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.