ABSTRACT - Methods of Regression Diagnostics for Hazard-Based Models.
Analysis of generalized residuals in hazard regression models
A large sample study of nonparametric proportional hazard regression model
Moving window estimation procedures for additive regression function
A nonparametric method of regression analysis from censored data
On cumulative process model and its statistical analysis
The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...
Hazard rate model and statistical analysis of a compound point process
A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process behaviour....
An application of nonprarametric Cox regression model in reliability analysis: a case study
The contribution deals with an application of the nonparametric version of Cox regression model to the analysis and modeling of the failure rate of technical devices. The objective is to recall the method of statistical analysis of such a model, to adapt it to the real–case study, and in such a way to demonstrate the flexibility of the Cox model. The goodness-of-fit of the model is tested, too, with the aid of the graphical test procedure based on generalized residuals.
On precision of stochastic optimization based on estimates from censored data
In the framework of a stochastic optimization problem, it is assumed that the stochastic characteristics of optimized system are estimated from randomly right-censored data. Such a case is frequently encountered in time-to-event or lifetime studies. The analysis of precision of such a solution is based on corresponding theoretical properties of estimated stochastic characteristics. The main concern is to show consistency of optimal solution even in the random censoring case. Behavior of solutions...
On quantile optimization problem based on information from censored data
Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore,...
Discrete random processes with memory: Models and applications
The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior of proposed...
A counting process model of survival of parallel load-sharing system
A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also...
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