Integrated Estimation of Functional-Coefficient Regression Models with Different Smoothing Variables

In this article, the functional-coefficient regression models with different smoothing variables in different coefficient functions are discussed. The integrated estimates of the coefficient functions are defined by marginal integration on the initial value obtained by local linear technique. Their asymptotical normalities are studied.     

Estimation of Some Nonlinear Panel Data Models With Both Time-Varying and Time-Invariant Explanatory Variables

The so-called “fixed effects” approach to the estimation of panel data models suffers from the limitation that it is not possible to estimate the coefficients on explanatory variables that are time-invariant. This is in contrast to a “random effects” approach, which achieves this by making much stronger assumptions on the relationship between the explanatory variables and the individual-specific effect. In a linear model, it is possible to obtain the best of both worlds by making random effects-type assumptions on the time-invariant explanatory variables while maintaining the flexibility of a fixed effects approach when it comes to the time-varying covariates. This article attempts to do the same for some popular nonlinear models.     

Method of Moments Estimation in Linear Regression with Errors in both Variables

Recently, in this journal, there has been revised attention on estimating the parameters of the errors in variables, linear structural model. For example, O’Driscoll and Ramirez (2011) used a geometric approach to give insight into the performance of various slope estimators for the linear structural model as introduced by the present author. This article aims to provide a unified method of moments approach for estimating the parameters in the linear structural model, concentrating attention on estimators using the higher moments, which to date has received only little attention in the literature.     

On the Product and Ratio of Gamma and Beta Random Variables

Summary: The distributions of the product XY and the ratio X/Y are derived when X and Y are gamma and beta random variables distributed independently of each other. Tabulations of the associated percentage points and illustrations of their practical use are also provided. * The authors would like to thank the referee and the editor for carefully reading the paper and for their help in improving the paper.     

Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables

In this article, we propose a new class of estimators to estimate the finite population mean by using two auxiliary variables under two different sampling schemes such as simple random sampling and stratified random sampling. The proposed class of estimators gives minimum mean squared error as compared to all other considered estimators. Some real data sets are used to observe the performances of the estimators. We show numerically that the proposed class of estimators performs better as compared to all other competitor estimators.     

Estimation of Finite Population Mean in Stratified Random Sampling with Two Auxiliary Variables under Double Sampling Design

In this article, a chain ratio-product type exponential estimator is proposed for estimating finite population mean in stratified random sampling with two auxiliary variables under double sampling design. Theoretical and empirical results show that the proposed estimator is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Chand (1975) chain ratio estimator, Choudhary and Singh (2012) estimator, chain ratio-product-type estimator, Sahoo et al. (1993) difference type estimator, and Kiregyera (1984) regression-type estimator. Two data sets are used to illustrate the performances of different estimators.     

Higher Moments and Prediction‐Based Estimation for the COGARCH(1,1) Model

COGARCH models are continuous time versions of the well‐known GARCH models of financial returns. The first aim of this paper is to show how the method of prediction‐based estimating functions can be applied to draw statistical inference from observations of a COGARCH(1,1) model if the higher‐order structure of the process is clarified. A second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process. Asymptotic results are given, and a simulation study shows that the method of prediction‐based estimating function outperforms the other available estimation methods.     

A Comparison of Utilized and Theoretical Covariance Weighting Matrices on the Estimation Performance of Quadratic Inference Functions

The quadratic inference function (QIF) method is increasingly popular for the marginal analysis of correlated data due to its advantages over generalized estimating equations. Asymptotic theory is used to derive analytical results from the QIF, and we, therefore, study three asymptotically equivalent weighting matrices in terms of finite-sample parameter estimation. Furthermore, to improve small-sample estimation, we study modifications to the estimation procedure. Examples are presented via simulations and application. Results show that although theoretical weighting matrices work best, the proposed estimation procedure, in which initial estimates are held constant within the matrix of estimated empirical covariances, is preferable in practice.     

Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables

This article develops a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability R = P(X > Y) where X and Y are data from independent normal distributions of unknown means and variances. Our method is based on third-order likelihood analysis and is compared to the conventional first-order likelihood ratio procedure as well as the approximate methods of Reiser and Guttman (1986 Reiser, B., Guttman, I. (1986). Statistical inference for Pr(Y < X): the normal case. Technometrics 28: 253257.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Guo and Krishnamoorthy (2004 Guo, H., Krishnamoorthy, K. (2004). New approximate inferential methods for the reliability parameter in a stress-strength model: the normal case. Commun. Statist. Theor. Meth. 33: 17151731.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The use of our proposed method is illustrated by an empirical example and its superior accuracy in terms of coverage probability and error rate are examined through Monte Carlo simulation studies.     

Estimation of a parametric function associated with the lognormal distribution

Estimation of the mean of the lognormal distribution has received much attention in the literature beginning with Finney (1941 Finney, D.J. (1941). On the distribution of a variate whose logarithm is normally distributed. Supp. J. Royal Stat. Soc. 7(2):155–161.[Crossref] , [Google Scholar]). The problem is of significant practical importance because of the ubiquitous use of log-transformation. In this article, we consider the estimation of a parametric function associated with the lognormal distribution of which the mean, median, and moments are special cases. We generalize various estimators from the literature for the mean to this parametric function and propose a new simple estimator. We present the estimators in a unified framework and use this framework to derive asymptotic expressions for their biases and mean square errors (MSEs). Next, we make asymptotic and small-sample comparisons via simulations between them in terms of their MSEs. Our proposed estimator outperforms many of the previously proposed estimators. A numerical example is given to illustrate the various estimators.     

