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### Checking proportional rates in the two-sample transformation model

Kybernetika

Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A~method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well...

### Globální obálkové testy aneb jak otestovat vhodnost statistického modelu na základě funkcionální charakteristiky

Pokroky matematiky, fyziky a astronomie

Obálkové metody představují populární nástroj pro testování hypotéz o vhodnosti statistického modelu. Tyto testy graficky porovnávají funkci $T:I\to ℝ$ vypočtenou ze statistických dat s jejím protějškem získaným simulacemi. Chyba prvního druhu $\alpha$, tj. pravděpodobnost zamítnutí platné hypotézy, je obvykle kontrolována pouze pro fixní hodnotu $r\in I$, zatímco funkce $T$ je definována na intervalu hodnot $I$. V tomto článku představíme nový globální obálkový test, který umožňuje kontrolovat chybu prvního druhu současně...

### Goodness-of-fit test for the accelerated failure time model based on martingale residuals

Kybernetika

The Accelerated Failure Time model presents a way to easily describe survival regression data. It is assumed that each observed unit ages internally faster or slower, depending on the covariate values. To use the model properly, we want to check if observed data fit the model assumptions. In present work we introduce a goodness-of-fit testing procedure based on modern martingale theory. On simulated data we study empirical properties of the test for various situations.

### On a robust significance test for the Cox regression model

Discussiones Mathematicae Probability and Statistics

A robust significance testing method for the Cox regression model, based on a modified Wald test statistic, is discussed. Using Monte Carlo experiments the asymptotic behavior of the modified robust versions of the Wald statistic is compared with the standard significance test for the Cox model based on the log likelihood ratio test statistic.

### On equivalence and bioequivalence testing.

SORT

Equivalence testing is the natural approach to many statistical problems. First, its main application, bioequivalence testing, is reviewed. The basic concepts of bioequivalence testing (2×2 crossover designs, TOST, interval inclusion principle, etc.) and its problems (TOST biased character, the carryover problem, etc.) are considered. Next, equivalence testing is discussed more generally. Some applications and methods are reviewed and the relation of equivalence testing and distance-based inference...

### On goodness-of-fit for the absence of memory model

Kybernetika

Logrank-type and Kolmogorov-type goodness-of-fit tests for the absence of memory model are proposed when the accelerated experiments are done under step-stresses. The power of the test against the approaching alternatives is investigated. The theoretical results are illustrated with simulated data.

### Sudden death testing versus traditional censored life testing. A Monte-Carlo study

Control and Cybernetics

### Testing a homogeneity of stochastic processes

Kybernetika

The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests...

### Univariate parametric survival analysis using GS-distributions.

SORT

The GS-distribution is a family of distributions that provide an accurate representation of any unimodal univariate continuous distribution. In this contribution we explore the utility of this family as a general model in survival analysis. We show that the survival function based on the GS-distribution is able to provide a model for univariate survival data and that appropriate estimates can be obtained. We develop some hypotheses tests that can be used for checking the underlying survival model...

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