A new class of median estimators using auxiliary information under PPS sampling: theoretical properties and empirical evaluation

Summary The problem of optimum allocation to strata has been earlier examined in the light of a priori distributions. In this context, under the criterion of minimum expected variance, the sampling strategy consisting of an unstratified πPS sampling scheme together with the Horvitz–Thompson (HT) estimator was shown to be inferior to the strategy consisting of a stratified πPS sampling scheme with the corresponding HT estimator with this optimum allocation. In this paper, when stratification is based on the auxiliary information, we study whether a stratified πPS sampling strategy with various non-optimal allocations is likely to be worth while and whether it should be attempted at all. For populations commonly met in practice, we derive sufficient conditions for unstratified πPS sampling to be preferable to non-optimal stratified πPS sampling. An illustrative example is provided towards the end of the paper.

PPS sampling has been widely used in the sampling survey, which uses the scale variable as the auxiliary information for the corresponding sampling design and estimation. With the development of various technologies and the advent of big data era, more and more available information turns up in the actual survey, how to select the appropriate variables as auxiliary information is a very important question. Indicator variable is introduced in the pps sampling. Then application method of auxiliary variable in the pps sampling is investigated.

The sustainable use of forests, which is one of the key principles of forest management in Finland, for instance, includes the goal of maintaining forest biodiversity. Dead wood (coarse woody debris, CWD) has been recognized as one of the main indicators of biodiversity in boreal forests and it plays a major role in nutrient cycling, for example. Much effort has therefore been put into the development of new cost-efficient methods for assessing CWD. However, if data are collected for large areas, field inventory may be expensive even when a sample-based method is used. In this thesis, sample-based CWD inventory methods were studied and since airborne laser scanning (ALS) is nowadays regarded as one of the most promising remote sensing methods and is gradually being adopted for predicting living tree characteristics, the possibilities for utilizing ALS data in CWD inventory were investigated. The material comprised data from three areas. Data for a conservation area in Koli were used to study the use of ALS data for estimating downed and standing dead wood volumes in natural forests, and data for commercially managed forests in Sonkajarvi and Juuka were used to study the efficiency of sample-based field inventory methods for assessing CWD. The sampling methods were compared in terms of the accuracy of the estimated mean CWD volume with a fixed input effort specified in fieldwork hours. Furthermore, it was studied how much the use of auxiliary information derived from ALS data or other sources could improve the sampling efficiency, i.e. reduce the standard error of the mean given the same inventory costs. The auxiliary information was used either in the design phase, for ‘probability proportional to size’ (PPS) sampling, or in the estimation phase, for ratio or regression estimation. ALS data proved useful for predicting CWD volumes in natural forests. The RMSEs for downed and standing dead wood, and for the total CWD volume estimates were 51.6%, 78.8% and 54.2%, respectively. It was also observed that ALS-based estimates for downed dead wood volume were substantially more accurate than those based on living tree characteristics measured in the field. The sample-based inventory methods developed for assessing CWD or other rare characteristics were observed to be most efficient field inventory methods, and especially the relascope-based sampling methods were highly efficient. The use of PPS sampling notably improved the efficiency of the CWD inventory, but efficiency was modest when auxiliary information was used in the estimation phase. The improvement in efficiency varied considerably between different inventory methods and CWD materials. Although the efficiency of other inventory methods could be improved more by introducing PPS sampling, relascope-based sampling methods remained the most efficient methods for assessing CWD. It was also observed that the sampling efficiency was not markedly better if ALS data were combined with either aerial photographs or standregister data, and it was usually preferable to use ALS data alone as the auxiliary data source.

This research paper deals with the problem of estimating population mean of study variable using information of auxiliary variable under varying probability and measurement error. Motivated by Kadilar and Cingi, App Math Lett, 2006, 19, 75 and Zaman, Stat Trans‐New Ser, 2020, 21, 159, generalized ratio and product enhanced regressed exponential (ERE) estimators are proposed to estimate the population mean using different auxiliary parameters under the sampling of probability proportional to size (pps) and extended for the case of measurement error. Further, following the strategies of Naik and Gupta, J Ind Soc Agr Stat, 1996, 48, 151; Jhajj et al., Pak J Stat, 2006, 23, 1; Singh et al., Auxiliary Information and A Priori Values in Construction of Improved Estimators, Renaissance High Press, 2007; and Solanki and Singh, Chil J Stat, 2013, 4, 3, conventional ratio, product, regression, generalized and many other types of estimators have been adopted under pps sampling with and without measurement error. Up to the first order of large sample approximation, the bias and mean square error (MSE) of the suggested ERE and adopted estimators are derived and their properties have been studied. Comparisons have been made theoretically and empirically to comprehend the merits of recommended estimators over the conventional and adopted estimators.

Novel Methods For Estimation Of Population Mean Using Auxiliary Information Under PPS Sampling: Application With Real And Simulated Data Sets

This research is centered on the modification of efficient estimators for the population coefficient of variation in the context of simple random sampling, utilizing a single auxiliary variable. The aim is to develop a set of generalized coefficients of variation estimators that enhance the precision and reliability of statistical inference. In this work, ten members of such generalized estimators are proposed, each constructed by integrating auxiliary variable information under the framework of simple random sampling without replacement (SRSWOR). The theoretical properties of these estimators are rigorously examined, with explicit expressions for their biases and mean square errors (MSE) derived up to the first-order approximation through the application of Taylor series expansion techniques. Furthermore, an empirical investigation is carried out using real and/or simulated datasets to compare the performance of the proposed estimators with that of existing ones. The findings reveal that the proposed estimators consistently demonstrate superior efficiency, thereby making them a more effective choice for practical applications in survey sampling and related statistical fields.

