Parametric vs. Nonparametric.

Cynderella

New Member
Suppose a researcher estimated a parameter in parametric way with correct distributional assumption.

Another researcher estimated the same parameter in non-parametric way.

Will there any difference of accuracy (bias) in estimation in these two situations?

Miner

TS Contributor
In general, nonparametric tests tend to be lower in power and have wider confidence intervals. Regarding bias, that will depend on the specific nonparametric test as well as your null hypothesis. Some nonparametric tests are based on the median vs. the mean. Some are based on the shape vs. the mean, etc. In those situations, there could be a potential bias relative to the mean.

hlsmith

Less is more. Stay pure. Stay poor.
I would imagine that if both methods met assumptions and were examining the same parameter construct, they would tend to generally merge given a large enough sample size. Though as Miner mentions it all depends on which statistical tests you are using.

GretaGarbo

Human
Another researcher estimated the same parameter in non-parametric way.
I believe that I understand that it is possible to estimate a parameter with parametric methods.

But I don't understand how it is possible to estimate a parameter in a non-parametric way, i.e. without assuming the existence of a parameter.

rogojel

TS Contributor
I believe that I understand that it is possible to estimate a parameter with parametric methods.

But I don't understand how it is possible to estimate a parameter in a non-parametric way, i.e. without assuming the existence of a parameter.
Yepp, one difference might be that the parametric method will estimate a mean. The non-parametric method most probably the median . If the distribution is not symmetrical there will be a difference.

regards

GretaGarbo

Human
Yepp, one difference might be that the parametric method will estimate a mean. The non-parametric method most probably the median . If the distribution is not symmetrical there will be a difference.
But isn't the median a parameter?

You can get the median from minimizing the absolute deviation (in contrast to least squares to get the mean). But isn't that a parametric method that estimates the parameter theta by minimizing Sum|y-theta| ?

hlsmith

Less is more. Stay pure. Stay poor.
Greta, I agree with the issues you are positing and have thought about them myself in the past. Yes, to me they are both parameters given the general definition of what parameters are. Though, it comes down to the distribution assumptions not being there in non-parameter approaches. So maybe we think the term parametric and non-parametric deal with the estimate, but it is actually dealing with the sampling distribution, etc.