On an Efficient Regression Type Estimator

The regression type estimator proposed by KAUR (1985) is considered. Another expression for the approximated mean square error (AMSE), to a first degree of approximation, is obtained. This AMSE is also minimized with respect to a parameter α. Three numerical examples are included. These numerical examples show that this estimator is not significantly more efficient than regression estimator and with respect to ratio and sample mean estimators, it does not always exhibit a high efficiency, as was contended by KAUR (1985). Moreover, an upper bound for the relative precision of the proposed estimator with respect to linear regression estimator is derived.     

A Combined Product Estimator in Sample Survey

For the estimation of the population mean in stratified random sampling a ‘Combined Product Estimator’ is proposed which is more efficient than the ‘Combined Ratio’ and ‘Separate Ratio’ estimators. Also, the proposed estimator have exact expressions for bias and mean square error. An empirical illustration is given to compare the efficiencies of different estimators.     

A Product-Type Estimator in Double Sampling

The use of ratio and product estimators, using auxiliary information, for estimating the mean of a finite population is well known. The efficiency of ratio estimator or product estimator is high depending on whether the auxiliary character is highly positively or negatively coorelated with the main character of interest. This paper proposes a product-type estimator which is more efficient than the usual ratio and product estimators in practical situations. We consider the case of double sampling from which the single sampling results may easily be derived.     

On the Estimation of Population Mean in Stratified Sampling

When stratified random sampling is used for the estimation of population mean, use of ‘Combined ratio estimator’ is well known. Some improved estimators for population mean are proposed which are better than ‘Combined ratio estimator’ and some other well known existing ones, from the point of view of bias and mean square error. An empirical illustration is given.     

二阶段等距抽样

本文提出了二阶段等距抽样的概念．分第二阶段样本为等距抽样和SRSWOR两种情况讨论了总体平均值的估计问题．在第二阶段抽样为SRSWOR情况下，讨论了辅助信息的利用问题，提出了总体平均值的比型估计和回归型估计．并通过一个实际计算的例子，对文中提出的不同估计量进行了比较．     

An Alternative Approach to Estimation in Two-Phase Sampling Using two Auxiliary Variables

Using two-phase sampling mechanism, two alternative estimators in the presence of the available knowledge on second auxiliary variable z are considered, when the population mean of the main auxiliary variable × is unknown. The suggested estimators are found to be more eficient than the ratio-type and regression-type estimators suggested by KIREGYERA (1980, 1984).     

Improved Generalized Ratio-Cum-Product Estimation

In this paper, a generalized ratio-cum-product estimator for estimating the ratio (product) of two population means using auxiliary information on two other variables is given of which the estimators by SINGH (1969) and SHAH and SHAH (1978) are particular cases. The estimator is regeneralized when the covariance between two auxiliary variables is known.     

Estimation of Population Regression Coefficient in Successive Sampling

An attempt has been made to derive the theory of successive sampling for estimation of regression coefficient. The situations considered are estimation of regression coefficient for current occasion, estimation of change of regression coefficients over two occasions and estimation of average of regression coefficients over two occasions. The expressions of optimum estimators along with their variances have been worked out. On comparing their efficiencies empirically, it has been observed that similar to the estimation of mean, successive sampling can also be used with advantage for estimation of regression coefficient.     

An Improved Estimator of the Variance of the Regression Estimator

In this paper, the problem of estimation of variance of the general linear regression estimator has been considered. It has been shown that the first order calibration approach is a special case of the class of estimators proposed by Deng and Wu (1987). A second order calibration approach is suggested. Some new estimators are shown to be the special case of the proposed calibration approach. The efficiency of the proposed strategy is shown to improve on the original strategy. An idea to find a non-negative estimate of variance has been suggested.     

Estimation of Partial Regression Coefficient

A sampling scheme providing unbiased partial regression coefficient has been proposed. The proposed sampling scheme is not only unbiased but also superior to simple random sampling and that due to Singh and Bathla (1990) for estimation of partial regression coefficient.     

