Application Notes for oneMKL Summary Statistics

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Date 3/31/2023
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Document Table of Contents
Document Table of Contents x
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics x
Legal Information About This Document About Summary Statistics Algorithms and Interfaces in Summary Statistics Common Usage Model of Summary Statistics Algorithms Processing Data in Blocks Detecting Outliers in Datasets Dealing with Missing Observations Computing Quantiles for Streaming Data Bibliography
About This Document x
Conventions and Symbols
Algorithms and Interfaces in Summary Statistics x
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and Variance-Covariance/Correlation/Cross-Product Matrix Computing Median Absolute Deviation Computing Mean Absolute Deviation Computing Minimum/Maximum Values Calculating Order Statistics Estimating Quantiles Estimating a Pooled/Group Variance-Covariance Matrices/Means Estimating a Partial Variance-Covariance Matrix Performing Robust Estimation of a Variance-Covariance Matrix Detecting Multivariate Outliers Handling Missing Values in Matrices of Observations Parameterizing a Correlation Matrix Sorting an Observation Matrix
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and Variance-Covariance/Correlation/Cross-Product Matrix x
Computing Estimations for Large Datasets Calculating Multiple Estimates
Estimating Quantiles x
Computing Quantiles for Streaming Data with VSL_SS_METHOD_SQUANTS_ZW
Handling Missing Values in Matrices of Observations x
Basic Assumptions for the MI Method Basic Components of the MI Method
Detecting Outliers in Datasets x
Using the BACON Algorithm for Outlier Detection Using Robust Methods
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics

Bibliography

[Billor2000] Nedret Billor, Ali S. Hadib, and Paul F. Velleman. BACON: blocked adaptive computationally efficient outlier nominators. Computational Statistics & Data Analysis, 34, 279-298, 2000.

[Maronna2002] R.A. Maronna and R.H. Zamar, Robust Multivariate Estimates for High-Dimensional Datasets. Technometrics, 44, 307-317, 2002.

[MKLMan] Intel® MKL Reference Manual.

[Rebonato1999] R. Rebonato and P Jackel, The most general methodology to create a valid correlation matrix for risk management and option pricing purposes, Quantitative Research Centre of the NatWest Group, October, 1999.

[Rocke96] David M. Rocke. Robustness properties of S-estimators of multivariate location and shape in high dimension. The Annals of Statistics, 24(3), 1327-1345, 1996

[Rubin1987] D.B. Rubin. Multiple Imputation for Nonresponse in surveys. J. Wiley & Sons, New York, 1987.

[Schafer1997] J.L. Schafer. Analysis of Incomplete Multivariate Data. Chapman & Hall, 1997.

[Schafer1998] J.L. Schafer and M.K. Olsen. Multiple Imputation for Missing-Data Problems: A Data Analyst’s Perspective. Multivariate Behavioral Research, 33(4), 545-571, 1998.

[West79] D.H.D. West. Updating Mean and Variance Estimates: An improved method. Communications of ACM, 22(9), 532-535, 1979

[Zhang2007]  Q. Zhang and W. Wang. A Fast Algorithm for Approximate Quantiles in High Speed Data Streams. SSDBM, p.29, 19th International Conference on Scientific and Statistical Database Management (SSDBM 2007), 2007.

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