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Estimation of grids, areas and volumes of intersection
Published in Martin Lloyd Smith, Geologic and Mine Modelling using Techbase and Lynx, 2020
Jackknife estimation is used to evaluate the estimation error for weighted average estimators. Each datum value is estimated based on the surrounding data using the same search and estimation parameters that are being considered for use in grid estimation. This corresponds to estimating random point locations which correspond in number and location to the data set. As each datum location is estimated from the surrounding data, the datum value at that location is cut from the data set. The result is that there is an estimated value for each data record. This procedure can be repeated for two or three parameter values such as inverse distance powers of one, two or three and the residuals can be calculated for each of the estimate values. The three sets of residuals can be compared to see which inverse distance power results in the lowest error variance and bias. The residuals can also be posted or contoured using random contouring to check for spatial bias.
Bayes and big data: the consensus Monte Carlo algorithm
Published in Jiuping Xu, Syed Ejaz Ahmed, Zongmin Li, Big Data and Information Theory, 2022
Steven L. Scott, Alexander W. Blocker, Fernando V. Bonassi, Hugh A. Chipman, Edward I. George, Robert E. McCulloch
Not all problems will exhibit meaningful small sample bias. In some cases the shard-level models will have sufficiently large sample sizes that small-sample bias is not an issue. In others, models can be unbiased even in small samples. When small sample bias is a concern, jackknife bias correction can be used to mitigate it through subsampling. The idea behind jackknife bias correction is to shift the draws from a distribution by a specified amount B determined by subsampling. Suppose E(θ|y) = θ + B/n, so that the posterior mean is a biased estimate of θ. On each worker machine, take a subsample of size αn, where 0 < α < 1. Let ysub denote the resulting distributed subsample, and construct consensus Monte Carlo draws from p(θ|ysub). Then E(θ|ysub) = θ + B/αn. Simple algebra gives an estimate of the bias term Bn≈E(θ|ysub)-E(θ|y)α1-α.
Estimation Using Confidence Intervals
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Tukey (1958) developed a “leave-one-out-at-a-time” approach to estimation, called the jackknife,* that is gaining increasing acceptance among practitioners. Let y1, y2, . . . , yn be a sample of size n from a population with parameter θ. An estimate θ^(i) is obtained by omitting the ith observation (i.e., yi) and computing the estimate based on the remaining (n – 1) observations. This calculation is performed for each observation in the data set, and the procedure results in n estimates of θ:θ^(1),θ^(2),. . . , θ^(n). The jackknife estimator of θ is then some suitably chosen linear combination (e.g., a weighted average) of the n estimates. Application of the jackknife is suggested for situations where we are likely to have outliers or biased samples, or find it difficult to assess the variability of the more traditional estimators.
Approaches for local calibration of mechanistic-empirical pavement design guide joint faulting model: a case study of Ontario
Published in International Journal of Pavement Engineering, 2020
Shi Dong, Jian Zhong, Susan L. Tighe, Peiwen Hao, Daniel Pickel
Jackknifing is effective in eliminating the variability caused by the changes of the random samples in statistics. The jackknife estimator of a parameter is found by systematically leaving out each observation from a dataset and calculating the estimate and then finding the average of these calculations. Given a sample of size n, the Jackknife estimate is found by aggregating the estimates of each (n−1) sized sub-sample. Then, the coefficients vectors were calculated through the Jackknifing method. The results showed that the coefficients through Jackknifing were close to that in Table 5 using the same approach. Therefore, there was no significant variability in the calibration results. These coefficients are suitable for the Ontario JPCP sections considering the existing database.
A simulation-based estimation method for bias reduction
Published in IISE Transactions, 2018
When it comes to reducing the bias of estimators, numerous methods have been proposed. Most of these methods directly estimate the bias and then perform the bias correction. For instance, the jackknife method (Wu, 1986) omits one data point from the original data each time and calculates the mean jackknife estimator to help estimate the jackknife bias. Asmussen and Glynn (2007) proposed a method that a applies Taylor expansion to the performance function and estimates the bias of the performance estimators based on the bias and variance of the input parameters. The parametric bootstrap method resamples data from the estimated parametric distribution and then uses the simulated sample to estimate the bias (see, for instance, Efron and Tibshirani (1994) for details). The bias is then corrected by subtracting the estimated bias from the previous estimator.
Estimation of state-wide and monthly domestic water use in India from 1975 to 2015
Published in Urban Water Journal, 2021
Naveen Joseph, Dongryeol Ryu, Hector M. Malano, Biju George, K. P. Sudheer
A power function model was found to best fit the per-capita GDP and per-capita domestic water demand relationship. Since there were only five observations of domestic water use, a jackknife cross-validation scheme was adopted. Jackknife method is a two-fold cross-validation scheme based on the resampling technique, which systematically leaves one observation of the dataset and calculates the error estimate of the remaining datasets (Quenouille 1949). Based on the cross-validation scheme, the model was trained with four data points, and the remaining point was used to validate the model. This procedure was repeated for all the possible combinations of the data.