fitting a smooth monotonic function to non noisy data

Hi guys,

I'm new to this field of kernel estimation/smooth isotonic regression/smooth monotonic regression.

I need to fit a model for my strictly monotonic data,

I got lost with all the info online.

more specifficaly, I have data set points , I know that the data is monoctonically increasing, no noise.

and I'm looking for a function f suct that .

can you recommend a good algorithem to do so? or a paper to read, I want to understand how this process works.

In which conditions I will be able to recover the original function of the samples data?

Thanks!

Nushi

[Ameer Hamza]

Do you have an equation of f(x), perhaps with few unknown parameters? You can use the data points to estimate the unknown parameters of f(x).

[Adam Danz]

There are lots of monotonic functions that differ greately in their parameters. Consider a straight line vs an exponential curve. Both can be monotonically increasing. If you don't have the function f(x), perhaps you could plot the data points and share the plot so someone could suggest where to start.