OptSig.Weight {OptSig}

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

Details

See Kim and Choi (2020)

Value

alpha.opt

Optimal level of significance

crit.opt

Critical value at the optimal level

Note

The figure shows the folded-normal distribution

Author(s)

Jae H. Kim

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

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)