| Large Sample Techniques for Statistics Contributor(s): Jiang, Jiming (Author) |
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ISBN: 1441968261 ISBN-13: 9781441968265 Publisher: Springer OUR PRICE: $142.49 Product Type: Hardcover - Other Formats Published: July 2010 * Not available - Not in print at this time * |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General |
| Dewey: 519.5 |
| LCCN: 2010930134 |
| Series: Springer Texts in Statistics |
| Physical Information: 1.31" H x 6.14" W x 9.21" (2.31 lbs) 628 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution, alsoknownasthe normaldistri- tion, is merelyonesuchexample, dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 "standard" situation, the asymptotic null distribution of the LRT is?, with the degreesoffreedomequaltothe di?erencebetweenthedimensions, de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson's? -test-the asymptotic distri- 2 2 bution of Pearson's? -test is not always? (e.g., Moore 1978). |