Showing papers on "U-statistic published in 1995"

Asymptotically Unbiased Estimation in Generalized Linear Models with Random Effects

Abstract: SUMMARY Obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model. In this paper, we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent. The method is motivated by iterative bias correction and can be applied in principle to any parametric model. A simulation-based approach of implementing the method is described and the relationship of the method proposed with other sampling-based methods is discussed. Results from a small scale simulation study show that the method proposed can lead to estimates which are nearly unbiased even for the variance components while the standard errors are only slightly inflated. A new analysis of the famous salamander mating data is described which reveals previously undetected between-animal variation among the male salamanders and results in better prediction of mating outcomes.

Sampling Methods to Estimate Foliage and Other Characteristics of Individual Trees

Abstract: The total foliar area or mass of a tree is difficult to measure, as is its bark or cambial area, and various other components of aboveground biomass. A variety of sampling methods is proposed and estimators of these characteristics are presented. Based on probability precepts, all estimators are unbiased. An unbiased estimator of variance for each estimator also is presented. The basis in probability rather than a fitted regression equation provides some important safeguards, and is a useful alternative when fitted re- gression functions are unavailable for a particular species and physiographic condition.

A Comparison of Unbiased and Plotting‐Position Estimators of L Moments

Abstract: Plotting-position estimators of L moments and L moment ratios have several disadvantages compared with the “unbiased” estimators. For general use, the “unbiased” estimators should be preferred. Plotting-position estimators may still be useful for estimating extreme upper tail quantiles in regional frequency analysis.

EXPONENTIAL AND MIXTURE FAMILIES IN QUANTUM STATISTICS : dual structure and unbiased parameter estimation(Analysis of Operators on Gaussian Space and Quantum Probability Theory)

Abstract: The differential-geometric formulation of statistics (the so-called information geometry) concerning the structure of a smooth manifold in the parameter space Θ of classical probabilities, S = {p(·,θ),θ ϵ Θ}, discussed by Amari, is extended to the same manifold but for quantum states (density matrices), S = {ϱ(θ);θ ϵ Θ} in N × N matrix algebras. This is done by introducing an n-tuple of tangent vectors {δ}ni = 1 in analogy to the classical ones {∂i}ni = 1. On this basis, a special problem of quantum information geometry is treated; namely, the analysis of the exponential and the mixture families defined, respectively, as (e) ϱ(θ) = exp(θi Ai − ψ(θ)). θ ϵ Θ = Rn. Ai ϵ Bs(HN) . (m) ϱ(θ) = θiAi + θ0 A0. θ ϵ Θ = (0,1)n + 1. ∑i=0nθi=1. Ai ϵ B+(HN) Tr Ai = 1 (the tensorial summation convention for repeated indices is used). We prove some of the basic theorems known in the classical information geometry by extending the formulation to a non-commutative smooth manifold. We establish the existence of a pair of dual affine coordinate systems in (e) or (m) and a projection theorem in order to ensure the Cramer-Rao inequality and an identification of the efficient estimator.

The rao-blackwell theorem in stereology and some counterexamples

Abstract: A version of the Rao–Blackwell theorem is shown to apply to most, but not all, stereological sampling designs. Estimators based on random test grids typically have larger variance than quadrat estimators; random s-dimensional samples are worse than random r-dimensional samples for s < r. Furthermore, the standard stereological ratio estimators of different dimensions are canonically related to each other by the Rao–Blackwell process. However, there are realistic cases where sampling with a lower-dimensional probe increases efficiency. For example, estimators based on (conditionally) non-randomised test point grids may have smaller variance than quadrat estimators. Relative efficiency is related to issues in geostatistics and the theory of wide-sense stationary random fields. A uniform minimum variance unbiased estimator typically does not exist in our context.

Efficiencies of six almost unbiased ratio estimators under a particular model

Abstract: Efficiencies of six almost unbiased estimators for the ratio of population means of two characters, are compared under a linear regression model.

A Jackknife Method for Estimation of Variance Components

Abstract: This paper concerns a method of estimation of variance components in a random effect linear model. It is mainly a resampling method and relies on the Jackknife principle. The derived estimators are presented as least squares estimators in an appropriate linear model, and one of them appears as a MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimator. Our resampling method is illustrated by an example given by C. R. Rao [7] and some optimal properties of our estimator are derived for this example. In the last part, this method is used to derive an estimation of variance components in a random effect linear model when one of the components is assumed to be known.

A note on the efficiencies of two almost unbiased predictive ratio estimators

Abstract: Using the predictive approach advocated by Basu (1971), we consider two almost unbiased ratio estimators of the population mean and study their efficiencies under a linear model.

