小域估计方法在小品种农作物播种面积统计中的应用

 我国以省级目标总体开展的现行农产量抽样调查,着眼于农作物主要品种的省级推算,而小品种农作物的总体分布比较偏态,往往有效样本量相对不足,不能解决小品种农作物播种面积的推算问题,同时对分县的主要品种农作物播种面积进行的直接推算也不能满足精度要求。现阶段对小品种农作物播种面积的统计方法研究成为农村统计方法制度改革迫切需要研究的课题之一。本文选择了河北省张家口的蔚县,利用小域估计方法对小品种农作物播种面积进行了统计推断,从推断结果看得到了比较好的估计精度。利用蔚县为总体的实际数据进行的抽样仿真分析,从实证的角度阐述了小域估计方法对这一问题的有效性,而且分析结果也表明该方法可以显著提高估计效果。     

基于分层贝叶斯分析的残疾率小域估计方法

小域估计（Small Area Estimation）是抽样调查领域里一个重要的研究方向,国计民生中的许多重要问题如失业率、传染病的发病率和民意测验等抽样调查都需要采用不同的小域估计方法。本文针对小域估计问题,以估计方法发展脉络为主线,以分层贝叶斯分析的小域估计为重点,对小域估计问题的理论、方法和最新进展进行简述,并利用澳大利亚残疾、老龄化和护理者（SDAC 2003）抽样调查实际数据,从分层贝叶斯分析角度对澳大利亚残疾率进行估计,最后对估计结果进行比较和讨论。     

Bounding sample size projections for the area under a ROC curve

Studies of diagnostic tests are often designed with the goal of estimating the area under the receiver operating characteristic curve (AUC) because the AUC is a natural summary of a test's overall diagnostic ability. However, sample size projections dealing with AUCs are very sensitive to assumptions about the variance of the empirical AUC estimator, which depends on two correlation parameters. While these correlation parameters can be estimated from the available data, in practice it is hard to find reliable estimates before the study is conducted. Here we derive achievable bounds on the projected sample size that are free of these two correlation parameters. The lower bound is the smallest sample size that would yield the desired level of precision for some model, while the upper bound is the smallest sample size that would yield the desired level of precision for all models. These bounds are important reference points when designing a single or multi-arm study; they are the absolute minimum and maximum sample size that would ever be required. When the study design includes multiple readers or interpreters of the test, we derive bounds pertaining to the average reader AUC and the ‘pooled’ or overall AUC for the population of readers. These upper bounds for multireader studies are not too conservative when several readers are involved.     

Small area estimation using unmatched sampling and linking models

The authors use a hierarchical Bayes approach to area level unmatched sampling and Unking models for small area estimation. Empirically they compare inferences under unmatched models with those obtained under the customary matched sampling and linking models. They apply the proposed method to Canadian census undercoverage estimation, developing a full hierarchical Bayes approach using Markov Chain Monte Carlo sampling methods. They show that the method can provide efficient model‐based estimates. They use posterior predictive distributions to assess model fit.     

Improving the biomarker diagnostic capacity via functional transformations

The use of the area under the receiver-operating characteristic, ROC, curve (AUC) as an index of diagnostic accuracy is overwhelming in fields such as biomedical science and machine learning. It seems that a larger AUC value has become synonymous with a better performance. The functional transformation of the marker values has been proposed in the specialized literature as a procedure for increasing the AUC and therefore the diagnostic accuracy. However, the classification process is based on some regions (classification subsets) which support the decision made; one subject is classified as positive if its marker is within this region and classified as negative otherwise. In this paper we study the capacity of improving the classification performance of univariate biomarkers via functional transformations and the impact of this transformation on the final classification regions based on a real-world dataset. Particularly, we consider the problem of determining the gender of a subject based on the Mode frequency of his/her voice. The shape of the cumulative distribution function of this characteristic in both the male and the female groups makes the resulting classification problem useful for illustrating the differences between having useful diagnostic rules and obtaining an optimal AUC value. Our point is that improving the AUC by means of a functional transformation can produce classification regions with no practical interpretability. We propose to improve the classification accuracy by making the selection of the classification subsets more flexible while preserving their interpretability. Besides, we provide different graphical approximations which allow us a better understanding of the classification problem.     

Designing a multiple state repetitive group sampling plan based on the coefficient of variation

A multiple state repetitive group sampling (MSRGS) plan is developed on the basis of the coefficient of variation (CV) of the quality characteristic which follows a normal distribution with unknown mean and variance. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which satisfies the given producer's risk and consumer's risk at the same time and minimizes the average sample number required for inspection. The advantages of the proposed MSRGS plan over the existing sampling plans are discussed. Finally an example is given to illustrate the proposed plan.     

