ON ESTIMATION OF LONG-MEMORY TIME SERIES MODELS

This paper discusses estimation associated with the long-memory time series models proposed by Granger & Joyeux (1980) and Hosking (1981). We consider the maximum likelihood estimator and the least squares estimator. Certain regularity conditions introduced by several authors to develop the asymptotic theory of these estimators do not hold in this model. However we can show that these estimators are strongly consistent, and we derive the limiting distribution and the rate of convergence.     

On equalities between BLUES,WLSEs, and SLSEs

Necessary and sufficient conditions for equalities between the best linear unbiased estimator, the weighted least-squares estimator, and the simple least-squares estimator of the expectation vector in a general Gauss-Markoff model are given in some alternative formulations. The main result states, somewhat surprisingly, that the weighted least-squares estimator cannot be identical with the simple least-squares estimator unless they both coincide with the best linear unbiased estimator.     

Robust designs and optimality of least squares for regression problems

Unbiased linear estimators are considered for the model

$\text{Y(}\text{x}{}_{\mathrm{i}}\text{)=θ}{}_0\text{+}\text{∑k}\text{j=1}\text{θ}{}_{\mathrm{j}}\text{x}{}_{\mathrm{ij}}\text{+ψ(}\text{x}{}_{\mathrm{i}}\text{)+ε}{}_{\mathrm{i}}\text{, i=1,2,…,n,}$

where ψ(x) is an unknown contamination. It is assumed that |ψ(x)|?φ(6x6) where φ is a convex function. Minimax analogues of Φ_p-optimality criteria are introduced. It is shown that, under certain (sufficient) conditions, the least squares estimators and corresponding designs are optimal in the class of all unbiased linear estimators and designs. It is also shown that, in the case when least squares estimators with symmetric design do not lead to an optimal solution, the relative efficiency of optimal least squares is not diminishing and has a uniform lower bound.     

Admissible estimators in finite population sampling employing various types of prior information

We consider some estimators of the total and variance of a finite population from Bayesian and pseudo-Bayesian perspectives. Recently, Meeden and Ghosh (1982a, 1982b) have provided quite simple but powerful tools for proving admissibility of estimators and estimator-design pairs is finite population sampling problems. We consider what these techniques yield in the way of admissibility results for the estimators discussed.     

An explicit formula for the risk of James-Stein estimators

Expressions for the risk of a Stein estimator and its principal derivatives involve a well-defined. but nonevaluated. expectation term. Stein (1966) has suggested a second-order approximation. In this paper we present an alternative exact expression.     

The Two-interval Line-segment Problem

In this paper we define and study the non-parametric maximum likelihood estimator (NPMLE) in the one-dimensional line-segment problem, where we observe line-segments on the real line through an interval with a gap which is smaller than the two remaining intervals. We define the self-consistency equations for the NPMLE and provide a quick algorithm for solving them. We prove supremum norm weak convergence to a Gaussian process and efficiency of the NPMLE. The problem has a geological application in the study of the lifespan of species     

Large sample properties of nonparametric copula estimators under bivariate censoring

A new nonparametric estimator is proposed for the copula function of a bivariate survival function for data subject to random right-censoring. We consider two censoring models: univariate and copula censoring. We show strong consistency and we obtain an i.i.d. representation for the copula estimator. In a simulation study we compare the new estimator to the one of Gribkova and Lopez [Nonparametric copula estimation under bivariate censoring; doi:10.1111/sjos.12144].     

An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model positively skewed data. An important issue is to develop a powerful goodness-of-fit test for the IG distribution. We propose and examine novel test statistics for testing the IG goodness of fit based on the density-based empirical likelihood (EL) ratio concept. To construct the test statistics, we use a new approach that employs a method of the minimization of the discrimination information loss estimator to minimize Kullback–Leibler type information. The proposed tests are shown to be consistent against wide classes of alternatives. We show that the density-based EL ratio tests are more powerful than the corresponding classical goodness-of-fit tests. The practical efficiency of the tests is illustrated by using real data examples.     

Modified Maximum Likelihood Estimator of Scale Parameter Using Moving Extremes Ranked Set Sampling

A modified maximum likelihood estimator (MMLE) of scale parameter is considered under moving extremes ranked set sampling (MERSS), and its properties are obtained. For some usual scale distributions, we obtain explicit form of the MMLE and prove the MMLE is an unbiased estimator under MERSS. The simulation results show that the MMLE using MERSS is always more efficient than the MLE using simple random sampling, when the same sample size is used. The simulation results also show that the loss of efficiency in using the MMLE instead of the MLE is very small for small sample.