Application Notes for oneMKL Summary Statistics

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ID 772991
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

Basic Assumptions for the MI Method

The MI method is provided under the following assumptions:

  1. The base model for the Summary Statistics version of MI is a multivariate normal distribution with parameters (μ, Σ) where

    1. μ is a vector of means.

    2. Σ is a variance-covariance matrix.

  2. Prior distribution of μ is a conditionally-multivariate Gaussian given Σ with parameters μ0∈R7 and τ-1Σ, where τ is a positive constant. The variance-covariance matrix Σ follows the inverted-Wishart distribution for fixed parameters m ≥ p and a positive-definite matrix Λ.

  3. Data points are Missed At Random (MAR).

The strict definition of this and other mechanisms supporting missing values are available in [Rubin1987].

Parent topic: Handling Missing Values in Matrices of Observations
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