This blog post is concerned with the milestones achieved and some upcoming features in statsmodels

The model implemented is

**NONLINEAR MODELS**

The model implemented is

y = f(x,θ) + e

where the y is one dimensional endogenous data matrix, f is the nonlinear function, x is exogenous data matrix, θ is parameter matrix and 'e' is the noise in data.

**Estimation**

The estimation of parameters is done using the 'leastq' method from scipy.optimize which minimizes the sum of squares of residuals. We subclass the model class 'NonlinearLS' and provide the 'expr' function which calculates 'f' in the above expression using the parameter values and exogenous data provided to it. It is encouraged that the user provides the analytical derivative of the given function by defining 'jacobian' function in the similar way as 'expr'.

For testing purposes we used the 'Misra1a' model from NIST data. Details regarding this given in previous post. In summary, we obtained satisfactory results as compared to 'Gretl' which uses the same minpack module used by scipy.

A complete example can be viewed here https://github.com/divyanshubandil/statsmodels/commit/db2e388232303323cc9bb36e0fe9f682892993ba

I have been working on the M-estimation of nonlinear models for some time now. The best research paper I found having all the tests, computational algorithm and simulation data is here. http://www.tandfonline.com/doi/abs/10.1080/03610920802074836

Recently, I have been able to implement the algorithm in my first commit regarding this topic here https://github.com/divyanshubandil/statsmodels/commit/1745e02b45ebe3f83a8e0d55f477fcef33621d6f

Now I am working with testing this model for the 'Numerical example' given in the paper.

**Testing**For testing purposes we used the 'Misra1a' model from NIST data. Details regarding this given in previous post. In summary, we obtained satisfactory results as compared to 'Gretl' which uses the same minpack module used by scipy.

**Miscellaneous****Features**- Parameters calculated at each iteration by the algorithm can be viewed using view_iter() method
- Prediction table with confidence intervals for each predicted value of endogenous data using prediction_table(alpha) method

**Example**A complete example can be viewed here https://github.com/divyanshubandil/statsmodels/commit/db2e388232303323cc9bb36e0fe9f682892993ba

**ROBUST NONLINEAR MODELS**I have been working on the M-estimation of nonlinear models for some time now. The best research paper I found having all the tests, computational algorithm and simulation data is here. http://www.tandfonline.com/doi/abs/10.1080/03610920802074836

Recently, I have been able to implement the algorithm in my first commit regarding this topic here https://github.com/divyanshubandil/statsmodels/commit/1745e02b45ebe3f83a8e0d55f477fcef33621d6f

Now I am working with testing this model for the 'Numerical example' given in the paper.