage estimator", and establish the consistency and asymptotic normality of the new estimators.

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Analysis of rounded data from dependent sequences

Cited by 15 publications

References 34 publications

Rounded data analysis based on ranked set sample

Rounded data analysis based on ranked set sample

Symmetric and asymmetric rounding: a review and some new results

Revisit of Sheppard corrections in linear regression

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