Applied Nonparametric Econometrics by Henderson Daniel J. & Parmeter Christopher F

Author:Henderson, Daniel J. & Parmeter, Christopher F. [Henderson, Daniel J.]
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2014-11-29T22:00:00+00:00

Ordered

The kernel we just described ignores any natural ordering in the discrete variable. It is likely in applied work that we will also have variables that possess a natural order. A common example is a time trend, but survey data where respondents are asked for a ranking or placing income into bins is also common. In these cases the discrete kernel in Equation (7.1) will not exploit this known ordinal relationship. The reason underlying this is that for the Aitchison and Aitken (1976) kernel, a constant weight is assigned to all values of the variable that do not equal the value under study (x). However, with an ordered variable, we can see that cells closer to the cell of interest should naturally be seen as “closer” than cells further away, as is the case in the continuous setting. In the time trend example, we might expect that the years 1999 and 2001 have more information to offer when smoothing for the year 2000 than the years 1990 and 2010.

Both Aitchison and Aitken (1976, 419) and Wang and van Ryzin (1981, 302) suggest kernels appropriate for estimating densities of an ordered discrete variable. Aitchison and Aitken (1976) do not provide a general formula for an ordered, discrete kernel function: they provide a single kernel function (for the case ). While Wang and van Ryzin (1981) only discuss the case where the discrete variable is countable. The kernel proposed by Aitchison and Aitken (1976) has the form

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.