On non-negative unbiased estimation of quadratic forms in finite population sampling

Abstract: Summary The paper investigates non-negative quadratic unbiased (NnQU) estimators of positive semi-definite quadratic forms, for use during the survey sampling of finite population values. It examines several different NnQU estimators of the variance of estimators of population total, under various sampling designs. It identifies an optimal quadratic unbiased estimator of the variance of the Horvitz-Thompson estimator of population total.

Non-Normal Error Patterns: How to Handle Them

Abstract: The problems of heteroscedasticity and autocorrelation of residuals can occur because of misspecificaiion of a regression model...before doing anything, make sure that the model is correctly specified...ARCH models can simultaneously make corrections for both heter-oscedasicity and autocorrelation. In a recent article in this journal, Wang and Akabay (W & A) discuss the problems associated with the detection and elimination of heteroscedastic error terms. Normally heteroscedasticity is a problem in cross sectional data, but it can be a problem in time series data, particularly when there has been a substantial increase or decrease in the value of the dependent variable in a short time interval, causing the regression variance to increase or decrease. Wang and Akabay's first example involves time series data, and they provide the data that are used in the analysis in their article. In order to generate unbiased regression results, using ordinary least squares (OLS), the error terms must be normally distributed, thus uncorrelated either to any of the independent variables or to themselves with any lag. In the first case, the issue of heteroscedasticity is being addressed; in the second, autocorrelation. W & A consider only the first issue in their article since their intent is to demonstrate the corrections tat are necessary to mitigate the effects of heteroscedasticity. In a subsequent article, the same authors demonstrate the correction techniques for autocorrelation. Normal practice, in examining errors for heteroscedasticity, is to plot the errors against the independent variables and to perform a Goldfeld-Quandt, Spearman, Glejser, Park, Likelihood ratio, or Breusch and Pagan test. Normal practice, in the case of autocorrelation, is to examine the correlation of the error term u sub t with u sub t-a using the Durbin-Watson test or Theil U Statistic (for regressions with lagged dependent variables). Adjoining error terms are used (a = 1) since, in the case presented, the data are annual and have no seasonality. If seasonality exists in the data, the model should include a set of seasonal variables to "explain" the seasonality pattern in the dependent variable. One of the key issues is how to proceed if both problems occur simultaneously in the data and are reflected in the OLS regression results. A second key issue is the evaluation of the regression equation to see if it has been correctly specified. Misspecified equations often have non-normal residuals, but the residuals in this case can be corrected by respecifying, the regression model rather than through a manipulation of the dependent and independent variables. This paper will discuss these two issues in further detail as a means of explaining alternative approaches to the problem of simultaneous presence of autocorrelation and heteroscedasticity in regression results. CAUSES AND CONSEQUENCES Regressions performed on business and economic data often have both auto-correlation and heteroscedasticity. This is particularly true in financial data which is often characterized by shocks or clusters of points that reflect both unusually large and autocorrelated errors. If these problems are left uncorrected in the model, they will adversely affect the accuracy of the forecast. Since the statistical correction procedures are different for each problem it may appear logical to first correct for one and then correct for the other. For example, it may appear logical to first correct for heteroscedasticity employing one of the approaches presented by W & A, and then applying the autocorrelation correction procedures presented by W & A in their subsequent article. Rather than using this methodology an alternative methodology has been developed that accounts for both autocorrelation and heteroscedasticity. This methodology assumes that the error terms are related to each other, lagged by one or more periods in both size and sign. …

An almost unbiased iterative ratio-product estimator

Abstract: In finite population sampling it is common to use information from one or several auxiliary variables through indirect estimators, such as ratio or product estimators. We propose an alternative estimator to the generalized multivariate estimator for cases where several auxiliary variables correlate either positively or negatively with the main variable. This new almost unbiased estimator based on the jackknife technique is always more precise than either the simple expansion estimator (the sample mean) or than the ratio, product, or ratio - product estimators built using any of the available auxiliary variables.

On the connection between polynomial and Poisson plans of random walks

Abstract: In the present paper we consider the relation between the distributions of probability of attaining the boundary point of a polynomial plan and that of a Poisson plan. This relation is used to compare the moments of the functions of the boundary point coordinates, the closedness and completeness conditions of plans, the classes of the unbiased estimates and the unbiased estimated functions of the unknown parameters.

Unbiased estimation for negative-binomial random walks

Abstract: Unbiased estimates are proposed for some functions of parameters of distributions generated by negative-binomial random walks.