代写RAD留学生、代做R, Matlab/C++编程语言、代写R设计

日期：2019-10-16 10:34

Homework #2

Due to Oct 23, 2019

No.1 The air data set contains the measures of ozone (OZ), solar radiation (RAD), temperature (TEMP)

and wind speed (WIND) for 111 consecutive days in a city of the state of New York. The four columns are

OZ, RAD, TEMP and WIND. Consider the nonparametric model

Yi = θ(Xi) + εi,where Y = OZ, X = W IND, εi v N(0, σ2)

1. Fit a linear model and a quadratic model of OZ on WIND and compare the parametric fits with a

nonparametric fit using the kernel method. Comment on your results.

2. Use the R functions ksmooth to estimate θ(t). Try a few bandwidths and a few kernel functions and

examine how the kernel estimator of θ(t) is affected by the bandwidth h and the kernel function K(u).

3. Use the R functions ksmooth, loess.smooth (loess) and supsmu to estimate θ(t) and compare their fits.

Use the loess function to calculate the 95% confidence interval of ˆθ(t).

4. Write a function using your favorite programming language, e.g., R, Matlab or C , to construct a local

linear kernel estimate of θ(t) using the Epanechnikov kernel with bandwidth h = 5. The Epanechnikov

kernel is defined as

K(u) = 3

4(1 − x2)I(|x| < 1)

The Epanechnikov kernel is optimal in the sense that it minimizes the integrated MSE. Estimate the SE

of ˆθ(x; h) and implement it. For simplicity, you can estimate σ

2 using ˆσ2 = n−1 Pn

i=1{Yi − ˆθ(Xi)}.

No.2 Generate data set (xi

, yi), i = 1, · · · , 400, where xi

is a 30 × 1 vector, yi = xi1 − 1.5xi3 + 0.8xi11 + εi.

1. Forget the real relation between xi and yi. Give the OLS estimator basing on data (xi, yi), i = 1, · · · , 400.

2. Using R package glmnet to implement LASSO to get a sparsity estimator. (Simulated the data NS =200)