Vilijandas Bagdonavičius

• Vilnius University

The paper reviews the scientific and pedagogical activities of Julius Kruopis, the pioneer of Lithuanian applied statistics. His contribution to statistics and cooperation with Lithuanian companies in the application of statistical methods in various fields of human activity is described in the most detail, especially in the quality control area an...

We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z-scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was d...

A new method for multiple outliers identification in linear regression models is developed. It is relatively simple and easy to use. The method is based on a result giving asymptotic properties of extreme studentized residuals. This result is proved under rather general conditions on estimation procedure and covariate distribution. An extensive sim...

Parametric models for analysis of survival data with possible crossing of hazard rates related with two treatment groups are introduced. Strategy for survival improvement through application of time-varying treatment is discussed. Complete and right-censored data with possible confounding covariates are considered. Estimators of the crossing points...

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data may be right censored. The limit distribution of the test statistic is derived. Power of the test against appr...

We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z-scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was d...

The accelerated failure time (AFT) model is most commonly used model in accelerated life testing (ALT). This model is restrictive as failure time distributions under different constant stresses differ only in terms of scale. If it is not the case, most papers on ALT use a generalization of the AFT model supposing that under different stresses not o...

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data may be right censored. The limit distribution of the test statistic is derived. Power of the test against appr...

The problem of multiple upper outliers detection in samples from location-scale and shape-scale families is considered. A new test statistic is proposed. The critical values of the new test statistic are tabulated by simulation. The power of the new test and other available tests are compared by simulation.

This article has no abstract.

The famous chi-square test of Pearson is well known, while different modifications of this test are not so well known. At present, the theory of chi-squared tests is developed very actively, especially in accelerated trials. We discuss here some applications of the theory of chi-squared tests in reliability and survival analysis for parametric regr...

Several classes of tests for the hypothesis H are used in statistical literature: tests based on weighted differences of non-parametric and parametric of the cumulative distribution function (CDF); tests based on the differences of logarithms of order statistics; tests based on empirical correlation coefficients between logarithms of order statisti...

The new kind of chi-squared tests are proposed

We give chi-squared goodness-of fit tests for parametric regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, and models with cross-effects of survival functions. Random right censored data are used. Choice of random grouping intervals as data functions is...

This chapter surveys the statistical methods for the validation of the two-parameter Weibull-Gnedenko distribution from type II censored samples. Likelihood ratio test statistics are used to test hypotheses and test statistics for the hypothesis. Michael used the arcsin transformation to stabilize the variances of the plotted points on the probabil...

Partial likelihood Asymptotic properties of estimators

Paired samples Logrank-type tests for homogeneity of related k > 2 samples Homogeneity tests for related samples against crossing marginal survival functions alternatives Exercises Answers

ML estimators: right censoring ML estimators: left truncation ML estimators: left truncation and right censoring Consistency and asymptotic normality of the ML estimators Parametric ML estimation for survival regression models

Stochastic process Counting process Martingale and local martingale Stochastic integral Predictable process and Doob–Meyer decomposition Predictable variation and predictable covariation Stochastic integrals with respect to martingales Central limit theorem for martingales

Chi-squared test for composite hypothesis Chi-squared test for exponential distributions Chi-squared tests for shape-scale distribution families Chi-squared tests for other families Exercises Answers

Data Weighted logrank statistics Logrank test statistics as weighted sums of differences between observed and expected number of failures Examples of weights Weighted logrank statistics as modified score statistics The first two moments of weighted logrank statistics Asymptotic properties of weighted logrank statistics Weighted logrank tests Homoge...

Right-censored data Left truncation Left truncation and right censoring Nelson-Aalen and Kaplan-Meier estimators Bibliographic notes

A survey of statistical methods for validation of shape-scale families of probability distributions from type II censored samples is given. We propose "integrated likelihood ratio tests" which are modifications of Zhang's tests from complete to type II censored data. We also give modifications of Cramér-von-Mises and Anderson-Darling tests using in...

We give chi-squared goodness-of-fit tests for homogeneous Markov processes with unknown transition intensities or with transition intensities of known form depending on a finite-dimensional parameter.RésuméOn propose des tests dʼajustement du type chi deux de lʼhypothèse selon laquelle un processus stochastique dʼespace dʼétats fini est un processu...

