W.F. Sheppard's Smoothing Method: A Precursor to Local Polynomial Regression
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Bibliographic record
Abstract
Summary W.F. Sheppard has been much overlooked in the history of statistics although his work produced significant contributions. He developed a polynomial smoothing method and corrections of moment estimates for grouped data as well as extensive normal probability tables that have been widely used since the 20th century. Sheppard presented his smoothing method for actuaries in a series of publications during the early 20th century. Population data consist of irregularities, and some adjustment or smoothing of the data is often necessary. Simple techniques, such as Spencer's summation formulae involving arithmetic operations and moving averages, were commonly practised by actuaries to smooth out equally spaced data. Sheppard's method, however, is a polynomial smoothing method based on central differences. We will show how Sheppard's smoothing method was a significant milestone in the development of smoothing techniques and a precursor to local polynomial regression.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it