Non-response is a regular occurrence in Sample Surveys. Developing estimators when non-response exists may result in large biases when estimating population parameters. In this paper, a finite population mean is estim...Non-response is a regular occurrence in Sample Surveys. Developing estimators when non-response exists may result in large biases when estimating population parameters. In this paper, a finite population mean is estimated when non-response exists randomly under two stage cluster sampling with replacement. It is assumed that non-response arises in the survey variable in the second stage of cluster sampling. Weighting method of compensating for non-response is applied. Asymptotic properties of the proposed estimator of the population mean are derived. Under mild assumptions, the estimator is shown to be asymptotically consistent.展开更多
In order to avoid the discussion of equation （1.1）, this paper employs the proof method of Liang （2012） to consider the re-weighted Nadaraya-Watson estimation of conditional density. The established results genera...In order to avoid the discussion of equation （1.1）, this paper employs the proof method of Liang （2012） to consider the re-weighted Nadaraya-Watson estimation of conditional density. The established results generalize those of De Gooijer and Zerom （2003）. In addition, this paper improves the bandwidth condition of Liang （2012）.展开更多
This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to o...This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to obtain a static equilibrium state of an elastic structure. Preliminary numerical experiments illustrate that, compared with existing methods, the proposed method finds a reasonable solution even if data points distribute coarsely in a given material data set.展开更多
Let (X, Y) be a two-dimensional random variable. A law of the iterated logarithm is established for a smoothed neighbor-typo estimator of the regression function m(x)=E(Y|X=x) under conditions much weaker than needed ...Let (X, Y) be a two-dimensional random variable. A law of the iterated logarithm is established for a smoothed neighbor-typo estimator of the regression function m(x)=E(Y|X=x) under conditions much weaker than needed for the Nadaraya-Watson estimator. Also the sharp pointwise rates of strong consistency of this estimator is discussed in detail.展开更多
Let f(x) be the density of a design variable X and m(x) = E[Y|X = x] the regression function. Then m(x)= G(x)/f(x), where G(x)= m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn(x) ...Let f(x) be the density of a design variable X and m(x) = E[Y|X = x] the regression function. Then m(x)= G(x)/f(x), where G(x)= m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn(x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions,so we introduce a local polynomial of order p approximation to Gn(.) which provides estimators of the function G(x) and its derivatives. The density f(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the proposed estimator with p = 1 compares favorably with the Nadaraya-Watson and the popular local linear regression smoother.展开更多
文摘Non-response is a regular occurrence in Sample Surveys. Developing estimators when non-response exists may result in large biases when estimating population parameters. In this paper, a finite population mean is estimated when non-response exists randomly under two stage cluster sampling with replacement. It is assumed that non-response arises in the survey variable in the second stage of cluster sampling. Weighting method of compensating for non-response is applied. Asymptotic properties of the proposed estimator of the population mean are derived. Under mild assumptions, the estimator is shown to be asymptotically consistent.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province(No.2014J01010)
文摘In order to avoid the discussion of equation （1.1）, this paper employs the proof method of Liang （2012） to consider the re-weighted Nadaraya-Watson estimation of conditional density. The established results generalize those of De Gooijer and Zerom （2003）. In addition, this paper improves the bandwidth condition of Liang （2012）.
基金supported in part by the National Nature Science Foundation of China(Nos.12071487,11461032 and 11401267)the Program of Qingjiang Excellent Young Talents,Jiangxi University of Science and Technology,the Science Foundation of Jiangxi Provincial Education Department(No.GJJ190461)the Key R&D plans of Jiangxi Province(No.20202BBEL53006)。
基金supported by JSPS KAKENHI (Grants 17K06633 and 18K18898)
文摘This paper presents a simple nonparametric regression approach to data-driven computing in elasticity. We apply the kernel regression to the material data set, and formulate a system of nonlinear equations solved to obtain a static equilibrium state of an elastic structure. Preliminary numerical experiments illustrate that, compared with existing methods, the proposed method finds a reasonable solution even if data points distribute coarsely in a given material data set.
文摘Let (X, Y) be a two-dimensional random variable. A law of the iterated logarithm is established for a smoothed neighbor-typo estimator of the regression function m(x)=E(Y|X=x) under conditions much weaker than needed for the Nadaraya-Watson estimator. Also the sharp pointwise rates of strong consistency of this estimator is discussed in detail.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.10001004 and 39930160)by the US NSF(Grant No.DMS-9971301).
文摘Let f(x) be the density of a design variable X and m(x) = E[Y|X = x] the regression function. Then m(x)= G(x)/f(x), where G(x)= m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn(x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions,so we introduce a local polynomial of order p approximation to Gn(.) which provides estimators of the function G(x) and its derivatives. The density f(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the proposed estimator with p = 1 compares favorably with the Nadaraya-Watson and the popular local linear regression smoother.
