Dário Ferreira

F-tests with a rare pathology

ANOVA is routinely used to compare pathologies. Nevertheless, in many situations, the sample dimensions may not be known when planning the study. This is specially relevant when one of the pathologies is rare. Thus, the sample size for that pathology or for all pathologies must be considered as random. Sample selection for the non-rare pathologies may be carried out to increase the balance of the model. This leads to F-tests with random non-centrality parameters and random degrees of freedom for the errors. The distribution of such tests statistics is obtained.

F Tests with Random Sample Sizes

ANOVA is routinely used to compare pathologies. We now want to consider the case in which one of the pathologies is rare so that it may not be possible to know the dimension of the corresponding sample. In this case the distribution of the F test have random non‐centrality parameters, when there are differences between the pathologies, and random degrees of freedom for the errors.

Fixed effects ANOVA: an extension to samples with random size

In many relevant situations, such as in medical research, sample sizes may not be previously known. The aim of this paper is to extend one and more than one-way analysis of variance to those situations and show how to compute correct critical values. The interest of this approach lies in avoiding false rejections obtained when using the classical fixed size F-tests. Sample sizes are assumed as random and we then proceed with the application of this approach to a database on cancer.

Control of the truncation errors for generalized F distributions

F-tests may not be used for all relevant hypothesis, even in rather simple models, which led to the introduction of generalized F-tests. The statistics of these tests are quotients of linear combinations of independent chi-squares, which may be non-central. When the observations are collected under non-standardized conditions, the non-centrality parameters may be random. The generalized F distributions are given by infinite sums. In this study, we show that there is an excellent control of the truncations errors for those sums. The case in which the non-centrality parameters have Gamma distributions is singled out.

ANOVA with random sample sizes: An application to a Brazilian database on cancer registries

We apply our results on random sample size ANOVA to a Brazilian database on cancer registries. The samples sizes will be considered as realizations of random variables. The interest of this approach lies in avoiding false rejections obtained when using the classical fixed size F-tests.

One-way random effects ANOVA: An extension to samples with random size

The aim of this paper is to extend one-way random effects ANOVA to situations in which we can not previously know the sample sizes. In this case it is more appropriate to consider the sample sizes as realizations of random variables. We will obtain the distribution of the F-tests, which has random degrees of freedom for the errors. Moreover we will show the equivalence between two expressions for the F-tests.

Nesting Segregated Mixed Models

A mixed model has segregation when its random effects part is segregated as a sub-model. It will be shown that under orthogonality condition, nesting a random effects model inside a segregated mixed model or a segregated mixed model inside a fixed effects model the result will be a segregated mixed model. Unbiased estimators will be obtained for the variance components in both classes of models which are UMVUE, once normality is assumed.

One-way fixed effects ANOVA with missing observations

The aim of this paper is to extend the theory of F-tests with random sample sizes to situations when missing observations may occur. We consider the one-way ANOVA with fixed effects. This approach is illustrated through an application to patients affected by melanoma skin cancer, from three different states of Brazil.

One-way Random Effects ANOVA with Random Sample Sizes: An Application to a Brazilian Database on Cancer Registries

ANOVA is routinely used in many situations, namely in medical research, where the sample sizes may not be previously known. This leads us to consider the samples sizes as realizations of random variables. The aim of this paper is to extend one-way random effects ANOVA to those situations and apply our results to a Brazilian database on cancer registries.

Inducing pivot variables and non-centrality parameters in elliptical distributions

We used inducing pivot variables to derive confidence intervals for the non-centrality parameters of samples with elliptical errors. A numerical application is presented.