W.F. Sheppard's Smoothing Method: A Precursor to Local Polynomial Regression. (11th June 2019)

• Record Type: Journal Article
• Authors: Murray, Lori; Bellhouse, David
• Is Part Of: International statistical review. Volume 87:Number 3(2019)
• Page Start: 604
• Page End: 612
• Publication Date: 2019-06-11
• Subjects: Data smoothing -- central differences -- local polynomial regression -- history of statistics; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12330
• Languages: English
• ISSNs: 0306-7734

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.