expectation-methods: Extraction of the Expectation, Variance and Covariance of the... In coin: Conditional Inference Procedures in a Permutation Test Framework

Description

Methods for extraction of the expectation, variance and covariance of the linear statistic.

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```## S4 method for signature 'IndependenceLinearStatistic' expectation(object, partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' expectation(object, partial = FALSE, ...) ## S4 method for signature 'Variance' variance(object, ...) ## S4 method for signature 'CovarianceMatrix' variance(object, ...) ## S4 method for signature 'IndependenceLinearStatistic' variance(object, partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' variance(object, partial = FALSE, ...) ## S4 method for signature 'CovarianceMatrix' covariance(object, ...) ## S4 method for signature 'IndependenceLinearStatistic' covariance(object, invert = FALSE, partial = FALSE, ...) ## S4 method for signature 'QuadTypeIndependenceTestStatistic' covariance(object, invert = FALSE, partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' covariance(object, invert = FALSE, partial = FALSE, ...) ```

Arguments

 `object` an object from which the expectation, variance or covariance of the linear statistic can be extracted. `partial` a logical indicating that the partial result for each block should be extracted. Defaults to `FALSE`. `invert` a logical indicating that the Moore-Penrose inverse of the covariance should be extracted. Defaults to `FALSE`. `...` further arguments (currently ignored).

Details

The methods `expectation`, `variance` and `covariance` extract the expectation, variance and covariance, respectively, of the linear statistic.

For tests of conditional independence within blocks, the partial result for each block is obtained by setting `partial = TRUE`.

Value

The expectation, variance or covariance of the linear statistic extracted from `object`. A matrix or array.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36``` ```## Example data dta <- data.frame( y = gl(3, 2), x = sample(gl(3, 2)) ) ## Asymptotic Cochran-Mantel-Haenszel Test ct <- cmh_test(y ~ x, data = dta) ## The linear statistic, i.e., the contingency table... (T <- statistic(ct, type = "linear")) ## ...and its expectation... (mu <- expectation(ct)) ## ...and variance... (sigma <- variance(ct)) ## ...and covariance... (Sigma <- covariance(ct)) ## ...and its inverse (SigmaPlus <- covariance(ct, invert = TRUE)) ## The standardized contingency table... (T - mu) / sqrt(sigma) ## ...is identical to the standardized linear statistic statistic(ct, type = "standardized") ## The quadratic form... U <- as.vector(T - mu) U %*% SigmaPlus %*% U ## ...is identical to the test statistic statistic(ct, type = "test") ```

coin documentation built on Oct. 8, 2021, 9:07 a.m.