A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations o...A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.展开更多
In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function ...In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.展开更多
The strong limit results of oscillation modulus of PL-process are established in this paper when the density function is not continuous function for censored data. The rates of convergence of oscillation modulus of PL...The strong limit results of oscillation modulus of PL-process are established in this paper when the density function is not continuous function for censored data. The rates of convergence of oscillation modulus of PL-process are sharp under week condition. These results can be used to derive laws of the iterated logarithm of random bandwidth kernel estimator and nearest neighborhood estimator of density under continuous conditions of density function being not assumed.展开更多
In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. wh...In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.展开更多
Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under...Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup a. s.,for S,T which together satisfy a certain condition.展开更多
A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error ...A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.展开更多
In this work, we consider statistical diagnostic for random right censored data based on K-M product limit estimator. Under the definition of K-M product limit estimator, we obtain that the relation formula between es...In this work, we consider statistical diagnostic for random right censored data based on K-M product limit estimator. Under the definition of K-M product limit estimator, we obtain that the relation formula between estimators. Similar to complete data, we define likelihood displacement and likelihood ratio statistic. Through a real data application, we show that our proposed procedure is validity.展开更多
Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribut...Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).展开更多
Let X<sub>1</sub>,X<sub>2</sub>,…, Y<sub>1</sub>,Y<sub>2</sub>,…, T<sub>1</sub>,T<sub>2</sub>,…be independent random variables such thatX<s...Let X<sub>1</sub>,X<sub>2</sub>,…, Y<sub>1</sub>,Y<sub>2</sub>,…, T<sub>1</sub>,T<sub>2</sub>,…be independent random variables such thatX<sub>i</sub> are real-valued and have a common continuous distribution function F. Y<sub>i</sub> are extendedreal-valued and have a common distribution G and T<sub>i</sub> are extended real-valued and have acommon distribution funtion D. The nonparametric maximum likelihood estimator of Fbased on X<sub>1</sub>,…, X<sub>n</sub> is the empirical distribution function F<sub>n</sub>.展开更多
The local behavior of oscillation modulus of the product-limit (PL) process and the cumulative hazard process is investigated when the data are subjected to random censoring. Laws of the iterated logarithm of local os...The local behavior of oscillation modulus of the product-limit (PL) process and the cumulative hazard process is investigated when the data are subjected to random censoring. Laws of the iterated logarithm of local oscillation modulus for the PL-process and the cumulative hazard process are established. Some of these results are applied to obtain the almost sure best rates of convergence for various types of density estimators as well as the Bahadur-Kiefer type process.展开更多
For left truncated and right censored data, based on a strong representation of the product-limit estimator of the survival function, we derive the sufficient and necessary condition for the rate of strong uniform con...For left truncated and right censored data, based on a strong representation of the product-limit estimator of the survival function, we derive the sufficient and necessary condition for the rate of strong uniform convergence of the product-limit estimator over the whole line.展开更多
For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n...For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.展开更多
For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are stro...For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.展开更多
基金Zhou's research was partially supported by the NNSF of China (10471140, 10571169)Wu's research was partially supported by NNSF of China (0571170)
文摘A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.
文摘In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.
基金This work was supported by Fund of National Natural Science(10171103)of China.
文摘The strong limit results of oscillation modulus of PL-process are established in this paper when the density function is not continuous function for censored data. The rates of convergence of oscillation modulus of PL-process are sharp under week condition. These results can be used to derive laws of the iterated logarithm of random bandwidth kernel estimator and nearest neighborhood estimator of density under continuous conditions of density function being not assumed.
文摘In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
文摘Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup a. s.,for S,T which together satisfy a certain condition.
文摘A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.
文摘In this work, we consider statistical diagnostic for random right censored data based on K-M product limit estimator. Under the definition of K-M product limit estimator, we obtain that the relation formula between estimators. Similar to complete data, we define likelihood displacement and likelihood ratio statistic. Through a real data application, we show that our proposed procedure is validity.
文摘Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).
基金Project supported by the National Natural Science Foundation of China.
文摘Let X<sub>1</sub>,X<sub>2</sub>,…, Y<sub>1</sub>,Y<sub>2</sub>,…, T<sub>1</sub>,T<sub>2</sub>,…be independent random variables such thatX<sub>i</sub> are real-valued and have a common continuous distribution function F. Y<sub>i</sub> are extendedreal-valued and have a common distribution G and T<sub>i</sub> are extended real-valued and have acommon distribution funtion D. The nonparametric maximum likelihood estimator of Fbased on X<sub>1</sub>,…, X<sub>n</sub> is the empirical distribution function F<sub>n</sub>.
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 19701037)
文摘The local behavior of oscillation modulus of the product-limit (PL) process and the cumulative hazard process is investigated when the data are subjected to random censoring. Laws of the iterated logarithm of local oscillation modulus for the PL-process and the cumulative hazard process are established. Some of these results are applied to obtain the almost sure best rates of convergence for various types of density estimators as well as the Bahadur-Kiefer type process.
基金the Postdoctoral Programme Foundation and the National Natural ScienceFoundation of China(No. 10071092).
文摘For left truncated and right censored data, based on a strong representation of the product-limit estimator of the survival function, we derive the sufficient and necessary condition for the rate of strong uniform convergence of the product-limit estimator over the whole line.
基金the National Natural Science Foundation of China (Grant No. 19971006) .
文摘For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.
文摘For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.
