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Emil Spjotvoll

Bio: Emil Spjotvoll is an academic researcher. The author has contributed to research in topics: Robust measures of scale & Mean squared error. The author has an hindex of 5, co-authored 5 publications receiving 203 citations.

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TL;DR: In this paper, the optimality criteria formulated in terms of the power functions of individual tests are given for problems where several hypotheses are tested simultaneously, subject to the constraint that the expected number of false rejections is less than a given constant gamma when all null hypotheses are true.
Abstract: : Optimality criteria formulated in terms of the power functions of the individual tests are given for problems where several hypotheses are tested simultaneously. Subject to the constraint that the expected number of false rejections is less than a given constant gamma when all null hypotheses are true, tests are found which maximize the minimum average power and the minimum power of the individual tests over certain alternatives. In the common situations in the analysis of variance this leads to application of multiple t-tests. Recommendations for choosing the value of gamma are given by relating gamma to the probability of no false rejections if all hypotheses are true. Based upon the optimality of the tests, a similar optimality property of joint confidence sets is also derived. (Author)

96 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of testing the hypothesis of the one-way classification of variance with variance components, where the test statistic is distributed like a ratio of linear combinations of independent chi-square distributed random variables is treated.
Abstract: In this paper the problem of testing the hypothesis $\Delta \leqq \Delta_0$ against $\Delta > \Delta_0$, where $\Delta$ is the ratio of variances in the one-way classification of the analysis of variance with variance components, is treated. The model is not restricted to equal class frequencies. It is found that the most powerful invariant test against an alternative $\Delta_1$ depends upon $\Delta_1$, but has the property of maximising the minimum power over the set of alternatives with $\Delta \geqq \Delta_1$. The test statistic is distributed like a ratio of linear combinations of independent chi-square distributed random variables. It is shown that a statistic used by Wald [6] to derive a confidence interval for $\Delta$ gives a test that is almost equal to the most powerful invariant tests against large alternatives $\Delta_1$. For the case $\Delta_0 = 0$ it is equal to the usual test in the fixed-effects model. In the balanced case the test reduces to the usual $F$-test which Herbach [2] has proved to be both uniformly most powerful invariant and uniformly most powerful unbiased.

37 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of testing the value of one parameter when the values of other parameters (nuisance parameters) are not specified, and established some results for testing hypotheses when the probability density of the observations does not constitute an exponential family under both the hypothesis and the alternative.
Abstract: We shall be concerned with the parametric problem of testing hypotheses concerning the value of one parameter when the values of other parameters (nuisance parameters) are not specified. Neyman [6] derived under certain conditions a locally most powerful two-sided test for this problem, i.e., he gave the form of the test maximizing the second derivative of the power function with respect to the parameter of interest at the point specified by the hypothesis. Generalizations of Neyman's results were given by Scheffe [7] and Lehmann [2], using the same technique as Neyman. They were also able to prove that the tests were UMP unbiased. A new technique for dealing with these problems was introduced by Sverdrup [9] and Lehmann and Scheffe [4] where the completeness of the sufficient statistics in an exponential family of densities is used to derive UMP unbiased tests. It is stated by Lehmann and Scheffe [4] that the conditions imposed earlier imply an exponential family of densities. When no UMP unbiased test exists we have little general theory. The problem is both one of principle and of technique. Most stringest tests exist under general conditions but are difficult to derive in particular cases. Lehmann [3] proposed maximin tests. Spjotvoll [8] has given an example of the form of a maximin test when no UMP unbiased and invariant test exists. This paper is an attempt to establish some results for testing hypotheses when the probability density of the observations does not constitute an exponential family under both the hypothesis and the alternative. The assumptions made in Section 2 are satisfied if we have an exponential family under the hypothesis, but do not say anything about the form of the density under the alternative. The results concern most powerful similar or unbiased tests, and under certain conditions the form of these tests for the particular family of densities studied, is given in Section 3. In Section 4 the theory in Section 3 is applied to the problem of testing serial correlation (not circular) in a first order autoregressive sequence. It is found that the usual tests are nearly UMP invariant. In Section 5 the problem of testing the value of the ratio of variances in the one-way classification variance components model is considered. Some numerical results are given for the power functions of the maximin test, the locally most powerful test and the standard $F$-test. The results indicate that the standard $F$-test performs well compared with the other tests.

15 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, a different approach to problems of multiple significance testing is presented, which calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate, which is equivalent to the FWER when all hypotheses are true but is smaller otherwise.
Abstract: SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.

83,420 citations

Journal ArticleDOI
Colin L. Mallows1
TL;DR: In this article, the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects is studied, and a particular configuration that is very commonly seen can arise in a simple way.
Abstract: I study the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects. I show that a particular configuration that is very commonly seen can arise in a simple way. I give a formula by means of which the risk incurred by the “minimum CP ” rule can be estimated.

2,400 citations

Journal ArticleDOI
TL;DR: In this paper, the first-order Bonferroni inequality and Simes equality were used to control the false discovery rate in a test procedure, and the results showed strong robustness and robustness.
Abstract: INTRODUCTION ..................................................................................................................... 561 ORGANIZING CO CEPTS ..................................................................................................... 564 Primary Hypotheses, Closure, Hierarchical Sets, and Minimal Hypotheses ...................... 564 Families ................................................................................................................................ 565 Type 1 Error Control ............................................................................................................ 566 Power ................................................................................................................................... 567 P-Values and Adjusted P-Values ......................................................................................... 568 Closed Test Procedures ....................................................................................................... 569 METHODS BA ED ON ORDERED P-VALUES ................................................................... 569 Methods Based on the First-Order Bonferroni Inequality .................................................. 569 Methods Based on the Simes Equality ................................................................................. 570 Modifications for Logically Related Hypotheses ................................................................. 571 Methods Controlling the False Discovery Rate ................................................................... 572 COMPARING NORMALLY DISTRIBUTED M ANS ......................................................... 573 OTHER ISSUES ........................................................................................................................ 575 Tests vs Confidence I tervals ............................................................................................... 575 Directional vs Nondirectional Inference ............................................................................. 576 Robustness ............................................................................................................................ 577 Others ........................................................................ ....................................................... 578 CONCLUSION .......................................................................................................................... 580

1,884 citations

Journal ArticleDOI
Colin L. Mallows1
TL;DR: In this paper, the interpretation of C p -plots and how they can be calibrated in several ways are discussed, including using the display as a basis for formal selection of a subset-regression model and extending the range of application of the device to encompass arbitrary linear estimates of the regression coefficients.
Abstract: We discuss the interpretation of C p -plots and show how they can be calibrated in several ways. We comment on the practice of using the display as a basis for formal selection of a subset-regression model, and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients, for example Ridge estimates.

1,219 citations

Journal ArticleDOI
TL;DR: In this paper, a method of determining whether all the parameters meet their respective standards is proposed, which consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test.
Abstract: The quality of a product might be determined by several parameters, each of which must meet certain standards before the product is acceptable. In this article, a method of determining whether all the parameters meet their respective standards is proposed. The method consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test. This simple method has some optimal properties including attaining exactly a prespecified consumer's risk and uniformly minimizing the producer's risk. These results are obtained from more general hypothesis-testing results concerning null hypotheses consisting of the unions of sets.

345 citations