Sign test Runs test McNemar's test Cochran test Special goodness-of-fit tests Bibliographic notes Exercises Answers

Introduction Ranks and their properties Rank tests for independence Randomness tests Rank homogeneity tests for two independent samples Hypothesis on median value: the Wilcoxon signed ranks test Wilcoxon's signed ranks test for homogeneity of two related samples Test for homogeneity of several independent samples: Kruskal–Wallis test Homogeneity hy...

Estimators;Fisher information matrix;Identifiable models;Parametric maximum likelihood;Probability measures

Test statistics based on the empirical process Kolmogorov–Smirnov test ω2, Cramér–von-Mises and Andersen–Darling tests Modifications of Kolmogorov–Smirnov, Cramér–von-Mises and Andersen–Darling tests: composite hypotheses Two-sample tests Bibliographic notes Exercises Answers

Stochastic process Examples of stochastic processes Weak convergence of stochastic processes Weak invariance of empirical processes Properties of Brownian motion and Brownian bridge

A new flexible and simple semiparametric model, including the cases when hazard rates cross, go away, are proportional, approach, or converge is proposed. Semiparametric estimation procedures are given. Tests for absence of hazard rates crossing and homogeneity are proposed.

A new flexible and simple semiparametric model including the cases where hazard rates cross, go away, are proportional, approach, or converge is proposed. Semiparametric estimation procedures for censored data are given. A test for absence of hazard rates crossing is proposed. Bibliography: 6 titles.

We give chi-squared goodness-of-fit tests for parametric models including various regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, models with cross-effects of survival functions. Choice of random grouping intervals as data functions is considered.

In this communication we consider chi-squared goodness-of-fit tests from censored data. Choice of random grouping intervals as data functions is considered. Simple formulas useful for computing of test statistics for mostly applied classes of survival distributions are given.

Parametric point and interval estimators of the cumulative distribution function of redundant systems with several “warm” stand-by units are proposed. The data are supposed to be right censored. Accuracy of interval estimators obtained from complete data was investigated by simulation. Keywords and phrasesAFT model; Asymptotic properties of estima...

Nonparametric and parametric methods of estimation of redundant systems with “warm” standby units reliability are given. Asymptotic properties of the estimators and asymptotic confidence intervals are obtained. Power of goodness-of-fit tests from finite samples is investigated by simulation. Keywords and phrases AFT model - confident interval -...

Models and estimation methods for failure process parameters and various reliability characteristics using censored multi-mode failure time-degradation data with covariates. Degradation data is supposed to be measured at discrete times. Modified likelihood function which uses predictors of degradation process is defined. Examples of predictors when...

We propose a test for the proportional hazards (Cox) model which is oriented against wide classes of alternatives including monotone hazard ratios and crossings of survival functions and can be used when data are left truncated and right censored. The limit distribution of the test statistics is derived. Bibliography: 20 titles.

Introduction Estimation in the AFT-GW model Properties of estimators: simulation results for the AFT-GW model Some remarks on the second plan of experiments Conclusion Appendix Bibliography

Introduction The models The tests Limit distribution of the test statistics Bibliography

Goodness-of-fit for the semi-parametric Cox model Chi-squared goodness-of-fit tests for parametric AFT models Chi-squared test for the exponential AFT model Chi-squared tests for scale-shape AFT models Bibliographic notes Exercises Answers

We consider semiparametric estimation of characteristics of degradation and failure process using degradation and multi-mode failure time data with covariates under the assumption that the component of hazard rate related to observable degradation is an unknown function of degradation and may depend on covariates. Bibliography: 17 titles.

The objective of this paper is to model the phenomenon of degradation-to-failure for assemblies used for lumbar arthrodesis, starting from the analysis of their structure/geometry, the load applied and the kind of failure when several occur. An AFT model is proposed to model the joint effects of the applied load and the structural dimensions of the...

