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Stats, Volume 2, Issue 4 (December 2019) – 5 articles

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Cover Story (view full-size image) This paper demonstrates the dependence of the linear regression on the selection of the reference [...] Read more.
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Open AccessArticle
Evaluating the Performance of Multiple Imputation Methods for Handling Missing Values in Time Series Data: A Study Focused on East Africa, Soil-Carbonate-Stable Isotope Data
Stats 2019, 2(4), 457-467; https://doi.org/10.3390/stats2040032 - 16 Dec 2019
Viewed by 386
Abstract
In all fields of quantitative research, analysing data with missing values is an excruciating challenge. It should be no surprise that given the fragmentary nature of fossil records, the presence of missing values in geographical databases is unavoidable. As in such studies ignoring [...] Read more.
In all fields of quantitative research, analysing data with missing values is an excruciating challenge. It should be no surprise that given the fragmentary nature of fossil records, the presence of missing values in geographical databases is unavoidable. As in such studies ignoring missing values may result in biased estimations or invalid conclusions, adopting a reliable imputation method should be regarded as an essential consideration. In this study, the performance of singular spectrum analysis (SSA) based on L 1 norm was evaluated on the compiled δ 13 C data from East Africa soil carbonates, which is a world targeted historical geology data set. Results were compared with ten traditionally well-known imputation methods showing L 1 -SSA performs well in keeping the variability of the time series and providing estimations which are less affected by extreme values, suggesting the method introduced here deserves further consideration in practice. Full article
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Open AccessArticle
Bayesian Prediction of Order Statistics Based on k-Record Values from a Generalized Exponential Distribution
Stats 2019, 2(4), 447-456; https://doi.org/10.3390/stats2040031 - 15 Nov 2019
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Abstract
We examine in this paper the implementation of Bayesian point predictors of order statistics from a future sample based on the k th lower record values from a generalized exponential distribution. Full article
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Open AccessArticle
Confidence Sets for Statistical Classification (II): Exact Confidence Sets
Stats 2019, 2(4), 439-446; https://doi.org/10.3390/stats2040030 - 07 Nov 2019
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Abstract
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. Liu et al. (2019) proposed a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to [...] Read more.
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. Liu et al. (2019) proposed a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. However, the classifier uses a conservative critical constant. In this paper, we show how to determine the exact critical constant in applications where prior knowledge about the proportions of the future objects from each class is available. As the exact critical constant is smaller than the conservative critical constant given by Liu et al. (2019), the classifier using the exact critical constant is better than the classifier by Liu et al. (2019) as expected. An example is provided to illustrate the method. Full article
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Open AccessArticle
Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms
Stats 2019, 2(4), 426-438; https://doi.org/10.3390/stats2040029 - 29 Oct 2019
Viewed by 344
Abstract
The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean Lq-norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, [...] Read more.
The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean Lq-norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, and the geometric interpretation of the errors. Typical fitting methods are mostly developed based on Euclidean norms, leading to the traditional least–square method. On the other hand, the theory of general fitting methods based on non-Euclidean norms is still under development; the normal equations provide implicitly the optimal values of the fitting parameters, while this paper completes the puzzle by improving understanding the derivations and geometric meaning of the optimal errors. Full article
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Open AccessArticle
Linear Regression with Optimal Rotation
Stats 2019, 2(4), 416-425; https://doi.org/10.3390/stats2040028 - 28 Sep 2019
Cited by 1 | Viewed by 471
Abstract
The paper shows how the linear regression depends on the selection of the reference frame. The slope of the fitted line and the corresponding Pearson’s correlation coefficient are expressed in terms of the rotation angle. The correlation coefficient is found to be maximized [...] Read more.
The paper shows how the linear regression depends on the selection of the reference frame. The slope of the fitted line and the corresponding Pearson’s correlation coefficient are expressed in terms of the rotation angle. The correlation coefficient is found to be maximized for a certain optimal angle, for which the slope attains a special optimal value. The optimal angle, the value of the optimal slope, and the corresponding maximum correlation coefficient were expressed in terms of the covariance matrix, but also in terms of the values of the slope, derived from the fitting at the nonrotated and right-angle-rotated axes. The potential of the new method is to improve the derived values of the fitting parameters by detecting the optimal rotation angle, that is, the one that maximizes the correlation coefficient. The presented analysis was applied to the linear regression of density and temperature measurements characterizing the proton plasma in the inner heliosheath, the outer region of our heliosphere. Full article
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