scholarly journals On covariance estimation when nonrespondents are subsampled

2008 ◽  
Vol 5 (2) ◽  
Author(s):  
Wojciech Gamrot
Keyword(s):  
Finite Population ◽  
General Procedure ◽  
Covariance Estimation ◽  
Sample Survey ◽  
Double Sampling ◽  
Parameter Estimates ◽  
Initial Sample ◽  
Two Phase ◽  
Special Cases ◽  
Combined Data

The phenomenon of nonresponse in a sample survey reduces the precision of parameter estimates and introduces the bias. Several procedures have been developed to compensate for these effects. An important technique is the two-phase (or double) sampling scheme which relies on subsampling the nonrespondents and re-approaching them in order to obtain the missing data. This paper focuses on the application of double sampling to estimate the finite population covariance. Two covariance estimators using combined data from the initial sample and the subsample are considered. Their properties are derived. Two special cases of the general procedure are discussed.

scholarly journals Use of Auxiliary Variables and Asymptotically Optimum Estimators in Double Sampling

2016 ◽  
Vol 5 (3) ◽  
pp. 55 ◽  
Author(s):  
M. E. Kanwai ◽  
O. E. Asiribo ◽  
A. Isah
Keyword(s):  
Mean Squared Error ◽  
Population Level ◽  
Auxiliary Variable ◽  
Sample Survey ◽  
Comparative Approach ◽  
Double Sampling ◽  
Auxiliary Variables ◽  
Two Phase ◽  
Optimum Estimator ◽  
The Mean

This paper explore the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators. The study proposed two types of estimators with two auxiliary variables for two phase sampling when there is no information about auxiliary variables at population level. The expressions for the Mean Squared Error (MSE) of the proposed estimators were derived to the first order of approximation. An empirical comparative approach of the minimum variances and percent relative efficiency were adopted to study the efficiency of the proposed and existing estimators. It was established that, the proposed estimators performed more efficiently than the mean per unit estimator and other previous estimators that don’t use auxiliary variable and that are not asymptotically optimum. Also, it was established that estimators that are asymptotically optimum that utilized single auxiliary variable are more efficient than those that are not asymptotically optimum with two auxiliary variables.

scholarly journals A class of ratio-type estimators under two-phase sampling in the presence of auxilary variables

2019 ◽  
Vol 53 (1) ◽  
pp. 79-91
Author(s):  
P. A. Patel ◽  
F. H. Shah
Keyword(s):  
Finite Population ◽  
Natural Populations ◽  
Small Scale ◽  
Two Phase ◽  
Population Mean ◽  
First Order ◽  
Special Cases ◽  
Phase Sampling ◽  
Class Of Estimators ◽  
Two Phase Sampling

This paper deals with the estimation of population mean under two-phase sampling. Utilizing information on two-auxiliary variables, a class of estimators for estimating the finite population mean is proposed, and its properties, up to the first order of approximation, are studied. Various estimators are suggested as special cases of this class. The performance of the suggested estimators is compared with some contemporary estimators of population mean through numerical illustrations carried over existing datasets of some natural populations. Also, a small scale Monte Carlo simulation is carried out for the empirical comparison.

Formulation of a General Multiphase, Multicomponent Chemical Flood Model

1981 ◽  
Vol 21 (01) ◽  
pp. 63-76 ◽  
Author(s):  
Paul D. Fleming ◽  
Charles P. Thomas ◽  
William K. Winter
Keyword(s):  
Phase Equilibrium ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Field Tests ◽  
Reservoir Rock ◽  
Phase System ◽  
Surfactant Flooding ◽  
Two Phase ◽  
Special Cases ◽  
Flood Model

