exactcdf

exactcdf finds exact p-values

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Syntax

Description

Function for finding the exact cdf of each element in the vector x with respect to the empirical distribution, represented by the vector empdist, i.e. the generic element i of the output vector p is the result of: \[ \frac{ \displaystyle \sum_{j=1}^K I_{empdist(j) \leq x_i}}{K} \] where $I$ is the indicator function and $K$ is the length of vector $empdist$

example

p =exactcdf(x) exactcdf with just one input argument.

example

p =exactcdf(x, empdist) exactcdf with two input arguments.

Examples

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  • exactcdf with just one input argument.

    • k=1000;
x=randn(k,1);
p=exactcdf(x);

  • exactcdf with two input arguments.

    • k=10;
x=randn(k,1);
K=100000;
empdist=randn(K,1);
% Compute empirical cdf for each element of vector x.
p=exactcdf(x,empdist);
% Compute theoretical cdf based on normcdf
pTheo=normcdf(x);
% Compare empirical cdf with theoretical cdf 
plot(p,pTheo,'o')
xlabel('Empirical cdf')
ylabel('Theoretical cdf')
    Click here for the graphical output of this example (link to Ro.S.A. website).

    Related Examples

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  • Using exactcdf for calculating exact p-values.

    • k=10;
x=randn(k,1);
K=100000;
empdist=randn(K,1);
% Compute empirical cdf for each of element of vector x.
p=exactcdf(x,empdist);
% Compute exact p-values for an unilateral right-tailed test
pval_rt=1-p;
% Compute exact p-values for an unilateral left-tailed test
pval_lt=p;

    Input Arguments

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    x — empirical replicates of a test. Vector.

    Vetor of length k containing the empirical realization of a generic test

    Data Types: double

    Optional Arguments

    empdist — empirical distribution of the same test. Vector.

    Vector of length $K$ generally with $K \geq k$ containig the empirical simulated distribution of the test. If this optional argument is not supplied the empirical distribution is taken from input vector x.

    Example: randn(K,1)

    Data Types: double

    Output Arguments

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    p —empirical cdf. Vector

    Vector with the same length of input vector x containing the empirical cdf of each element of input vector x. More precisely: $p(i)$ is computed as \[ \frac{ \displaystyle \sum_{j=1}^K I_{empdist(j) \leq x_i}}{K} \]

    References

    Athey, S., Eckles, D., & Imbens, G. W. (2018). Exact p-values for network interference, "Journal of the American Statistical Association", Vol. 113, pp. 230-240.

    See Also

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