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  "Title": "Proper Scoring Rules for Missing Value Imputation",
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  "Description": "Provides tools for evaluating and ranking missing value\nimputation methods using proper scoring rules. Implements the\nEnergy-I-Score and the DR-I-Score for the assessment of\ndeterministic, stochastic and multiple imputation methods for\nnumerical and mixed datasets, following Näf et al. (2022)\n<doi:10.48550/arXiv.2106.03742> and Näf et al. (2025)\n<doi:10.48550/arXiv.2507.11297>.",
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    "random_mcar_data",
    "random_mcar_mixed_data"
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    {
      "page": "compare_Iscores",
      "title": "Calculates IScores for multiple imputation functions",
      "topics": [
        "compare_Iscores"
      ]
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    {
      "page": "DR_IScore",
      "title": "Compute the imputation KL-based scoring rules",
      "topics": [
        "DR_IScore"
      ]
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      "page": "edistance",
      "title": "Energy distance",
      "topics": [
        "edistance"
      ]
    },
    {
      "page": "energy_IScore",
      "title": "Calculates Imputation Score for imputation function",
      "topics": [
        "energy_IScore"
      ]
    },
    {
      "page": "exp_imputation",
      "title": "Standard exponential imputation",
      "topics": [
        "exp_imputation"
      ]
    },
    {
      "page": "median_mode_imputation",
      "title": "Median/mode imputation",
      "topics": [
        "median_mode_imputation"
      ]
    },
    {
      "page": "norm_imputation",
      "title": "Standard normal imputation",
      "topics": [
        "norm_imputation"
      ]
    },
    {
      "page": "random_mcar_data",
      "title": "Generate random data with MCAR missing values",
      "topics": [
        "random_mcar_data"
      ]
    },
    {
      "page": "random_mcar_mixed_data",
      "title": "Generate random mixed data with MCAR missing values",
      "topics": [
        "random_mcar_mixed_data"
      ]
    }
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      "title": "Energy-I-Score: First Steps",
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      "headings": [
        "Introduction",
        "Installation",
        "Preparing data",
        "Imputation Function",
        "Calculating the energy-I-Score",
        "Important parameters",
        "Number of imputations: N",
        "Limiting the number of scored variables: max_length",
        "Handling incomplete training sets: skip_if_needed",
        "Scaling variables: scale",
        "Energy-I-Score for mixed data",
        "Calculating the DR-I-Score",
        "Parameters",
        "Comparing multiple imputation methods",
        "Comparing methods using multiple scores",
        "Summary of best practices",
        "Energy score",
        "References"
      ],
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        "Notation",
        "Algorithm Overview",
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        "Step 2: Data Partitioning",
        "Step 3: Multiple Imputations",
        "Step 4: Energy Distance Calculation",
        "For each $i \\in L_j$, the energy-I-Score component is computed as:[\\widehat{S}^j_{\\mathrm{NA}}(H,P) =\\frac{1}{|L_j|} \\sum_{i \\in L_j}\\left[\\frac{1}{2N^2} \\sum_{l=1}^N \\sum_{\\ell=1}^N|\\tilde{X}{i,j}^{(l)} - \\tilde{X}{i,j}^{(\\ell)}|",
        "Step 5: Weighting",
        "Step 6: Final Score",
        "Practical Interpretation",
        "References"
      ],
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      "modified": "2026-06-08 18:20:25",
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