Wald statistic

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Description

Compute the Wald statistic for a given value of the stress-strength R = P(Y<X), that is the parameter of interest, under given parametric model assumptions.

Usage

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wald(ydat, xdat, psi, distr = "exp")

Arguments

ydat

data vector of the sample measurements from Y.

xdat

data vector of the sample measurements from X.

psi

scalar for the parameter of interest. It is the value of the quantity R, treated as a parameter under the parametric model construction.

distr

character string specifying the type of distribution assumed for Y and X. Possible choices for distr are "exp" (default) for the one-parameter exponential, "norm_EV" and "norm_DV" for the Gaussian distribution with, respectively, equal or unequal variances assumed for the two random variables.

Details

The two independent random variables Y and X with given distribution distr are measurements from two different populations. For the relationship of the parameter of interest (R) and nuisance parameters with the original parameters of distr, look at the details in loglik.

Value

Wald

Value of the Wald statistic for a given psi

Jphat

Observed profile Fisher information

Note

Values of the Wald statistic can be also used for testing statistical hypotheses on the probability R.

Author(s)

Giuliana Cortese

References

Cortese G., Ventura L. (2013). Accurate higher-order likelihood inference on P(Y<X). Computational Statistics, 28:1035-1059.

Brazzale AR., Davison AC., Reid N. (2007). Applied Asymptotics. Case-Studies in Small Sample Statistics. Cambridge University Press, Cambridge.

See Also

rp, rpstar, MLEs, Prob

Examples

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	# data from the first population
	Y <- rnorm(15, mean=5, sd=1) 
	# data from the second population       
	X <- rnorm(10, mean=7, sd=1.5) 
	# value of Wald for \code{psi=0.9}     
	wald(Y, X, 0.9,"norm_DV")