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8

We will describe how a spline can be used through Kalman Filtering (KF) techniques in relation with a State-Space Model (SSM). The fact that some spline models can be represented by SSM and computed with KF was revealed by C.F. Ansley and R. Kohn in the years 1980-1990. The estimated function and its derivatives are the expectations of the state conditional ...

4

You can do spectacularly well with a standard least-squares routine, provided you have a reasonable idea of the relative sizes of the random errors made for each derivative. There is no restriction on the number of measurements you make for each $x$ value--you can even simultaneously measure different derivatives at each one. The only limitation in the use ...

3

Yes/no is categorical. http://www.stat.yale.edu/Courses/1997-98/101/catdat.htm Categorical variables represent types of data which may be divided into groups. Examples of categorical variables are race, sex, age group, and educational level.

3

100% accuracy can clearly be achieved (also on the validation or unknown data) for some problem settings, but I guess those are rare cases. At the latest when the influence of the random noise "blurs" the borders of the data enough, the accuracy most likely will go down on unknown data, while it still may be up on the training data due to overfitting. An ...

3

If you plot Size against Time for each Group you will find that the points all lie on a straight line. Since you are fitting a model with the interaction between Time and Group you get a perfect fit overall which is what the software is telling you. Without knowing more about the process which generates your data it is impossible to say what implications ...

2

This question has relationships with several other questions How to fit exponential y=A(1-exp(B*X)) function to a given data set? Especially how to determine the initial start parameters? How to minimize residual sum of squares of an exponential fit? Why is nls() giving me "singular gradient matrix at initial parameter estimates" errors? I have ...

1

This depends on how you are thinking about the likelihood function: If you have the same regression model but two different data sets then yes the likelihood function takes the same mathematical form. See for example (this is a log likelihood which is just the natural log of the likelihood) equation 3 here: https://www.stat.cmu.edu/~cshalizi/mreg/15/lectures/...

1

Your question is very broad, so this is more of a comment. One possible problem is that the (generalized) likelihood ratio test might be suboptimal in some cases, this paper points to some such examples. You say Indeed, many, if not all, of the above mentioned tests can be shown to be equivalent to a LRT, but I was referring to LRTs directly constructed by ...

1

First of all, I want to thank you for posing this question. It's a REALLY interesting question. I love splines and the cool things you can do with them. And this gave me an excuse to do some research. :-) BLUF: The short answer is no. I don't know of any functionality in R that will do this for you automatically. The long answer is... much more ...

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