This paper deals with estimation of population median in simple and stratified random samplings by using auxiliary information. Auxiliary information is rarely used in estimating population median, although there have been many studies to estimate population mean using auxiliary information. In this study, we suggest some estimators using auxiliary information such as mode and range of an auxiliary variable and correlation coefficient. We also expand these estimators to stratified random sampling for combined and separate estimators. We obtain mean square error equations for all proposed estimators and find theoretical conditions. These conditions are also supported by using numerical examples.

To simultaneously improve parameter estimation and variable selection for a target model by the auxiliary information from source models, a weighted likelihood transfer learning (WL-TL), together with a l 1 -penalty, is proposed for high-dimensional generalized linear models. To implement the transfer learning, the relevant techniques, including iterative algorithm and the choice of weight, are suggested. The methodology is computational simple, without need for the bias-correction used in the existing literature of parameter-transfer learning. The theoretical properties such as the quadratic error bound of the parameter estimator and the estimation consistency are established. A specific weight selection method based on the Bayesian decision theory has been proposed and studied. Comprehensive simulation experiments and real data analyzes are conducted to further illustrate the performance of the new method.

SummarySurveys usually include questions where individuals must select one in a series of possible options that can be sorted. On the other hand, multiple frame surveys are becoming a widely used method to decrease bias due to undercoverage of the target population. In this work, we propose statistical techniques for handling ordinal data coming from a multiple frame survey using complex sampling designs and auxiliary information. Our aim is to estimate proportions when the variable of interest has ordinal outcomes. Two estimators are constructed following model‐assisted generalised regression and model calibration techniques. Theoretical properties are investigated for these estimators. Simulation studies with different sampling procedures are considered to evaluate the performance of the proposed estimators in finite size samples. An application to a real survey on opinions towards immigration is also included.

Inference on covariance-mean regression

We introduce a general model for the local obfuscation of probability distributions by probabilistic perturbation, e.g., by adding differentially private noise, and investigate its theoretical properties. Specifically, we relax a notion of distribution privacy (DistP) by generalizing it to divergence, and propose local obfuscation mechanisms that provide divergence distribution privacy. To provide f-divergence distribution privacy, we prove that probabilistic perturbation noise should be added proportionally to the Earth mover's distance between the probability distributions that we want to make indistinguishable. Furthermore, we introduce a local obfuscation mechanism, which we call a coupling mechanism, that provides divergence distribution privacy while optimizing the utility of obfuscated data by using exact/approximate auxiliary information on the input distributions we want to protect.

The correct estimation of the population variance plays a vital role in the sampling procedure in surveys, especially when simple random sampling techniques are used. In this work, we propose a new generalized statistical inference in order to estimate the population variance using auxiliary information. We can use the relationship between the study variable and the auxiliary variable to construct a novel generalized class of estimators that is better performing in terms of minimum mean squared error (MSE) and has a higher percentage of relative efficiency than the traditional estimators. The proposed methodology is based on the existing methods of inference with the introduction of modifications to cover the known population parameters of additional auxiliary variables, like the mean, the coefficient of variation, skewness, or kurtosis. Theoretical properties such as bias and mean squared error are obtained with regard to the first-order approximation. The performance of the proposed class of estimators is checked by comparing with that of the classical variance estimators in different population conditions based on real-life data sets and a simulation study. The numerical findings have indicated that the suggested class of estimators is more effective compared to classical methods, especially in cases where there is a very high linear correlation between the auxiliary and the study variables. Also, the estimators are robust, as confirmed using various sample sizes and population structures. The research has made a significant contribution to the development of statistical procedures in survey sampling because the practical and efficient tools provided in the study were useful in estimating the variance. The results have been of great importance when applied by researchers and practitioners active in large-scale surveys. Subsequently, in the case of efficient utilization of auxiliary information, it is feasible to have more accurate and cost-effective statistical inference.

Adaptive cluster sampling is a methodology designed for data collection in contexts where the population is rare and spatially clustered. This approach has been effectively applied in various disciplines, including epidemiology and resource management. The present study introduces novel estimators that incorporate auxiliary variable information to improve estimation efficiency. These estimators were developed using the jackknife resampling technique to improve the performance of ratio-type estimators. Theoretical properties, including bias and mean square error (MSE), were derived, and a simulation study was conducted to validate the theoretical findings. The results demonstrated that the proposed estimators consistently outperformed conventional estimators that do not utilize auxiliary variables across all network sample sizes. Furthermore, in several scenarios, the proposed estimators also exhibited superior efficiency to existing ratio estimators that do incorporate auxiliary information.

The present work intended to emphasize the role of several varying auxiliary variates at both the occasions to improve the precision of estimates at current occasion in two-occasion successive sampling. Two different efficient estimators are proposed and their theoretical properties are examined. Relative comparison of efficiencies of the proposed estimators with the sample mean estimator when there is no matching from previous occasion, and the optimum successive sampling estimator when no auxiliary information is used have been incorporated. Empirical studies are significantly justifying the composition of proposed estimators.

The present work emphasizes the role of several stable auxiliary variables at both the occasions to improve the precision of estimates at current occasion in two-occasion successive sampling. A chain-type multiple linear regressions in ratio estimator has been proposed and its theoretical properties are examined. Relative comparison of efficiencies of the proposed estimator with the sample mean estimator, when there is no matching from the previous occasion and the natural successive sampling estimator, when no auxiliary information is used have been made. Theoretical results have been well supported with empirical illustrations. DOI: http://dx.doi.org/10.4038/sljastats.v12i0.4970 Sri Lankan Journal of Applied Statistics Vol.12 2011 pp.101-116