Maximum likelihood estimation of the linearly structured correlation matrix by a Jacobi-type iterative scheme

Mukherjee and Maiti [Q-procedure for solving likelihood equations in the analysis of covariance structures, Comput. Statist. Quart. 2 (1988), pp. 105–128] proposed an iterative scheme to derive the maximum likelihood estimates of the parameters involved in the population covariance matrix when it is linearly structured. The present investigation provides a Jacobi-type of iterative scheme, MSIII, when the underlying correlation matrix is linearly structured. Such scheme is shown to be quite competent and efficient compared to the prevalent Fisher-scoring (FS) and the Newton–Raphson iterative scheme (NR). An illustrative example is provided for a numerical comparison of the iterates of MSIII, FS and NR choosing the Toeplitz matrix as the population correlation matrix. Numerical behaviour of such schemes is studied in the context of ‘bad’ initial try-out vectors. Additionally a simulation experiment is performed to judge the superiority of MSIII over FS.     

Borrowing strength from past data in small domain prediction by kalman filtering - a case

Point and interval estimators for small domains based exclusively on current and domain specific sample observations are generally ineffective because of inadequate sample-sizes. So, borrowing strength from sample values for analogous domains and simultaneously from all relevant past and auxiliary data is useful in deriving improved small domain statistics. Postulating for simplicity a linear regression model with a single covariate and a zero intercept but a time-specific domain-invariant slope we start with “synthetic” generalized regression predictors for the domain totals. These borrow across only domains. For further improvements a simple autoregressive model is postulated for the slope parameters. Employing Kalman filtering the previous predictors are revised to borrow supplementary strength across time. As drastic simplifying assumptions are needed in such predictions the efficacy of the procedure is examined through an empirical exercise using live data as well as simulations. The numerical findings turn out encouraging.     

Bias correction in logistic regression with missing categorical covariates

Logistic regression plays an important role in many fields. In practice, we often encounter missing covariates in different applied sectors, particularly in biomedical sciences. Ibrahim (1990) proposed a method to handle missing covariates in generalized linear model (GLM) setup. It is well known that logistic regression estimates using small or medium sized missing data are biased. Considering the missing data that are missing at random, in this paper we have reduced the bias by two methods; first we have derived a closed form bias expression using Cox and Snell (1968), and second we have used likelihood based modification similar to Firth (1993). Here we have analytically shown that the Firth type likelihood modification in Ibrahim led to the second order bias reduction. The proposed methods are simple to apply on an existing method, need no analytical work, with the exception of a little change in the optimization function. We have carried out extensive simulation studies comparing the methods, and our simulation results are also supported by a real world data.     

Small-area estimation based on survey data from a left-censored Fay-Herriot model

This paper develops methodology for survey estimation and small-area prediction using Fay-Herriot (1979) models in which the responses are left-censored. Parameter and small-area estimators are derived both by censored-data likelihoods and by an estimating-equation approach which adjusts a Fay-Herriot analysis restricted to the uncensored observations. Formulas for variances of estimators and mean-squared errors of small-area predictions are provided and supported by a simulation study. The methodology is applied to provide diagnostics for the left-censored Fay-Herriot model which are illustrated in the context of the Census Bureau's ongoing Small-Area Income and Poverty Estimation (SAIPE) project.     

研究古丝路上族群跨国流动的经验推动“一带一路”的发展

古丝绸之路上的族群流动,曾促使一些帝国崛起;也曾使一些国家民族间构建起利益共同体而放弃战争;还有经贸、科技文化跨国交流而使文明共享和民富国强的经验,如此等等.这类古丝路的人文宝藏,如果进行深入研究发掘,对今天一带一路建设会起举足轻重的作用.本文试图选择一些有关史实进行这方面探讨.     

Prediction Error of Small Area Predictors Shrinking Both Means and Variances

The article considers a new approach for small area estimation based on a joint modelling of mean and variances. Model parameters are estimated via expectation–maximization algorithm. The conditional mean squared error is used to evaluate the prediction error. Analytical expressions are obtained for the conditional mean squared error and its estimator. Our approximations are second‐order correct, an unwritten standardization in the small area literature. Simulation studies indicate that the proposed method outperforms the existing methods in terms of prediction errors and their estimated values.     

A note on non-negative mean square error estimation of regression estimators in randomized response surveys

Generalized regression estimators are considered for the survey population total of a quantitative sensitive variable based on randomized responses. Formulae are presented for ‘non-negative’ estimators of approximate mean square errors of these biased estimators when population and sample sizes are large.     

A NOTE ON COMPETING VARIANCE ESTIMATORS IN RANDOMISED RESPONSE SURVEYS

When gathering randomised rather than direct responses on a variable of interest relating to sensitive issues, one may use a modified version of the well-known generalised regression predictor of a finite population total. To construct confidence intervals, this paper proposes four alternative variance estimators – modifications to those usable with direct responses – and examines their relative efficiencies through simulations from simple super-population models.     

Modelling of low count heavy tailed time series data consisting large number of zeros and ones

In this paper, we construct a new mixture of geometric INAR(1) process for modeling over-dispersed count time series data, in particular data consisting of large number of zeros and ones. For some real data sets, the existing INAR(1) processes do not fit well, e.g., the geometric INAR(1) process overestimates the number of zero observations and underestimates the one observations, whereas Poisson INAR(1) process underestimates the zero observations and overestimates the one observations. Furthermore, for heavy tails, the PINAR(1) process performs poorly in the tail part. The existing zero-inflated Poisson INAR(1) and compound Poisson INAR(1) processes have the same kind of limitations. In order to remove this problem of under-fitting at one point and over-fitting at others points, we add some extra probability at one in the geometric INAR(1) process and build a new mixture of geometric INAR(1) process. Surprisingly, for some real data sets, it removes the problem of under and over-fitting over all the observations up to a significant extent. We then study the stationarity and ergodicity of the proposed process. Different methods of parameter estimation, namely the Yule-Walker and the quasi-maximum likelihood estimation procedures are discussed and illustrated using some simulation experiments. Furthermore, we discuss the future prediction along with some different forecasting accuracy measures. Two real data sets are analyzed to illustrate the effective use of the proposed model.