Jackknife Inference

In statistical analysis, the researcher is usually interested in obtaining not only a point estimate of a statistic but also an estimate of the variation in this point estimate and a confidence interval for the true value of the parameter. For example, a researcher may calculate not only a sample mean but also the standard error of the mean and a confidence interval for the mean.

The traditional methods for calculating standard errors and confidence intervals generally rely upon a statistic, or some known transformation of it, being asymptotically normally distributed. If this normality assumption does not hold, the traditional methods may be inaccurate.

Resampling techniques, such as the bootstrap and jackknife, provide estimates of the standard error, confidence intervals, and distributions for any statistic. To use these procedures, the user must supply the name of the data set under examination and an S-PLUS function or expression that calculates the statistic of interest.

The Jackknife Inference dialog performs jackknife inference for a specified statistic and data set. See the Guide to Statistics for details.

To perform jackknife inference

Choose Statistics __image\arrow5.gif Resample __image\arrow5.gif Jackknife. The dialog shown below appears.

Model page

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In the Jackknife Inference dialog, the Model page has the following options:

Data

Data Set

Specify the data to bootstrap or jackknife. This may be a vector, matrix, or data set.

Statistic to Estimate

Expression

This field applies to Bootstrap and Jackknife inference. In the Expression field, specify the expression describing the statistic to be bootstrapped or jackknifed. It may be a function that accepts data as the first argument and returns a vector or matrix, or a call referring to the data that evaluates to a vector or matrix.

For example, to bootstrap or jackknife the regression coefficients for regressing Mileage on Weight in the fuel.frame data, use the expression coef(lm(Mileage~Weight, fuel.frame)) and specify fuel.frame as the Data Set. To bootstrap or jackknife the mean of Mileage, use the expression mean(Mileage).

Save Model Object

Save Model Object

In the Save As field, enter the name for the object in which to save the results of the analysis. If an object with this name already exists, its contents are overwritten. The model object can be used in later functions such as plotting.

Options page

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In the Jackknife Inference dialog, the Options page has the following options:

Resampling Options

Assign Resampled Data to Frame 1

Select this to assign the resampled data to frame 1 as each sample is generated. See the language help for bootstrap or jackknife for details.

Results page

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In the Jackknife Inference dialog, the Results page has the following options:

Printed Results

Summary Statistics

Select this to print basic summaries such as the bootstrap or jackknife estimates of bias, mean, and standard error.

Empirical Percentiles

Select this to print empirical percentiles for the statistic under consideration.

Correlation Matrix of Estimates

Select this to print the correlation matrix for the estimates. Note that this is only relevant if the statistic under consideration is a vector, such as a vector of regression coefficients.

Percentile Options

Percentile Levels

Specify a vector of percentile levels at which to evaluate the empirical or BCa percentiles.

Plot page

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In the Jackknife Inference dialog, the Plot page has the following options:

Plots

Distribution of Replicates

Select this to plot the distribution of the replicates for each statistic of interest.

Normal Quantile-Quantile

Select this to plot a normal quantile-quantile plot for each statistic of interest.

Related programming language functions

jackknife