ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478356

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478357

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478358

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478359

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The static features of beliefs, namely those structures that relate to one's beliefs at a particular moment, are described. It is argued that expectation (or prevision) should be the fundamental quantification of individual statements of uncertainty and that inner product spaces (or belief structures) should be the fundamental organizing structure for collections of such statements. Objections are given to the usual Bayesian justification of relative frequency-based statistical models via exchangeability. I offer an alternative approach, via exchangeable and co-exchangeable belief structures, and derive the representation theorem, and thus the implied statistical models, for these structures.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478360

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Generalized linear models are regression-type models for data not normally distributed, appropriately fitted by maximum likelihood rather than least squares. Typical examples are models for binomial or Poisson data, with a linear regression model for a given, ordinarily nonlinear, function of the expected values of the observations. Use of such models has become very common in recent years, and there is a clear need to study the issue of appropriate residuals to be used for diagnostic purposes.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478361

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Detection of outliers and other diagnostics based on residuals have gained widespread use in linear regression. Logistic regression has been both blessed and hindered by this development. Certainly logistic regression requires procedures to detect global and local model weaknesses. Thus the wealth of work done in linear regression provides guides and suggestions that may, with care and ingenuity, be applied to logistic regression. Several innovative attempts in this direction have been made by authors such as Tsiatis (1980), Pregibon (1979, 1981), Landwehr, Pregibon, and Shoemaker (1984), and Cook and Weisberg (1982). Unfortunately the similarities that allow such techniques to adapt to logistic regression seem, in addition, to hide many of the differences.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478362

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The techniques of exploratory data analysis include a resistant rule for identifying possible outliers in univariate data. Using the lower and upper fourths,FLandFU(approximate quartiles), it labels as “outside” any observations belowFL− 1.5(FU—FL) or aboveFU+ 1.5(FU—FL). For example, in the ordered sample −5, −2, 0, 1, 8,FL= −2 andFU= 1, so any observation below −6.5 or above 5.5 is outside. Thus the rule labels 8 as outside. Some related rules also use cutoffs of the formFL—k(FU— FL) andFU+k(FU— FL). This approach avoids the need to specify the number of possible outliers in advance; as long as they are not too numerous, any outliers do not affect the location of the cutoffs.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478363

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In this article an investigation is made of the maximum familywise error rate (MFWER) of Fisher's least significant difference (LSD) test for testing the equality ofkpopulation means in a one-way layout. An exact expression for the MFWER is derived (see Theorem 1) for all balanced models and for an unbalanced model withk= 3 populations (Type I models). A close upper bound for the MFWER is derived for all unbalanced models with four or more populations (Type II models). These expressions are used to illustrate that the MFWER may greatly exceed the nominal size α of the LSD test. In addition, a simple modification of the LSD test is proposed to control the MFWER. This modified procedure has MFWER equal to the nominal level α for Type I models and no greater than α for Type II models (Theorem 2) and is, therefore, recommended as an improvement over the LSD test. The key to the analysis is two theorems concerning the ranges of independent normal random variables, which are contained in the Appendix. The first of these theorems (Theorem A.1) is concerned with the conservative nature of unbalanced models as compared with balanced models and was published in Hayter (1984), although in a different context. The second theorem (Theorem A.2) presents a new chain of inequalities concerning the ranges of independent normal random variables partitioned into groups of differing sizes. It is believed that this new latter theorem may be of independent interest.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478364

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Although all of these statistics are asymptotically χ2in the usual situation ofKfixed andN→ ∞, this is not the case if the multinomial is sparse; specifically, Morris (1975) showed that, under certain regularity conditions withKandN→ ∞, bothX2andG2are asymptotically normal (with different mean and variance) under a simple null hypothesis. Cressie and Read (1984) extended these results to the general 2NIλfamily. Although these results have not been proven for composite nulls, it is certainly reasonable to expect that they continue to hold. Clearly, testing would require an estimate of the variance of the statistic that is valid under composite hypotheses in the sparse situation.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478365

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor