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A New Distribution-Free Approach to Constructing the Confidence Region for Multiple Parameters

Figure 1

The confidence region constructed for an arbitrary reference line.

The simulated population is an equal-proportional mixture of the observations sampled from two bivariate normal distributions which are given by and , respectively. The two parallel dashed lines are the boundaries of the confidence region for the reference line with angle . The black and gray open circles are points outside and within the boundaries, respectively. The histogram shows the distribution of the distances with respect to the reference line and the heights of the bars are the observed frequencies multiplied by 5.

Figure 1

doi: https://doi.org/10.1371/journal.pone.0081179.g001