Estimation of the hazard function when the data are censored is an important problem in medical research. In this article, we propose a simple non-parametric estimator of the hazard function. Its asymptotic properties are derived, and numerical comparisons with other existing estimators are made. The proposed estimator is shown to be at least as good as the other estimators from both the theoretical and the numerical points of view.

a b s t r a c tUsing the diagnostic results in the ridge regression model, we propose an approximate version of Cook's distance in the lasso regression model since the analytic expression of the lasso estimator is not available. Also, we express the proposed Cook's distance in terms of basic building blocks such as residuals and leverages. We verify that the proposed statistic successfully detects potentially influential observations on estimators of regression coefficients and on the model selection in the lasso regression model. An illustrative example based on a real dataset is given.

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Deletion diagnostics, Influential observations, Local polynomial estimation, Reference values,

We derive a test statistic for the general linear test in the ridge regression model. The exact distribution for the test statistic is too difficult to derive; therefore, we suggest an approximate reference distribution. We use numerical studies to verify that the suggested distribution for the test statistic is appropriate. A asymptotic result for the test statistic also is considered.

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination R 2 and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in R 2 and F-statistic.

In this paper we suggest an efficient method to estimate the distribution function using the Bezier curve, and compare it with existing methods by simulation studies. In addition, we suggest a robust version of crossvalidation criterion to estimate the number of Bezier points, and showed that the proposed method is better than the existing methods based on simulation studies.

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