Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Using local linear kernel smoothers to test the lack of fit of nonlinear regression models

Herein, we propose a data-driven test that assesses the lack of fit of nonlinear regression models. The comparison of local linear kernel and parametric fits is the basis of this test, and specific boundary-corrected kernels are not needed at the boundary when local linear fitting is used. Under the parametric null model, the asymptotically optimal bandwidth can be used for bandwidth selection. This selection method leads to the data-driven test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The finite-sample property of the proposed data-driven test is illustrated, and the power of the test is compared with that of some existing tests via simulation studies. We illustrate the practicality of the proposed test by using two data sets.     

Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

增长曲线模型非齐次线性估计的可容许性

讨论增长曲线模型Y =X1BX2 +ε中回归矩阵B的函数C1BC2 的估计L1YL2 +A ,在矩阵损失 (LT2 L1)Y +A - (ST2 XT2 S1X1)B (LT2 L1)Y +A - (ST2 XT2 S1X1)B T 下 ,我们得到了非齐次线性估计L1YL2 +A在非齐次线性估计类Г ={L1YL2 +A|L1:t×p ,L2 ;n×n ,A :t×s均为已知实阵 }中可容许的充要条件 :L1YL2在Г0 ={L1YL2 |L1:t×p ,L2 :n×s均为已知实阵 }中容许且当LT2 XT2 L1X1=ST2 XT2 S1X1时有A =0。     

Merging information for semiparametric density estimation

Summary.  The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed.     

Living Arrangements, Employment Status, and the Economic Well-Being of Mothers: Evidence from Brazil, Chile, and the U.S

Using data from Brazil, Chile, and the U.S., we estimate country specific models of household income that characterize mothers according to their marital status, living arrangement, and employment status. We assess the predicted economic well-being of each type of mother relative to a benchmark of married mothers in the same country, and at various points in the income distribution. We find dramatic cross-country differences in the distribution of mothers across categories, but few differences in each type's relative economic status. In all three countries and at all points in the income distribution, mothers who are the only adults in their households have the lowest levels of predicted income, while married mothers—followed closely by cohabitors—have the highest levels.     

A Semi-parametric Regression Model with Errors in Variables

Abstract.  In this paper, we consider a partial linear regression model with measurement errors in possibly all the variables. We use a method of moments and deconvolution to construct a new class of parametric estimators together with a non-parametric kernel estimator. Strong convergence, optimal rate of weak convergence and asymptotic normality of the estimators are investigated.     

A general inverse sampling scheme and its application to adaptive cluster sampling

Not having a variance estimator is a seriously weak point of a sampling design from a practical perspective. This paper provides unbiased variance estimators for several sampling designs based on inverse sampling, both with and without an adaptive component. It proposes a new design, which is called the general inverse sampling design, that avoids sampling an infeasibly large number of units. The paper provide estimators for this design as well as its adaptive modification. A simple artificial example is used to demonstrate the computations. The adaptive and non‐adaptive designs are compared using simulations based on real data sets. The results indicate that, for appropriate populations, the adaptive version can have a substantial variance reduction compared with the non‐adaptive version. Also, adaptive general inverse sampling with a limitation on the initial sample size has a greater variance reduction than without the limitation.     

Local dependence estimation using semiparametric archimedean copulas

The authors define a new semiparametric Archimedean copula family which has a flexible dependence structure. The generator of the family is a local interpolation of existing generators. It has locally‐defined dependence parameters. The authors present a penalized constrained least‐squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bi‐variate survival example.     

A Semi-Parametric Quantile Function Estimator for Use in Bootstrap Estimation Procedures

In this note we develop a new quantile function estimator called the tail extrapolation quantile function estimator. The estimator behaves asymptotically exactly the same as the standard linear interpolation estimator. For finite samples there is small correction towards estimating the extreme quantiles. We illustrate that by employing this new estimator we can greatly improve the coverage probabilities of the standard bootstrap percentile confidence intervals. The method does not reqiure complicated calculations and hence it should appeal to the statistical practitioner.