Moment Estimation of the Parameters in Rayleigh Distribution with Two Parameters

In this article, the moment estimation of the parameters in two-parameter Rayleigh distribution is studied. For given sample values, the necessary and sufficient conditions on the estimating equations which have unique solution are obtained, and it is also proved that these conditions are satisfied on asymptotic probability 1. Furthermore, the strong consistency and asymptotic normality are obtained. Finally, some simulation experiments are made to show the conclusions.     

基于半参数估计的能源消费与经济增长关系研究

能源消费与经济增长的内在关系对国家能源政策的制定有着重要的影响,然而大量的研究得出的结论并未趋于一致。鉴此,使用半参数回归法,在不预先设定二者服从何种函数关系的情况下,对中国1998——2008年30个省份的能源消费与经济增长关系进行研究。结果显示:中国不同地区的能源消费与经济增长的内在依存关系呈现出不同的特征。从全国范围看,能源消费与经济增长之间呈现出扁平S型的非线性关系,该非线性关系总体呈现上升趋势;东部地区能源消费与经济增长之间呈现出logistic型非线性关系,西部地区呈现宽U型非线性关系。     

Regression analysis of longitudinal data with time-dependent covariates in the presence of informative observation and censoring times

In longitudinal observational studies, repeated measures are often correlated with observation times as well as censoring time. This article proposes joint modeling and analysis of longitudinal data with time-dependent covariates in the presence of informative observation and censoring times via a latent variable. Estimating equation approaches are developed for parameter estimation and asymptotic properties of the proposed estimators are established. In addition, a generalization of the semiparametric model with time-varying coefficients for the longitudinal response is considered. Furthermore, a lack-of-fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite-sample behavior of the proposed methods is examined in simulation studies, and an application to a bladder cancer study is illustrated.     

Estimation of parameters in latin squares and graeco-latin squares with missing observations

We show that if in an additive model with p-2 MOLS if one omits up to p-1 observations from the same row, the same column or which correspond to the same letter in any of the squares all effects are estimable. On the other hand with only two missing observations not from the same row, the same column or corresponding to the same letter in any of the squares one degree of freedom is lost for each set of effects.     

A comparison of population average and random-effect models for the analysis of longitudinal count data with base-line information

The generalized estimating equation (GEE) approach to the analysis of longitudinal data has many attractive robustness properties and can provide a 'population average' characterization of interest, for example, to clinicians who have to treat patients on the basis of their observed characteristics. However, these methods have limitations which restrict their usefulness in both the social and the medical sciences. This conclusion is based on the premise that the main motivations for longitudinal analysis are insight into microlevel dynamics and improved control for omitted or unmeasured variables. We claim that to address these issues a properly formulated random-effects model is required. In addition to a theoretical assessment of some of the issues, we illustrate this by reanalysing data on polyp counts. In this example, the covariates include a base-line outcome, and the effectiveness of the treatment seems to vary by base-line. We compare the random-effects approach with the GEE approach and conclude that the GEE approach is inappropriate for assessing the treatment effects for these data.     

Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term

This article studies the estimation of change point in panel models. We extend Bai (2010 Bai, J. (2010). Common breaks in means and variances for panel data. Journal of Econometrics 157:78–92.[Crossref], [Web of Science ®] , [Google Scholar]) and Feng et al. (2009 Feng, Q., Kao, C., Lazarová, S. (2009). Estimation and Identification of Change Points in Panel Models, Working paper, Syracuse University. [Google Scholar]) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.     

Estimation of the intensity function of an inhomogeneous Poisson process with a change‐point

Recent work on point processes includes studying posterior convergence rates of estimating a continuous intensity function. In this article, convergence rates for estimating the intensity function and change‐point are derived for the more general case of a piecewise continuous intensity function. We study the problem of estimating the intensity function of an inhomogeneous Poisson process with a change‐point using non‐parametric Bayesian methods. An Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain estimates of the intensity function and the change‐point which is illustrated using simulation studies and applications. The Canadian Journal of Statistics 47: 604–618; 2019 © 2019 Statistical Society of Canada     

Regression Analysis of Longitudinal Data with Time‐Dependent Covariates and Informative Observation Times

Abstract. Longitudinal data frequently occur in many studies, and longitudinal responses may be correlated with observation times. In this paper, we propose a new joint modelling for the analysis of longitudinal data with time‐dependent covariates and possibly informative observation times via two latent variables. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. In addition, a lack‐of‐fit test is presented for assessing the adequacy of the model. The proposed method performs well in finite‐sample simulation studies, and an application to a bladder tumour study is provided.     

Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

Estimation of small area event rates and of the associated standard errors

We develop empirical best estimators for small area event rates based on the hierarchical Poisson model with log-normal mixing distribution, when the basic data consists of area level measurements. We derive an approximate expression to the mean squared error of the estimators and we provide a method for estimating this expression.