OptSig (version 2.1)

OptSig.Weight: Weighted Optimal Significance Level for the F-test based on the assumption of normality in the error term

Description

The function calculates the weighted optimal level of significance for the F-test

The weights are obtained from a folded-normal distribution with mean m and staradrd deviation delta

Usage

OptSig.Weight(df1, df2, m, delta = 2, p = 0.5, k = 1, Figure = TRUE)

Arguments

df1

the first degrees of freedom for the F-distribution

df2

the second degrees of freedom for the F-distribution

m

a value of of the non-centality paramter, the mean of the folded-normal distribution

delta

standard deviation of the folded-normal distribution

p

prior probability for H0, default is p = 0.5

k

relative loss from Type I and II errors, k = L2/L1, default is k = 1

Figure

show graph if TRUE (default); No graph if FALSE

Value

alpha.opt

Optimal level of significance

crit.opt

Critical value at the optimal level

Details

See Kim and Choi (2020)

References

Kim and Choi, 2020, Choosing the Level of Significance: A Decision-theoretic Approach, Abacus, Wiley. <https://doi.org/10.1111/abac.12172>

See Also

Leamer, E. 1978, Specification Searches: Ad Hoc Inference with Nonexperimental Data, Wiley, New York.

Kim, JH and Ji, P. 2015, Significance Testing in Empirical Finance: A Critical Review and Assessment, Journal of Empirical Finance 34, 1-14. <DOI:http://dx.doi.org/10.1016/j.jempfin.2015.08.006>

Kim, Jae H., 2020, Decision-theoretic hypothesis testing: A primer with R package OptSig, The American Statistician. <https://doi.org/10.1080/00031305.2020.1750484.>

Examples

# NOT RUN {
data(data1)
# Define Y and X
y=data1$lnoutput; x=cbind(data1$lncapital,data1$lnlabor)
# Restriction matrices to test for constant returns to scale
Rmat=matrix(c(0,1,1),nrow=1); rvec=matrix(0.94,nrow=1)
# Model Estimation and F-test
M=R.OLS(y,x,Rmat,rvec) 

# Degrees of Freedom and estimate of non-centrality parameter 
K=ncol(x)+1; T=length(y)
df1=nrow(Rmat);df2=T-K; NCP=M$ncp

OptSig.Weight(df1,df2,m=NCP,delta=3,p=0.5,k=1,Figure=TRUE)
# }