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STAT 778 Lab

创建日期：2024-04-07 14:48:42

所属分类：计算机computer science

标签： STAT 778

Make utilities

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STAT 778 Lab 4

Make utilities
Go along with the notes at your own pace. Seek help from me or TA at our office hours or
send us an e-mail message if you have any question. All codes referenced in this Lab are in
/usr/local/shared/STAT778/lab4/
1 What is the default RNG in R
Search in Google using the proper key phrase, such as, “What is the default RNG in R,”. Read
at your leisure and summarize it for later use.
2 Velleman’s Experiment and Make Utility
In this section we mimic parts of simulation studies by Johnstone and Velleman (1985, JASA) for the
comparison of three regression estimates of the slope of a simple linear regression, and introduce the make
utility. Most source code and write-ups are modified from Faraway’s. The design for the regression is
Yi = Xi + σi
where xi = i/n and var(i) = 1. The estimators are least squares (LS), least absolute deviations (LAD)
and a Huber-type estimator (Huber) where βˆ is computed by minimizing
∑
ρ(Yi − α− βXi), where ρ(x) =
{
(x/σˆ)2 if |x| < σˆ
|x|/σˆ otherwise
In other words, the Huber-type estimator is a hybrid of the first two estimators and we substitute the “line
resistant estimator” by the Huber estimator in this demonstration. (σˆ is an estimate of the error SD).
Since we want to check the performance of three estimators over a fairly “complete crossing”, there will
be many subroutines in separate files for this simulation experiment. Now copy the relevant code to your
home directory.
mkdir simul — make a new directory
cp /usr/local/shared/STAT778/lab4/* simul - copy the content of “lab4” to your “simul” directory
cd simul; ls — put two Unix commands (separated by “;”) in one line.
The code is written in C but there is nothing special about it and it could just as easily be written in
Fortran or any practical language. First take a look at the file rgenl.c, which uses the system random
number generator drand48() with a period of 248 from an Unix workstation, such as zeus.vse.gmu.edu.
You are advised to use your own RNG or one from “Numerical Recipes” (NR, thereafter) if you don’t trust
a built-in RNG. There are seven different distributions allowed for. The file reg.c has the least squares
code which uses a naive algorithm. huber.c has the Huber-type estimator, computed by iteratively re-
weighted least-squares. The LAD code is in medfit.c, rofunc.c and shell.c. LAD regression is difficult
because the absolute value function is not differentiable at zero. This code is adapted from one in NR.
The main program is in main.c which reads in the input values, sets up the x and y and calls the three
estimating subroutines. Finally, constant.h is a header file which defines the maximum allowable sample
size.
1
The make utility becomes handy1 for a program of this size with many subroutines in separate files.
It keeps track of which files have been changed since the last compile and what commands are used to
compile these files etc. The necessary information on what is going on is recorded in a file, usually called
Makefile. Read Makefile in the directory simul and type
more Makefile
make
to see what happens. make does the first target (here prog) by default while others can be specified, e.g.
make clean
cleans out the files generated by make. Some of source files depend on the file constant.h which specifies
the maximum allowable sample size. These files are main.c, huber.c and rofunc.c. Now if you change
constant.h these three files will be automatically recompiled when you make. This beats searching through
source files for all the necessary dependencies! To demonstrate type
make
Now edit constant.h to change the maximum sample size and type make again. Type man make for more
details on make.
Let’s try running the program. Input is expected in 4 fields, the scale of the added error σ, the sample
size, the choice of error distribution (see rgenl.c for which distribution corresponds to which number)
and the number of replications. Input can be entered at the terminal or from a file. Now try running it
prog 1.0 10 2 40
What error distribution does the choice 2 correspond to? If we want to try Beta(2,2) error distribution,
what’s the input (of third field) should be?
It is often a good idea to first run a program with a small simulation size (i.e. number of replications) to
see if it is working as expected and time it for predicting how long this program will take to run for a large
