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Introduction to Statistics through Resampling Methods and R/S-Plus®: Good/Introduction
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Its foundation is good, but it feels a little outdated; thus, its added value is questionable.
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For those who want to save their money, I suggest another book , by the same author, as an interesting alternative. That book shows a significant overlap to say the least with the book reviewed. There are also other alternatives by the same author [2,3]. Resampling methods: a practical guide to data analysis. Introduction to statistics through resampling methods and Microsoft Office Excel. Computing reviews , CR In: Computing reviews.
In: Computing reviews , If we repeat the process of randomly splitting the sample set into two parts, we will get a somewhat different estimate for the test MSE each time. I illustrate below, which displays ten different validation set MSE curves from the auto data set, produced using ten different random splits of the observations into training and validation sets. All ten curves indicate that the model with a quadratic term has a dramatically smaller validation set MSE than the model with only a linear term. Furthermore, all ten curves indicate that there is not much benefit in including cubic or higher-order polynomial terms in the model.
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But it is worth noting that each of the ten curves results in a different test MSE estimate for each of the ten regression models considered. And there is no consensus among the curves as to which model results in the smallest validation set MSE.
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A second concern with the validation approach, only a subset of the observations, those that are included in the training set rather than in the validation set, are used to fit the model. Since statistical methods tend to perform worse when trained on fewer observations, this suggests that the validation set error rate may tend to overestimate the test error rate for the model fit on the entire data set. Leave-one-out cross-validation LOOCV is closely related to the validation set approach as it involves splitting the set of observations into two parts.
However, instead of creating two subsets of comparable size i. The statistical learning method is fit on the training observations, and a prediction is made for the excluded observation. Since the validation observation was not used in the fitting process, the estimate error provides an approximately unbiased estimate for the test error. But even though is unbiased for the test error, it is a poor estimate because it is highly variable, since it is based upon a single observation. However, we can repeat the procedure by selecting a different row for the validation data, training the statistical learning procedure on the other observations and computing.
We can repeate this approach n times, where each time we holdout a different, single observation to validate on. This produces a total of n squared errors,. To perform this procedure in R we first need to understand an important nuance. But if we use glm to fit a model without passing in the family argument, then it performs linear regression, just like the lm function. So, for instance:. Why is this important? You can bootstrap a single statistic e.
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The result we primarily care about is the cross-validation estimate of test error Eq. Our cross-validation estimate for the test error is approximately This estimate is a far less biased estimate of the test error compared to our single test MSE produced by a training - testing validation approach.
We can repeat this procedure to estimate an ubiased MSE across multiple model fits. For example, to assess multiple polynomial fits as we did above to identify the one that represents the best fit we can integrate this procedure into a function. Our results illustrate a sharp drop in the estimated test MSE between the linear and quadratic fits, but then no clear improvement from using higher-order polynomials. Thus, our unbiased MSEs suggest that using a 2nd polynomial quadratic fit is likely the optimal model balancing interpretation and low test errors. For example we could use it with logistic regression or linear discriminant analysis.
Introduction to Statistics Through Resampling Methods and R, 2nd Edition by Phillip I. Good
For example, if we wanted to perform this approach on the ggplotdiamonds data set for a linear regression model, which contains 53, observations, the computation time is nearly 30 minutes! This resampling method involves randomly dividing the data into k groups aka folds of approximately equal size. The first fold is treated as a validation set, and the statistical method is fit on the remaining data.
The mean squared error, , is then computed on the observations in the held-out fold.
This procedure is repeated k times; each time, a different group of observations is treated as the validation set.
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