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Particle size analysis in composite materials has mostly been based on the use of sample moments.
We develop asymptotic results for the high-dimensional GMM shrinkage estimator, allowing for non-smooth sample moments and weakly dependent observations.
The results show the PDF of rock variables can be accurately derived from LPA method with sample moments and the proposed method is suitable for approximating probability distributions of rock random variable.
Fig. 4 Sample moments by cohorts.
For the computation of empirical CV, sample moments are to be evaluated.
24 In total, we look for six parameters by matching 20 sample moments.
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"Properties of Successive Sample Moment Estimators". Barouch, E., S. Chow, G. Kaufman, and T. Wright, Working Paper.
To calculate the sample moment, we subtracted the holder magnetization from each sample measurement.
E y being a sample moment, we invoke here its asymptotical normal distributions [28].
( {overline{X}}_n={n}^{-1}{displaystyle sum_{i=1}^n{X}_i} ) and ( {overline{X}}_n^r={n}^{-1}{displaystyle sum_{i=1}^n{X}_i^r} ) are the mean of samples and rth sample moment, respectively, then the random weighting estimation of the ( {overline{X}}_n ) and ( {overline{X}}_n^r ) can be defined as {H}_n={displaystyle sum_{i=1}^n{xi}_i{X}_i} (5).
MoM works by setting the population moment equal to the sample moment.
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