LATEX留学生讲解、辅导Simulation Report 、辅导R设计

Assignment 2—Simulation Report Semester 2, 2018–2019

[Deadline: 13 February (5PM)]

Write a 3 page simulation report with the goal of comparing the performance of the kernel density

estimator with that of another density estimator. It is recommended (but not compulsory) that

you typeset your report in LATEX.

Kernel density estimation

Let X1, . . . , Xn

iid～ f. The kernel estimator of f is defined as

fb(x) = 1,

where Kh(·) = K(·)/h, K is a density (kernel), and h > 0 is a

parameter controlling smoothness of the estimate (bandwidth).

The estimator is readily available from R, using density.

Consider dividing your report into two sections:

1 Data Generating Processes and Preliminary Experiments

Identify the goal of the experiment and what competitors of the kernel density estimator

you will be comparing against. The histogram is a natural option, but with some extra research

you could find other natural competitors. Remember to include on the bibliography

references to methods that you have used.1

Describe formally what are the simulation scenarios (or data generating processes) from

which you will be simulating data [say, Scenario 1: f1(x) = φ(x); Scenario 2: f2(x) = ... ].

Run a one-shot experiment and illustrate in a figure the methods being compared, against

the true densities [say, f1(x), f2(x), and f3(x)]. Interpret the figure. Are the methods

recovering ‘well’ the true curves? If yes, comment on that. To keep the inquiry simple, you

can use R default option for the bandwidth parameter. Yet other options exist (e.g. crossvalidation).

Remember to add references on any methods that you have used.

Anticipate strengths and weaknesses with the methods, but keeping in mind the disclaimer

that this is a one-shot experiment.

2 Monte Carlo Simulation Study

Explain in a coherent way what experiment you will be conducting now.

Conduct the Monte Carlo simulation study for the sample sizes n = 250, 500, and 1000.

1While a clear and organized comparison with several methods would be the most interesting one, for the

purposes of this report a clear comparison against a single method (say, histogram) will be more appreciated than

an unclear one with several methods.

? For each fixed sample size, report in a figure the ISE (Integrated Squared Error), underlying

each simulated data set ISE = R

{fb(x) f(x)}2 dx.

What happens when you increase n?