Small area estimation has received a lot of attention in recent years due to growing demand for reliable small area statistics. Traditional area-specific estimators may not provide adequate precision because sample sizes in small areas are seldom large enough. This makes it necessary to employ indirect estimators based on linking models. Basic area level and unit level models have been extensiv...

We investigate in this paper a variety of equalities for the ordinary least-squares estimators and the best linear unbiased estimators under the general linear (Gauss-Markov) model {y, Xβ, σΣ} and the restrained model {y, Xβ |Aβ = b, σΣ}.

We consider a random-design regression model with vector-valued observations and develop nonparametric estimation of smooth conditional moment functions in the predictor variable. This includes estimation of higher order mixed moments and also functionals of the moments, such as conditional covariance, correlation, variance, and skewness functions. Our asymptotic analysis targets the limit dist...

The knowledge of the cross correlation of the errors of local estimates is needed in many techniques for distributed fusion. In fact, this cross covariance is a key quantity for the best linear unbiased estimation (BLUE), also known as linear minimum mean-square error (LMMSE) estimation, and optimal weighted least squares (WLS) fusion rules presented in Part I [8]. This paper presents exact, ex...

This paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, we discuss the notions of variance and covariance of set-valued and interval-valued random variables. Then, we give the definition of the intervalvalued linear model and its le...

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the second-order bias correction has been derived mainly based on Taylor series expansions. However, thi...

Nonparametric regression approaches are used when the shape of curve between response variable and predictor is assumed to be unknown. excess has high flexibility. A frequently nonparametric approach a truncated spline that excellent ability handle data whose behavior at certain sub-intervals. The aim this study was obtain best model multivariable with linear quadratic using Generalized Cross V...