A new flexible and simple semiparametric model, including the cases when hazard rates cross, go away, are proportional, approach or converge, is proposed. Semiparametric estimation procedures are given. A test for absence of hazard rates crossing is proposed. To cite this article: V. Bagdonavičius et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

A test for the equality of marginal distributions of bi-dimensional distribution functions represented by a parametric copula and completely unknown marginals is proposed. To cite this article: V. Bagdonavičius et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Mathematical formulation of fluent switching from "warm" to "hot" conditions of standby units is given using the well known Sedyakin's and accelerated failure time (AFT) models. Non-parametric estimators of cumulative distribution function and mean failure time of a redundant system with several stand-by units are proposed. Goodness-of-fit tests fo...

Non-parametric estimators of various competing modes intensities and failure probabilities from linear degradation-failure time data with partial renewals are given. Decompositions of counting processes associated with degradation and failure moments are obtained. Some of these decompositions imply estimation procedures. Others are used to obtain a...

We present a test for the equality of marginals of bi-dimensional distribution functions under censoring. The asymptotic power of the test under approaching alternatives and the simulation analysis for finite samples are done. The test is more powerful than classical tests in situations where the marginals differ in shape parameters. To cite this a...

The classical goodness-of-fit tests for homogeneity and proportional hazards have small power in the case of alternatives when crossings of survival functions are possible. We give test statistics which are oriented against wide classes of alternatives including single or multiple crossings of survival functions. The limit distributions of the test...

We consider some methods of semiparametric regression estimation in multivariate models when the common distribution function is represented using a copula and the marginals satisfy a generalized regression model using a transfer functional. Sufficient conditions for consistency and joint asymptotic normality of the finite-dimensional parameters ar...

IntroductionModelsParametric and semiparametric estimationGoodness-of-fit for the Cox model against the cross-effects modelsExamplesConcluding remarksAppendix: Proof of Theorem 12.1

The paper considers the analysis of disablement process of the elderly using the general path model with noise. The impact of dementia and sex on degradation is analysed. These joint model for survival and longitudinal data is discussed.

A joint model for linear degradation and competing failure data with partial renewals is proposed. Non-parametric estimation procedures for failure intensities and failure probabilities as functions of degradation level are given. Asymptotic properties of the estimators are investigated. To cite this article: V. Bagdonavičius et al., C. R. Acad. Sc...

This article considers degradation and failure time models with multiple failure modes which used to study the problem of longevity and aging in survival analysis and reliability. Degradation process is modeled using general nonparametric, nonlinear path models. Semi-parametric models for the intensities of the traumatic failures are used supposing...

Nonparametric estimators of the minimal number of reserved units from non renewable reliability data are given. Cases of stationary and non stationary renewal processes are considered. Numerical methods for estimator computing are proposed. Asymptotic confidence intervals are given. Real tire failure time data are analyzed.

We present a statistical model and semiparametric estimation procedure for analysis of survival data with multiple cross-effects (MCE) of survival functions. A goodness-of-fit test for the proportional hazards model against the MCE model is proposed. To cite this article: V. Bagdonavičius, M. Nikulin, C. R. Acad. Sci. Paris, Ser. I 340 (2005).Résum...

The models describing dependance of thelifetime distribution on the time-depending explanatory variables are considered. Such models are useful in reliability and survival analysis to study the reliability of bio-medical systems.

Failures of highly reliable units are rare and it may be not possible to gather the failure time data needed for reliability estimation. One way of obtaining failures during the time given for experiments is to apply methods of accelerated life testing (ALT). In ALT units are tested at higher than usual (design) stress conditions. The purpose is to...

We propose two tests to test the hypothesis of the equality of two survival functions against the alternative of crossing of these functions for right-censured data. The asymptotic laws of test statistics are given. The powers of the tests are calculated. To cite this article: V. Bagdonavičius et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

SUMMARY We present a model and semiparametric estimation procedures for analyzis of survival data with crosseffects (CE) of survival functions. Finite sample properties of the estimators are analyzed by simulation. A goodness-of-fit test for the proportional hazards model against the CE model is proposed. The well known data concerning effects of c...

The paper considers the semiparametric analysis of several new degradation and failure time regression models without and with time depending covariates. These joint models for survival and longitudinal data measured with errors can be applied in studies of longevity, aging and degradation in survival analysis, biostatistics, epidemiology, demograp...

