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Gaussian linear models are often insufficient in practical applications, where noise can be heavy- tailed. In this problem, we consider a linear model of the form yi = a · xi + b + ei. The (ei) are independent noise from a distribution that depends on x as well as on global parameters; however, the noise distribution has conditional mean zero given x. The goal is to derive a good estimator for the parameters a and b based on a sample of observed (x, y) pairs. 1.1 Instructions: 1. Load the data, which is provided as (x, y) pairs in CSV format. Each file contains a data set generated with different values of a and b. The noise distribution, conditional on x, is the same for all data sets. 2. Formulate a model for the data-generating process. 3. Based on your model, formulate a loss function for all parameters: a, b, and any additional parameters needed for your model. 4. Solve a suitable optimization problem, corresponding to your chosen loss function, to obtain point estimates for the model parameters. 5. Formulate and carry out an assessment of the quality of your parameter estimates. 6. Try additional models if necessary, repeating steps 2 − 5.
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Member of the Research Staff

Interviewed at Voleon

4.5★
Apr 28, 2017

Gaussian linear models are often insufficient in practical applications, where noise can be heavy- tailed. In this problem, we consider a linear model of the form yi = a · xi + b + ei. The (ei) are independent noise from a distribution that depends on x as well as on global parameters; however, the noise distribution has conditional mean zero given x. The goal is to derive a good estimator for the parameters a and b based on a sample of observed (x, y) pairs. 1.1 Instructions: 1. Load the data, which is provided as (x, y) pairs in CSV format. Each file contains a data set generated with different values of a and b. The noise distribution, conditional on x, is the same for all data sets. 2. Formulate a model for the data-generating process. 3. Based on your model, formulate a loss function for all parameters: a, b, and any additional parameters needed for your model. 4. Solve a suitable optimization problem, corresponding to your chosen loss function, to obtain point estimates for the model parameters. 5. Formulate and carry out an assessment of the quality of your parameter estimates. 6. Try additional models if necessary, repeating steps 2 − 5.

You need to forecast the number that will be drawn from a continues uniform distribution between and 60. You will be charged 3 dollars for every unit overestimated and 1 dollar for every unit underestimated. No charge if the number is forecasted correctly. What number to forecast to minimize the cost?
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Research Analyst

Interviewed at WorldQuant

4.2★
Apr 2, 2018

You need to forecast the number that will be drawn from a continues uniform distribution between and 60. You will be charged 3 dollars for every unit overestimated and 1 dollar for every unit underestimated. No charge if the number is forecasted correctly. What number to forecast to minimize the cost?

I own a property and what to have it surveyed for resources. 10% chance oil will be found, in which case the property is worth $1 million 30% chance Coal will be found, in which case the property is worth $500 thousand and if no resources are found, property can be sold for $200,000, What is the value of this property?
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Equity Research Associate

Interviewed at Susquehanna International Group

3.8★
Sep 30, 2021

I own a property and what to have it surveyed for resources. 10% chance oil will be found, in which case the property is worth $1 million 30% chance Coal will be found, in which case the property is worth $500 thousand and if no resources are found, property can be sold for $200,000, What is the value of this property?

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