Which of the following statements is TRUE. Group of answer choices Neither parametric nor non-parametric bootstrapping will give us a more reliable point estimate of the statistic of interest. The parametric bootstrap gives a more relaible sampling distribution when the model assumptions are violated. For the non-parametric bootstrap we expect approximately 50% of the observations are not included in any given bootstrap sample. The non-parametric bootstrap is useful in situations where the observations are not independent. The non-parametric bootstrap takes samples from the set of observations without replacement.
Question
Which of the following statements is TRUE. Group of answer choices
Neither parametric nor non-parametric bootstrapping will give us a more reliable point estimate of the statistic of interest.
The parametric bootstrap gives a more relaible sampling distribution when the model assumptions are violated.
For the non-parametric bootstrap we expect approximately 50% of the observations are not included in any given bootstrap sample.
The non-parametric bootstrap is useful in situations where the observations are not independent.
The non-parametric bootstrap takes samples from the set of observations without replacement.
Solution
The statement that is TRUE is: "For the non-parametric bootstrap we expect approximately 50% of the observations are not included in any given bootstrap sample."
Here's why:
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The first statement is FALSE because both parametric and non-parametric bootstrapping can provide reliable point estimates, depending on the situation.
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The second statement is FALSE because the parametric bootstrap is more reliable when the model assumptions are met, not violated.
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The third statement is TRUE. In non-parametric bootstrapping, each observation has an equal chance of being included in the bootstrap sample. Because of this, some observations may be included multiple times, while others may not be included at all. On average, about 63.2% of the original observations are included in the bootstrap sample, leaving about 36.8% of the observations out. So, it's not exactly 50%, but it's close.
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The fourth statement is FALSE because the non-parametric bootstrap assumes that the observations are independent and identically distributed (i.i.d). If the observations are not independent, the bootstrap sample may not be a good representation of the population.
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The fifth statement is FALSE because the non-parametric bootstrap samples with replacement, not without. This means that an observation can be included in the bootstrap sample more than once.
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