Counterexamples in Probability And StatisticsThis volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included. |
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Índice
is not almost surely equal to X | 134 |
CHAPTER SEVEN | 154 |
Construction of Estimators | 175 |
CHAPTER NINE | 190 |
variance unbiased estimator differ and both are inadmissible | 211 |
Hypothesis Testing | 232 |
large values | 243 |
Additional Counterexamples | 267 |
| 11 | |
| 12 | |
| 13 | |
| 14 | |
| 17 | |
| 23 | |
| 31 | |
| 38 | |
| 53 | |
| 70 | |
CHAPTER FIVE | 83 |
Gaussian | 119 |
Conditional Expectation Martingales and Almost Sure Convergence | 126 |
Sequences of random variables | 269 |
Stochastic processes and martingales | 270 |
Estimation | 271 |
Sufficiency | 272 |
Likelihood procedures | 273 |
Admissibility | 274 |
Hypothesis testing | 275 |
Confidence intervals | 276 |
Miscellaneous | 277 |
References | 278 |
Index | 287 |
Outras edições - Ver tudo
Counterexamples in probability and statistics Joseph P. Romano,Andrew F. Siegel Visualização de excertos - 1986 |
Palavras e frases frequentes
a-field alternative asymptotically called characteristic function complete conditional Consider consistent constant construct continuous converge almost surely converges converges in distribution counterexample defined density function depend discrete distribution with mean equal equivalent example exist expectation exponential fact finite fixed follows Gaussian distribution given gives Hence hold hypothesis identically distributed implies independent and identically independent random variables infinite integrable interval invariant Lehmann likelihood ratio limit loss martingale maximum likelihood estimator measure method minimum variance unbiased moments Note observe otherwise parameter positive possible powerful test probability problem rejects respect result risk sample sample mean satisfies sequence shown simple squared error standard Gaussian statistic subset sufficient statistic Suppose surely symmetric takes tends Theorem uniform uniformly minimum variance uniformly most powerful unique values variance unbiased estimator zero
Passagens conhecidas
Página 279 - Inadmissibility of the Usual Estimators of Scale Parameters in Problems with Unknown Location and Scale Parameters . . LAWRENCE D.
Página 278 - BARANCHIK, AJ (1973) : Inadmissibility of maximum likelihood estimators in some multiple regression problems with three or more independent variables, Ann.
Página 273 - Bayesian analysis that assumes a small prior probability for the null hypothesis and a diffuse distribution over the alternative hypotheses (Lindley, 1957; Cox and Hinkley, 1974).
Página 81 - Although we advocate the use of regression models, it is important to realize that the estimated regression line of Y on X is not the same as that for X on Y.
Página xvii - Here, standardization was achieved through a change of random variables by subtracting the mean and dividing by the standard deviation of the original random variable.
Página 279 - McGill. 1983. A color-caused optical illusion on a statistical graph.
Página viii - University as the senior thesis of the first author under the supervision of the second author.
Página 19 - Define an equivalence relation so that x and y are equivalent if and only if there exists a rational number r such that (x + r\ = y.
Página 65 - X and Y are independent if, and only if, they are uncorrelated, ie, p = 0.
Referências a este livro
Informação bibliográfica
| Título | Counterexamples in Probability And Statistics Wadsworth and Brooks/Cole Statistics/Probability Series |
| Autores | Joseph P. Romano, A.F. Siegel |
| Edição | revista |
| Editora | CRC Press, 1986 |
| ISBN | 0412989018, 9780412989018 |
| Número de páginas | 328 páginas |
| Exportar citação | BiBTeX EndNote RefMan |