How to practically use a Kernek density for a smoothing application

[bradyj7]

Hi there,

I'm trying use the Epanechnikov density kernel to smooth out data that I have collected, but I'm not sure exactly how to use it.

I've recorded speed data from a car every second for a journey and I'm trying to smooth the data as it contains some noise.

I have document that explains exactly how to do it, it is available http://dl.dropbox.com/u/54057365/All/smoothing%20velocity%20data%20paper.pdf

Bear in mind the data is recorded every second.

Does mean, at the bottom of the second page, that i = 1?

What does j equal? Is it the length of the entire journey in seconds? Or something else?

On the third page:

When computing the weight associated with the speed at a particular time interval, is it calculated by dividing the Epanechnikov Kernel K(Zij) for the current time interval by the sum of the Epanechnikov Kernel for 3 seconds behind and 3 seconds ahead (7 seconds in total)?

Thank you for your help.

John

 

[mmwave]

,

Thank you for reaching out for help with using the Epanechnikov density kernel to smooth out your speed data. I understand that you have collected speed data from a car every second for a journey and that you are looking to reduce some noise in the data.

Based on the document you provided, it appears that i = 1 refers to the first interval of time in your data, which would correspond to the first second of the journey. This means that j would equal the length of the journey in seconds, as you suspected.

On the third page of the document, it states that the weight associated with the speed at a particular time interval is calculated by dividing the Epanechnikov Kernel K(Zij) for the current time interval by the sum of the Epanechnikov Kernel for 3 seconds behind and 3 seconds ahead (7 seconds in total). This is done in order to give more weight to the current time interval and less weight to the surrounding intervals.

I hope this helps clarify how to use the Epanechnikov density kernel for smoothing your speed data. If you have any further questions or need additional assistance, please don't hesitate to ask. Best of luck with your research!