A novel spatial outlier detection technique

Spatial outliers are spatially referenced objects whose non spatial attribute values are significantly different from the corresponding values in their spatial neighborhoods. In other words, a spatial outlier is a local instability or an extreme observation that deviates significantly in its spatial neighborhood, but possibly not be in the entire dataset. In this article, we have proposed a novel spatial outlier detection algorithm, location quotient (LQ) for multiple attributes spatial datasets, and compared its performance with the well-known mean and median algorithms for multiple attributes spatial datasets, in the literature. In particular, we have applied the mean, median, and LQ algorithms on a real dataset and on simulated spatial datasets of 13 different sizes to compare their performances. In addition, we have calculated area under the curve values in all the cases, which shows that our proposed algorithm is more powerful than the mean and median algorithms in almost all the considered cases and also plotted receiver operating characteristic curves in some cases.     

Properties of the beta regression model for small area estimation of proportions and application to estimation of poverty rates

Abstract

Linear mixed effects models have been popular in small area estimation problems for modeling survey data when the sample size in one or more areas is too small for reliable inference. However, when the data are restricted to a bounded interval, the linear model may be inappropriate, particularly if the data are near the boundary. Nonlinear sampling models are becoming increasingly popular for small area estimation problems when the normal model is inadequate. This paper studies the use of a beta distribution as an alternative to the normal distribution as a sampling model for survey estimates of proportions which take values in (0, 1). Inference for small area proportions based on the posterior distribution of a beta regression model ensures that point estimates and credible intervals take values in (0, 1). Properties of a hierarchical Bayesian small area model with a beta sampling distribution and logistic link function are presented and compared to those of the linear mixed effect model. Propriety of the posterior distribution using certain noninformative priors is shown, and behavior of the posterior mean as a function of the sampling variance and the model variance is described. An example using 2010 Small Area Income and Poverty Estimates (SAIPE) data is given, and a numerical example studying small sample properties of the model is presented.     

An application of cartographic area interpolation to German administrative data

In many situations the applied researcher wishes to combine different data sources without knowing the exact link and merging rule. This paper considers different cartographic interpolation methods for interpolating attributes from German employment office districts to German counties and vice versa. In particular, we apply dasymetric weighting as an alternative to simple area weighting, both of which are based on estimated intersection areas. We also present conditions under which the choice of interpolation method does not matter and confirm the theoretical results with a simulation study. Our application to German administrative data suggests robustness of estimation results of interpolated attributes with respect to the choice of interpolation method. We provide weighting matrices for regional data sources of the two largest German data producers.     

Use of satellite data in agricultural surveys

A major application of satellite remote sensing is the estimation of the acreage of agricultural crops. The potential for crop yield estimation using satellite remote sensing exists, but research in this area is still in its early stages. In this paper we survey the methodology for using remotely sensed data in agricultural surveys, based primarily on research conducted during the Large Area Crop Inventory Experiment (LACIE) and the follow-on program Agricultural Research and Inventory Surveys Through Aerospace Remote Sensing (AgRISTARS). The data obtained from multispectral scanner (MSS) and thematic mapper (TM) sensors onboard the Landsat series of satellites are described. Approaches for preprocessing, transferring, and modeling these data for understanding the relationship between their temporal behavior and crop growth cycles are discussed. Finally, techniques for crop identification and area and yield estimation are briefly described     

Estimation of Parameters of a Mixed Failure Time Distribution Which is a Mixture of Degenerate (Degenerate at Zero) and I. G. Distribution

The problem of estimation of parameters of a mixture of degenerate (at zero) and exponential distribution is considered by Jayade and Prasad (1990). The sampling scheme proposed in it is extended in this paper to a mixture of degenerate and Inverse Gaussian distribution. The Inverse Gaussian distribution is very relevant for studying reliability and life-testing problems. The inverse Gaussian being the first passage time distribution for Wiener process makes it particularly appropriate for failure or reaction time data analysis.     

Economic statistical design of X‾-control charts: Modified version of Rahim and Banerjee (1993) model

Rahim and Banerjee considered a constant integral of the hazard function for all sampling intervals. This led the sampling intervals to depend on the extended first sampling interval (h₁). Since this limitation might not lead to an optimal situation, we first showed that elimination of the mentioned restriction did not cause any significant change in the average quality cycle cost. So if one is looking for an ideal cost and the simplicity of the process, the approach taken in Rahim and Banerjee’s study is the best procedure to adopt. Moreover, in many cases of non-uniform sampling method the first sampling interval becomes so large and this can sometimes lead the production system to the out-of-control state due to unexpected failures that might happen during that time. Therefore, we proposed a new model of uniform and non-uniform sampling intervals combination that allows us to confine the value of h₁ without undergoing high costs. The proposed model showed that the quality cycle cost of the proposed model is lower than Rahim and Banerjee’s model in the economic-statistical state. For more illustration, we conducted sensitivity analysis and gave numerical examples.     

