knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width=7 )
library(EstimDiagnostics) library(doParallel) library(ggplot2) registerDoSEQ() s<-c(1e1,1e2,1e3) Nmc=6e2
The main function is Estim_diagnost
which takes the simulation and estimation procedure Inference
with a sample size as an argument. Inference
can return a named vector, a list or a data frame. Estim_diagnost
returns a data frame.
Inference<-function(s){ rrr<-rnorm(n=s) list(Mn=mean(rrr), Var=var(rrr)) } experiment <- Estim_diagnost(Nmc, s=s, Inference) head(experiment)
This data frame consists of columns with estimates (Mn
and Var
in this case) and a sample size s
at which estimates were evaluated.
There are two plot functions that can visualize the results of the simulation study- estims_qqplot
and estims_boxplot
. The following line plots both estimators from experiment against standard normal distribution. It is known that empirical variance in this case is distributed according to chi-square law. As expected, we see that the distribution of variance converges to a Gaussian law but at small sample sizes notably differs from it.
estims_qqplot(experiment) estims_boxplot(experiment)
Each plot has argument sep
allowing to switch between plotting different estimators together or separately. If sep=TRUE
then the functions return a list of ggplot objects that can be treated and then plotted independently. Here for each plot we set custom distributions qq-plots will be based on:
library(gridExtra) dist1 <- function(p) stats::qchisq(p, df=1e1) p1<-estims_qqplot(experiment[experiment$s==1e1,], sep=TRUE, distribution = dist1) dist2 <- function(p) stats::qchisq(p, df=1e2) p2<-estims_qqplot(experiment[experiment$s==1e2,], sep=TRUE, distribution = dist2) dist3 <- function(p) stats::qchisq(p, df=1e3) p3<-estims_qqplot(experiment[experiment$s==1e3,], sep=TRUE, distribution = dist3) grid.arrange(arrangeGrob(p1[[2]], p2[[2]], p3[[2]], ncol=2))
Once it is shown by means of exploratory analysis that the estimators of interest follow some theoretical distribution, it is desirable to write unit tests for them. This package provides the following expect_
type functions as an extension of testthat package:
expect_distfit
expect_gaussian
expect_mean_equal
In order to test correctness of the mu estimator, expect_mean_equal
is called. It uses t-test to test the hypothesis that the empirical mean is different from a chosen value.
s <- 1e1 set.seed(1) experiment <- Estim_diagnost(Nmc, s=s, Inference) sam_m <- experiment[,1] expect_mean_equal(x=sam_m, mu=0)
For variance estimator we make a unit test based on the fact that the empirical variance follows a chi-square distribution. Tests for matching empirical distributions to parametric ones are implemented in expect_distfit
function.
sam_v <- experiment[,2]*10 expect_distfit(sample = sam_v, nulldist=pchisq, df=10)
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