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In this paper we assess the suitability of weighted-indexed semi-Markov chains (WISMC) to study risk measures as applied to high-frequency financial data. The considered measures are the drawdown of fixed level, the time to crash, the speed of crash, the recovery time and the speed of recovery; they provide valuable information in portfolio management and in the selection of investments. The results obtained by implementing the WISMC model are compared with those based on the real data and also with those achieved by GARCH and EGARCH models. Globally, the WISMC model performs much better than the other econometric models for all the considered measures unless in the cases when the percentage of censored units is more than 30% where the models behave similarly.

In order to predict future patients' survival time based on their microarray gene expression data, one interesting question is how to relate genes to survival outcomes. In this paper, by applying a semi-parametric additive risk model in survival analysis, we propose a new approach to conduct a careful analysis of gene expression data with the focus on the model's predictive ability. In the proposed method, we apply the correlation principal component regression to deal with right censoring survival data under the semi-parametric additive risk model frame with high-dimensional covariates. We also employ the time-dependent area under the receiver operating characteristic curve and root mean squared error for prediction to assess how well the model can predict the survival time. Furthermore, the proposed method is able to identify significant genes, which are significantly related to the disease. Finally, the proposed useful approach is illustrated by the diffuse large B-cell lymphoma data set and breast cancer data set. The results show that the model fits the data sets very well.

In clinical studies, a proportion of patients might be unsusceptible to the event of interest and can be considered as cured. The survival models that incorporate the cured proportion are known as cure rate models where the most widely used model is the mixture cure model. However, in cancer clinical trials, mixture model is not the appropriate model and the viable alternative is the Bounded Cumulative Hazard (BCH) model. In this paper we consider the BCH model to estimate the cure fraction based on the lognormal distribution. The parametric estimation of the cure fraction for survival data with right censoring with covariates is obtained by using EM algorithm.

Suppose the random vector (X, Y) satisfies the heteroscedastic regression model Y = m(X) + σ(X)ε, where m(·) = E(Y∣·), σ²(·) = Var(Y∣·) and ε (with mean zero and variance one) is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. New goodness-of-fit testing procedures for m and σ²(·) are proposed. They are based on a modified integrated regression function technique which uses the method of [Heuchenne and Van Keilegom, 2006b] to construct new versions of functions of the data points. Asymptotic representations of the processes are obtained and weak convergence to gaussian processes is deduced.

We develop a kernel smoothing based test of a parametric mean-regression model against a nonparametric alternative when the response variable is right-censored. The new test statistic is inspired by the synthetic data approach for estimating the parameters of a (non)linear regression model under censoring. The asymptotic critical values of our tests are given by the quantiles of the standard normal law. The test is consistent against any fixed alternative, against local Pitman alternatives and uniformly over alternatives in Hölder classes of functions of known regularity.

Three parameter Weibull distributions do not satisfy the usual regularity conditions for maximum likelihood estimation of parameters. Again, as the threshold parameter becomes very close to the smallest observation the log-likelihood function becomes unbounded. Further, a shape parameter with a value lass than unity makes the density J-shaped which excludes the availability of a consistent local maximum. The presence of censoring increases the complexity further. The present paper performs maximum likelihood estimation through Differential Evolution, an evolutionary computation method which does not require the differentiability of the likelihood function, for censored Weibull data. It successfully obtains maximum likelihood estimates and their precision for simulated data sets.