number of replications, so that potential problems could be fixed before wasting lots of your and computer
time.
Remark: FYI: Sometimes you may need to replace prog by ./prog to activate the executable prog,
depending on how your default path is set up. Here we should not need to in zeus.vse.gmu.edu. Likewise,
all ./prog below can be replaced by prog.
Timing can be done using the time command. Try a sample size of 1000 and say 10 replications and
then
time ./prog 1.0 1000 2 10 > /dev/null
The redirection of the output to /dev/null effectively throws the output away since you are only interested
in timing here. The real time is third field in the output. For more information on time, type man time.
You can now estimate how long a larger number of replications will take. One way of speeding up the
program is to compile it with optimization. Edit the Makefile so that the CFLAGS= -g now reads CFLAGS=
-O and clear out the old object code and executable by make clean and then make again and retime the
code. These options -g and -O work similarly for Fortran code.2
We now want to analyze the output. Right now the estimates for each replication are just printed. We
could write some extra code to compute some summary statistics like means and variances but a more
flexible approach is to read the output data into R/Splus. Change the number of replications to a larger
number and write the data to a file instead of the terminal, say,
./prog 1.0 1000 2 100 > outfile
module add r3 or module add r4
1Even if you do not write a software package using make, it is still worthwhile knowing its basics since many archived
software/freeware packages use it.
2Warning: sometimes -O does funny things and may not speed up the running time or give a correct answer. So, try it out
before running a very large simulation. You can use other tricks/good algorithms learned in the class to speed up the program,
too.
2
R – enter R. You can also use R-studio instead.
where “1.0 1000 2 100” indicates that the simulation size is 100 (you now know how long it will take -
you can increase the simulation size if you wish but don’t overdo it.) We now read the data into R and
compute some summary statistics.
d <-read.table("outfile") — assuming you started R in the directory where “outfile” resides.
apply(d,2,mean) — the column means - an estimate of the expected value which should be 1
apply(d,2,var) — the column variances - which is small, which is large?
sqrt(apply(d,2,var)/length(d[,1])) — se for the means
Since we know the true value of β is 1, MSE is a useful summary of the performance of an estimate
mse <- function(x) sum((x-1)^2)/length(x) — a function that estimates the MSE about 1
apply(d,2,mse) — the column MSE’s - which is smallest?
We can also use summary in R to get summary statistics: Min, 1st Qu, Median, Mean, 3rd Qu and Max.
Since I’d like to know se of the mean and mse as well, I can modify summary by attaching the them to
summary:
mysummary<-function(x){c(summary(x), sqrt(var(x)/length(x)),mse(x))}
mysummary(runif(100)) — see how it works.
apply(d,2,mysummary) — apply it to what we are interested in.
Looking at the output of mse and mysummary, we don’t know if the observed difference is real or is just
simulation sampling error due to having a finite number of replications. We need to estimate the se of
the estimated MSE and/or the output of mysummary. Let’s estimate the se of MSE, say, using a batching
method.
z <- matrix(d[,1] ,ncol=10,byrow=T) — divide LS data into batches of 10.
ms <- apply(z,1,mse) — apply mse to each row
ms — these are independent estimates of the MSE
sqrt(var(ms)/length(ms)) — the estimated se of the mean of MSE for LS - will need same for the
other three
motif() — This step is only needed in Splus or older version of R
par(mfrow=c(3,1)) — if you’d like to see all three histograms together
apply(d, 2 ,hist)
par(mfrow=c(1,1)) — reset to one plot per window
boxplot(d[,1],d[,2],d[,3],names=c("LS","HUBER","LAD")) — side by side boxplots - useful for iden-
tifying outliers and distributional comparison
pairs(d,labels=c("LS","HUBER","LAD")) — a matrix of scatter-plots, notice the correlations between
estimates.
Exercises: Conduct experiments for all possible error distributes provided in rgenl.c, summarize the
results in a nice and clean table and make any sensible comments as you wish.

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 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MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 IE5600 ECOS 3997 EDST2003 FIN 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