Report

Report#

Part 1#

1. Describe your chosen initial values for the Gauss-Newton iteration and reflect on how your choice of initial values for the Gauss-Newton iteration influenced the convergence of your solution. What did you observe about the number of iterations needed and the stability of the estimated parameters when using different initial values? After how many iterations does it converge? (2pt) To include in your answer:

  • A plot of your estimates for each parameter versus the iteration number (horizontal axis: iteration number, vertical axis: parameter estimate)

Part 2#

2. Analysis the fitted model and residuals, do you think the initial fitted model is correct? Is the initial hypothesis accepted or rejected? (2 pt)
To include in your answer:

  • Whether the distribution of the residuals is as expected, and why or why not

  • The outcome of the overall model test

  • How would the critical value need to change in order to accept the null hypothesis \(H_0\)?

Part 3#

4. For the alternative model using the Generalized Likelihood Ratio Test (GLRT), estimate the most likely day the shift occurred. Identify the day \(\mathbf{k}_{\text{hat}}\) corresponding to the maximum test statistic and report this estimated day of shift. Is the alternative hypothesis accepted or rejected?(2 pt)

Part 4#

6. Compare the final, selected model against the initial model in terms of estimated parameters, overall model fit and residual statistics. Explain in detail why it is essential to rely on the statistical tests rather than solely on visual inspection, especially when the simpler model might appear “good enough” when simply plotted against the observations. (3pt) To include in your answer:

  • Your estimated parameters from \(H_0\) and \(H_a\) and their quality

By Sandra Verhagen and Lina Hagenah, Delft University of Technology. CC BY 4.0, more info on the Credits page of Workbook.

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