Some Improved Estimators of Population Mean using Two-Phase Sampling Scheme in the Presence of Non-Response

In the present paper, we have proposed some improved estimators of the population mean utilizing the information on two auxiliary variables adopting the idea of two-phase sampling under non-response. In order to propose the estimators, we have assumed that the study variable and first auxiliary variable suffer from non-response while the second (additional) auxiliary variable is free from non-response. We have derived the expressions for biases and mean square errors of the proposed estimators and compared them with that of usual estimator and some well known existing estimators of the population mean. The theoretical results have also been illustrated with some empirical data.

The Estimation of Finite Population Variance Under Stratified Sampling Technique

The efficiency of the study variable can be improved by incorporating the information from the known auxiliary variables. Usually two techniques ratio and regression estimation are used with the help of auxiliary information in different approaches to acquire the high precision of the estimators. Considering the very heterogeneous population to get the size of the sample it may be originating impossible to get a sufficiently accurate and precise estimate by taking the simple random sampling technique from the complete population. Occasionally taking sample issue may differ significantly in different part of the entire population. For example, under study population consists of people living in apartments, own homes, hospitals and prisons or people living in plain regions and hill regions so in such situations the stratified sampling is one of the most commonly used approach to get a representative sample in survey sampling from different cross units of the population. The present study is set out on the recommendation of generalized variance estimators for finite population variance incorporating stratified sampling scheme with the information of single and two transformed auxiliary variables. The expressions of bias and mean square error (MSE) are obtained for the advised exponential type estimators. The conditions are obtained for which the anticipated estimators are better than the usual estimator. An empirical and simulation study is conducted to prove the superiority of the recommended estimator.

The Capability Index when Some Assumptions are not Satisfied: Analysis and Empirical Comparisons

The process capability index (PCI) evaluates the ability of a process to produce items with certain quality requirements. The PCI depends on the process standard deviation, which is usually unknown and estimated by using the sample standard deviation. The construction of confidence intervals for the PCI is also an important topic. The usual estimator of the PCI and its corresponding confidence interval are based on various assumptions, such as normality, the fact that the process is under control, or samples selected from infinite populations. The main aim of this paper is to investigate the empirical properties of estimators of the PCI, and analyze numerically the effect on confidence intervals when such assumptions are not satisfied, since these situations may arise in practice.

On the Bias of Precision Estimation Under Separate Sampling

Observational case-control studies for biomarker discovery in cancer studies often collect data that are sampled separately from the case and control populations. We present an analysis of the bias in the estimation of the precision of classifiers designed on separately sampled data. The analysis consists of both theoretical and numerical results, which show that classifier precision estimates can display strong bias under separating sampling, with the bias magnitude depending on the difference between the true case prevalence in the population and the sample prevalence in the data. We show that this bias is systematic in the sense that it cannot be reduced by increasing sample size. If information about the true case prevalence is available from public health records, then a modified precision estimator that uses the known prevalence displays smaller bias, which can in fact be reduced to zero as sample size increases under regularity conditions on the classification algorithm. The accuracy of the theoretical analysis and the performance of the precision estimators under separate sampling are confirmed by numerical experiments using synthetic and real data from published observational case-control studies. The results with real data confirmed that under separately sampled data, the usual estimator produces larger, ie, more optimistic, precision estimates than the estimator using the true prevalence value.

Education composition and growth: A pooled mean group analysis of OECD countries

This paper uses the pooled mean group (PMG) estimator and a dataset restricted to OECD countries to examine the relationship between different levels of education, i.e. between education composition and growth. The PMG estimator allows a greater degree of parameter heterogeneity than the usual estimator procedures used in empirical growth studies by imposing common long run relationships across countries while allowing for heterogeneity in the short run responses and intercepts. Results point to a significant longterm relationship not only between higher education and growth but also between lower schooling levels and growth. This indicates that public spending on education in OECD countries should be spread across the different levels of education in a balanced way.

Using auxiliary information to estimate stand tables

The problem of estimating stand tables in stands with few sample points is considered. The usual point-sampling estimate of trees per hectare by diameter class is examined, along with two alternative estimators: a precision-weighted composite estimator and a pseudo-Bayes estimator. A large-scale forest inventory is simulated, and stand tables are estimated for each stand with each of the three estimators. Both the composite and pseudo-Bayes estimator appear superior (in terms of mean absolute error and mean squared error) to the usual estimator. The pseudo-Bayes estimator appears to perform the best (with an 80% reduction in mean squared error). This estimator also is easier to use than the composite estimator because it does not require within diameter class variance estimates.

Outlier-resistant estimators for Poisson sampling: a note

Poisson (3P) sampling is a commonly used method for generating estimates of timber volume. The usual estimator employed is the adjusted estimator, Y hata. The efficiency of this estimator can be greatly influenced by the presence of outliers. We formalize such a realistic situation for high-value timber estimation for which Y hata is inefficient. Here, yi approx beta xi for all but a few units in a population for which yi is large and xi very small. This situation can occur when estimating the net volume of high-value standing timber, such as that found in the Pacific Northwest region of the United States. A generalized regression estimator and an approximate Srivastava estimator are not affected by such data points. Simulations on a small population illustrate these ideas.

The Improved Estimation of σ in Quality Control, Revisited

Recently, Derman and Ross (1995, An improved estimator of a in quality control, Probability in the Engineering and Informational Sciences 9: 411–415) derived an estimator of the standard deviation in the standard quality control model and showed that it had smaller mean squared error than the usual estimator. The new estimator was also shown to be consistent even when the underlying distribution deviates from normality, unlike the usual estimator. In this note, the mean squared error is further improved via shrinkage of the Derman-Ross estimator, and a consistent minimum variance unbiased estimator is presented. Finally, by making use of additional subgroup statistics, a minimum variance unbiased estimator is derived and further improved via shrinkage.

An Improved Estimator of σ in Quality Control

We present a new estimator for the standard deviation parameter in the standard quality control model. We argue that it has a smaller mean square error than the usual estimator when the data are normal and that, unlike the usual estimator, it remains consistent even when the data are not normal.