Shrinkage and Pretest Nonparametric Estimation of Regression Parameters from Censored Data with Multiple Observations at Each Level of Covariate

A simple linear regression model is considered where the independent variable assumes only a finite number of values and the response variable is randomly right censored. However, the censoring distribution may depend on the covariate values. A class of noniterative estimators for the slope parameter, namely, the noniterative unrestricted estimator, noniterative restricted estimator and noniterative improved pretest estimator are proposed. The asymptotic bias and mean squared errors of the proposed estimators are derived and compared. The relative dominance picture of the estimators is investigated. A simulation study is also performed to asses the properties of the various estimators for small samples.     

Ratio Estimators in Stratified Random Sampling

This paper considers some ratio‐type estimators and their properties are studied in stratified random sampling. The results are supported by an application with original data.     

Some Remarks on the Estimation of Mean in the Normal Population

This paper generalizes the estimator proposed by Searles (1964) and further studied by SRIVASTAVA (1980) and gives some expressions for the first two moments and an integral representation for the α^th raw moment. The latter is found suitable for computational purposes. Some points in SRIVASTAVA'S (1980) paper are also clarified. Efficiencies of 3 estimators belonging to this class are analyzed with respect to the usual sample mean.     

Sampling strategy matters to accurately estimate response curves' parameters in species distribution models

Aim

Assessing how different sampling strategies affect the accuracy and precision of species response curves estimated by parametric species distribution models.

Major Taxa Studied

Virtual plant species.

Location

Abruzzo (Italy).

Time Period

Timeless (simulated data).

Methods

We simulated the occurrence of two virtual species with different ecology (generalist vs specialist) and distribution extent. We sampled their occurrence following different sampling strategies: random, stratified, systematic, topographic, uniform within the environmental space (hereafter, uniform) and close to roads. For each sampling design and species, we ran 500 simulations at increasing sampling efforts (total: 42,000 replicates). For each replicate, we fitted a binomial generalised linear model, extracted model coefficients for precipitation and temperature, and compared them with true coefficients from the known species' equation. We evaluated the quality of the estimated response curves by computing bias, variance and root mean squared error (RMSE). Additionally, we (i) assessed the impact of missing covariates on the performance of the sampling approaches and (ii) evaluated the effect of incompletely sampling the environmental space on the uniform approach.

Results

For the generalist species, we found the lowest RMSE when uniformly sampling the environmental space, while sampling occurrence data close to roads provided the worst performance. For the specialist species, all sampling designs showed comparable outcomes. Excluding important predictors similarly affected all sampling strategies. Sampling limited portions of the environmental space reduced the performance of the uniform approach, regardless of the portion surveyed.

Main Conclusions

Our results suggest that a proper estimate of the species response curve can be obtained when the choice of the sampling strategy is guided by the species' ecology. Overall, uniformly sampling the environmental space seems more efficient for species with wide environmental tolerances. The advantage of seeking the most appropriate sampling strategy vanishes when modelling species with narrow realised niches.     

Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.     

A Note on Balanced Sampling and Robust Genetic Predictors

The concept of balanced sampling is applied to prediction in finite samples using model based inference procedures. Necessary and sufficient conditions are derived for a general linear model with arbitrary covariance structure to yield the expansion estimator as the best linear unbiased predictor for the mean. The analysis is extended to produce a robust estimator for the mean squared error under balanced sampling and the results are discussed in the context of statistical genetics where appropriate sampling produces simple efficient and robust genetic predictors free from unnecessary genetic assumptions.     

Overlapping Clusters of Tuberculosis Contacts: An Improved Sampling Strategy

A two stage without replacement strategy is proposed for estimating the population mean of overlapping clusters of contacts of tuberculosis cases. This sampling strategy is an improvement over the two sampling strategies proposed by SINGH (1988). A numerical illustration is provided by taking two populations of tuberculosis contacts from New York City; the percentage gain in efficiency varies from 3.70 to 24.99. The proposed improved sampling strategy may be useful to other contagious diseases in the different fields of biomedical sciences or similar situations in other fields.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

Shrinkage Pre-Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student-t Errors

In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student-t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.