Survival-regression models relate lifetime distribution to the explanatory variables (covariates) and are used for the estimation of the effect of covariates on survival and for estimation of survival under given covariate values. Survival-regression models may also be used for the analysis of failure-time-regression data in reliability, applied in...

A tire wear model including dependence of the distribution of the traumatic failures of various modes on the wear is proposed. Non-parametric, semi-parametric and parametric methods of estimation for the main reliability characteristics of tires are given. The model makes it possible not only to estimate unconditional functions such as the survival...

The paper considers degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Non-parametric estimators of various reliability characteristics are proposed. Theorems on simultaneous asymptotic distribution of random functions characterizing deg...

Failure Time Distributions Introduction Parametric Classes of Failure Time Distributions Accelerated Life Models Introduction Generalized Sedyakin's Model Accelerated Failure Time Model Proportional Hazards Model Generalized Proportional Hazards Models Generalized Additive and Additive-Multiplicative Hazards Models Changing Shape and Scale Models G...

Human vital functions can degrade due to genetic aging, violent factors and diseases. Most (∼90%) people are affected by diseases. Degradation of the body functions can slope when disease is cured and progress to death when it is incurable. We propose human organism degradation model caused by disease which is based on the course of the vital funct...

A goodness-of-fit test for the generalized Sedyakin's model is proposed when accelerated experiments are carried out under step-stresses. Various alternatives, such as the Cox proportional hazards model with time-varying stresses, are considered. The test power against the neighbouring alternatives is studied.RésuméUn test d'ajustement pour le modè...

Human vital functions can degrade due to genetic aging, violent factors and diseases. Most (∼90%) people are affected by diseases. Degradation of the body functions can slope when disease is cured and progress to death when it is incurable. We propose human organism degradation model caused by disease which is based on the course of the vital funct...

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

The generalization of the additive-multiplicative model of Lin and Ying is considered. Estimators of the regression parameters, the baseline survival function, and the survival function under any stress are proposed. The asymptotic properties of estimators are investigated. Bibliography: 7 titles.

A model of degradation with covariates is considered. Possible dependence of the intensity of traumatic events on degradation is included into the model. Parametric and nonparametric models are studied.

The accelerated failure time model with time dependent stresses is considered. Plans of experiments with step-stresses for which nonparametric estimation from accelerated life data can be done are proposed. Asymptotic properties of reliability function estimators are investigated.

Accelerated life models including cycling effect are introduced. These models are modifications of the additive accumulation of damages and generalized proportional hazards models Semiparametric estimation procedures are proposed.

Additive accumulation of damage models and generalizations are considered. A semiparametric estimation procedure of the survival function under the normal stress from accelerated life testing data is proposed. Experiments with step stresses with random switch up moments are considered. Asymptotic properties of estimators are investigated.

A review of main known and new models used in accelerated life testing is done. An unifying approach of model formulation is used. Only models for which estimation procedures are known are considered.

Generalization of the proportional hazards model taking into account dependence of the rate of resource using on the value of the used resource is considered. Modified partial likelihood approach for parameters estimation is proposed. The asymptotic properties of estimators are investigated.

The accelerated life model when the baseline reliability function is not known is considered. Estimators of the reliability function corresponding to the normal conditions of functionning are proposed when the step stresses are used for the accelerated life testing. Asymptotic properties of estimators are investigated.

A general approach to semiparametric regression model construction is proposed, using the notation of a transfer functional. Estimators of unknown regression parameters are proposed, generalising the estimators of the parameters of the proportional hazards and the additive risk models.

Classes of semiparametric models, generalizing the proportional and additive hazards, proportional odds and other models are considered. Asymptotical properties of estimators of regression parameters and baseline survival function arc investigated in the case of one of considered classes.

A general approach to semiparametric regression model construction is proposed, using the notation of a transfer functional. Estimators of unknown regression parameters are proposed, generalising the estimators of the parameters of the proportional hazards and the additive risk models.

In this paper modified moment estimators (m.m.e.) of parameters u, b, 0 are given; asymptotical properties of m.m.e, are investigated; estimators of the m.m.e, variances are given; graphical goodness of fit tests for the classes/(;1 and K:2 are proposed. Calculation of the m.m.e, is considerably simpler than calculation of the above mentioned estim...