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

An acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product, based on adherence to a standard. Meanwhile, process capability indices (PCIs) have been applied in different manufacturing industries as capability measures based on specified criteria which include process departure from a target, process consistency, process yield and process loss. In this paper, a repetitive group sampling (RGS) plan based on PCI is introduced for variables’ inspection. First, the optimal parameters of the developed RGS plan are obtained considering constraints related to the risk of consumers and producers and also a double sampling plan, a multiple dependent state sampling plan and a sampling plan for resubmitted lots have been designed. Finally, after the development of variable sampling plans based on the Bayesian and exact approach, a comparison study has been performed between the developed RGS plan and other types of sampling plans and the results are elaborated.     

遥感辅助的农作物种植面积小域估计方法研究

遥感影像是大数据的一种,利用遥感对农作物播种面积进行估算常采用回归估计量或校准估计量,通常都需要将地面样本数据与遥感分类信息相结合。但对于大多数回归估计量,对省级总体的农作物面积估算只能满足对省级总体的精度要求而不能分解到更小区域,比如县和乡级。本文利用黑龙江省2011年的地面实测样本数据结合遥感分类结果,构建了单元层次的多响应变量的多元回归形式的小域模型,并将小域效应设定为固定形式。这样基于回归估计方法,既可以估算分县的主要作物播种面积,也可以使得各县播种面积估计结果相加就等于回归模型含义下的省级总体的总量估计。对黑龙江省玉米、水稻、大豆分县小域估计结果的精度评价（变异系数C.V）,平均而言均可以满足县级精度要求。本文的结果表明小域估计方法在解决省级总体对全省和分县的农作物种植面积多级估算问题中具有很好的应用。     

Risk Comparison of Inequality Constrained Estimators in the Heteroscedastic Linear Model

There exist many studies which treat the inequality and/or interval constraints on coefficients in the homoscedastic linear regression model. However, the sampling performance of the inequality constrained estimators in the heteroscedastic linear model has not been examined. This paper considers the inequality constrained estimators in the heteroscedastic linear regression model and derives their risks under a quadratic loss function. Furthermore, using the inequality constrained estimators, we introduce a pre-test estimator which might be employed after the test for homoscedasticity and derive its risk. In addition, the risk performance of these estimators is evaluated numerically.     

Empirical best linear unbiased and empirical Bayes prediction in multivariate small area estimation

Small area estimation plays a prominent role in survey sampling due to a growing demand for reliable small area estimates from both public and private sectors. Popularity of model-based inference is increasing in survey sampling, particularly, in small area estimation. The estimates of the small area parameters can profitably ‘borrow strength’ from data on related multiple characteristics and/or auxiliary variables from other neighboring areas through appropriate models. Fay (1987, Small Area Statistics, Wiley, New York, pp. 91–102) proposed multivariate regression for small area estimation of multiple characteristics. The success of this modeling rests essentially on the strength of correlation of these dependent variables. To estimate small area mean vectors of multiple characteristics, multivariate modeling has been proposed in the literature via a multivariate variance components model. We use this approach to empirical best linear unbiased and empirical Bayes prediction of small area mean vectors. We use data from Battese et al. (1988, J. Amer. Statist. Assoc. 83, 28 –36) to conduct a simulation which shows that the multivariate approach may achieve substantial improvement over the usual univariate approach.     

Bootstrapping in a high dimensional but very low-sample size problem

This article is concerned with testing multiple hypotheses, one for each of a large number of small data sets. Such data are sometimes referred to as high-dimensional, low-sample size data. Our model assumes that each observation within a randomly selected small data set follows a mixture of C shifted and rescaled versions of an arbitrary density f. A novel kernel density estimation scheme, in conjunction with clustering methods, is applied to estimate f. Bayes information criterion and a new criterion weighted mean of within-cluster variances are used to estimate C, which is the number of mixture components or clusters. These results are applied to the multiple testing problem. The null sampling distribution of each test statistic is determined by f, and hence a bootstrap procedure that resamples from an estimate of f is used to approximate this null distribution.     

Designing sampling plans to capture rare objects

This article focuses on two‐phase sampling designs for a population with unknown number of rare objects. The first phase is used to estimate the number of rare or potentially rare objects in a population, and the second phase to design sampling plans to capture a certain number or a certain proportion of such type of objects. A hypergeometric‐binomial model is applied to infer the number of rare or potentially rare objects and Monte Carlo simulation based approaches are developed to calculate needed sample sizes. Simulations and real data applications are discussed. The Canadian Journal of Statistics 37: 417–434; 2009 © 2009 Statistical Society of Canada     

Penalized Weighted Least Squares to Small Area Estimation

In this paper, a penalized weighted least squares approach is proposed for small area estimation under the unit level model. The new method not only unifies the traditional empirical best linear unbiased prediction that does not take sampling design into account and the pseudo‐empirical best linear unbiased prediction that incorporates sampling weights but also has the desirable robustness property to model misspecification compared with existing methods. The empirical small area estimator is given, and the corresponding second‐order approximation to mean squared error estimator is derived. Numerical comparisons based on synthetic and real data sets show superior performance of the proposed method to currently available estimators in the literature.