Abstract A general multiphase, multicomponent chemical flood model has been formulated. The set of mass conservation laws for each component in an isothermal system is closed by assuming local thermodynamic (phase) equilibrium, Darcy's law for multiphase flow through porous media, and Fick's law of diffusion. For the special case of binary, two-phase flow of nonmixing incompressible fluids, the equations reduce to those of Buckley and Leverett. The Buckley-Leverett equations also may be obtained for significant fractions of both components in the phases if the two phases are sufficiently incompressible. To illustrate the usefulness of the approach, a simple chemical flood model for a ternary, two-phase system is obtained which can be applied to surfactant flooding, polymer flooding, caustic flooding, etc. Introduction Field tests of various forms of surfactant flooding currently are under way or planned at a number of locations throughout the country.1 The chemical systems used have become quite complicated, often containing up to six components (water, oil, surfactant, alcohol, salt, and polymer). The interactions of these components with each other and with the reservoir rock and fluids are complex and have been the subject of many laboratory investigations.2–22 To aid in organizing and understanding laboratory work, as well as providing a means of extrapolating laboratory results to field situations, a mathematical description of the process is needed. Although it seems certain that mathematical simulations of such processes are being performed, models aimed specifically at the process have been reported only recently in the literature.23–31 It is likely that many such simulations are being performed on variants of immiscible, miscible, and compositional models that do not account for all the facets of a micellar/polymer process. To help put the many factors of such a process in proper perspective, a generalized model has been formulated incorporating an arbitrary number of components and an arbitrary number of phases. The development assumes isothermal conditions and local phase equilibrium. Darcy's law32,33 is assumed to apply to the flow of separate phases, and Fick's law34 of diffusion is applied to components within a phase. The general development also provides for mass transfer of all components between phases, the adsorption of components by the porous medium, compressibility, gravity segregation effects, and pressure differences between phases. With the proper simplifying assumptions, the general model is shown to degenerate into more familiar special cases. Numerical solutions of special cases of interest are presented elsewhere.35

scholarly journals Generalized second-order slip for unsteady convective flow of a nanofluid: a utilization of Buongiorno’s two-component nonhomogeneous equilibrium model

2020 ◽  
Vol 9 (1) ◽  
pp. 156-168
Author(s):  
Seyed Mahdi Mousavi ◽  
Saeed Dinarvand ◽  
Mohammad Eftekhari Yazdi
Keyword(s):  
Boundary Layer ◽  
Equilibrium Model ◽  
Second Order ◽  
Model Parameters ◽  
Slip Parameter ◽  
Two Phase ◽  
Convective Boundary ◽  
First Order ◽  
Special Cases ◽  
Two Component

AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

A Simulation Procedure for Panel Age Forming

1998 ◽  
Vol 120 (2) ◽  
pp. 183-190 ◽  
Author(s):  
S. P. Narimetla ◽  
J. Peddieson ◽  
G. R. Buchanan ◽  
S. Foroudastan
Keyword(s):  
Aluminum Alloy ◽  
General Procedure ◽  
7075 Aluminum Alloy ◽  
Simulation Procedure ◽  
Special Cases ◽  
Tool Shape ◽  
Loading And Unloading ◽  
Linear Loading ◽  
Three Phases

A method of simulating the age forming of initially flat panels is proposed. It conceptually divides the process into three phases (loading, aging, and unloading) and simulates each phase separately. Some sample simulations are presented for 7075 aluminum alloy based on a simplified version of the general procedure (linear loading and unloading, nonlinear aging). The results of these simulations are used to illustrate several aspects of the predictions. An interesting finding is that the part shape and tool shape are geometrically similar in two important special cases.

A general procedure for rational inequalities

2015 ◽  
Vol 08 (01) ◽  
pp. 1550014
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
General Procedure ◽  
General Theorem ◽  
Type Inequality ◽  
Special Cases ◽  
Rational Type

Recently Bhatt, Chaukiyal and Dimri proved a fixed point theorem for a pair of maps satisfying a rational type inequality. It is the purpose of this paper to show that this result, along with a number of others, are all special cases of a general theorem of Sehie Park.

A Class of Estimators for a Finite Population Mean Based on Multivariate Information and General two Phase Sampling

1995 ◽  
Vol 45 (3-4) ◽  
pp. 203-218 ◽  
Author(s):  
T. P. Tripathi ◽  
M. S. Ahmed
Keyword(s):  
Finite Population ◽  
Population Data ◽  
Two Phase ◽  
Population Means ◽  
Population Mean ◽  
Phase Sampling ◽  
Optimum Estimator ◽  
Class Of Estimators ◽  
Relative Gains ◽  
Two Phase Sampling

A class of estimators for a finite population mean is presented for the situations where population means of some auxiliary variables are known while those of others are unknown. The results for general two phase sampling are indicated while the detailed discussion is made for the case when SRSWOR is used at both the phases. While several known estimators belong to the proposed clas~ some new estimators are identified as well. The optimum estimator in the proposed class is found to be better than the so-called chain ratio and regression estimators discu ssed by Chand (1975). Kiregyera (1984) and Mukerjee et al. (1987). The relative gains in efficiency of tho proposed optimum estimator over the others are obtained for a natural population data and found to be quite appreciable.

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