If you have and IPAD/IPOD/TABLET or other device in bag that has WiFi what should you do when arriving at the exam venue?Single choice
A
Turn off WiFi on the device
B
Leave in bag outside the exam
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A researcher is analysing the time until job loss for a sample of workers. The following Cox proportional hazards model has been estimated: where • Training = 1 if participated in job training, 0 otherwise • Age = age of worker • Union = 1 if union member, 0 otherwise (a) Explain the structure of this Cox proportional hazards model. What does the baseline hazard represent, and what does the proportional hazards assumption imply? [2] (b) Describe the partial likelihood estimation method for estimating the coefficients here. [4] (c) Calculate the hazard ratio for the following two individuals and interpret the result. Individual A: Age = 40, Training = 1, Union = 0 Individual B: Age = 40, Training = 0, Union = 0 [4][Fill in the blank]
You are given crude age-specific mortality rates for a population ranging from age 0 to age 90. The observed crude mortality curve shows high mortality in infancy, a decline in early childhood, and then a steep rise in older ages. To model this nonlinear pattern, a cubic spline is used to smooth the log mortality curve, with n = 3 knots at ages x1 = 1, x2 = 20, and x3 = 65: (a) Explain what a cubic spline is and why modelling the log of mortality rates with a spline is more appropriate than modelling mortality rates on the original scale. [3] (b) Given the parameter estimates , , , , , , and , calculate the log mortality rates at ages 0, 10, 30, 60, and 80 and plot the log mortality curve. Comment on the shape of the curve.[4] (c) Describe how you would evaluate the quality and appropriateness of the spline model. Include both a graphical method and a statistical test for model adequacy, and explain what signs might indicate overfitting or underfitting. [2] (d) Discuss one real-world scenario in which the cubic spline may perform poorly for a particular country. [1][Fill in the blank]
(a) Derive the conditions under which the standard OLS estimator is unbiased. Clearly state the assumptions and provide a step-by-step derivation. Provide an example of a data situation where the OLS estimator is not appropriate, and explain which assumption is violated and why. [math: [4]] (b) Explain the role of [math: λ] in the Ridge and Lasso objective functions, and describe what happens to the bias and variance of the estimator as [math: λ→0] and as [math: λ→∞]. Discuss how [math: λ] can be selected in practice. [math: [3]] (c)In a simulation study with [math: 10,000] replications, three estimators -- OLS, Ridge, and Lasso -- are used to estimate the same regression coefficient. The figure below displays the resulting histograms of the coefficient estimates from the three methods. The true parameter value is [math: 3]. Using the shape, spread, and location of the three histograms, identify which colour corresponds to each method: OLS, Ridge, and Lasso. Justify your answer. [math: [3]][Fill in the blank]
Question text 2Marks You are given the following variance – covariance matrix on two shares and the market portfolio. Risk free rate is 6% per annum. Expected market return is 14% per annum. You have $500,000 available to invest. Assume that you are forming a portfolio by investing $200,000 in Share A, $200,000 in Share B and the balance of the $500,000 in risk free asset. What is the standard deviation of this portfolio in percentage terms? [Type only the final answer into the response box below (NOT into the Notes box) and in pure numeric format (e.g. 10 or -10). Do NOT use %/$ signs, commas or spaces (e.g. only enter 10 if it is 10 days/$10/10%)] Answer 1[input]Notes Report question issue Question 6 Notes
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