Estimating time to detect time trends in continuous cropping

SUMMARY In long-term field trials comparing different sequences of crops and husbandry practices, the identification and understanding of trends in productivity over time is an important issue of sustainable crop production. This paper presents a statistical technique for the estimation of time trends in yield variables of a seasonal annual crop under continuous cropping. The estimation procedure incorporates the correlation structure, which is assumed to follow first-order autocorrelation in the errors that arise over time on the same plot. Because large differences in annual rainfall have a major effect on crop performance, rainfall has been allowed for in the estimation of the time trends. Expressions for the number of years (time) required to detect statistically significant time trends have been obtained. Illustrations are based on a 7-year data set of grain and straw yields from a trial in northern Syria. Although agronomic interpretation is not intended in this paper, the barley yield data indicated that a significant time trend can apparently be detected even in a suboptimal data set of 7 years' duration.     

A note on the estimation methods of crop production at the block level

This paper presents a method of estimation of crop-production statistics at smaller geographical levels like a community development block (generally referred to as a block) to make area-specific plans for agricultural development programmes in India. Using available district-level data on crop yield from crop-cutting experiments and data on auxiliary variables from various administrative sources, a suitable regression model is fitted. The fitted model is then used to predict the crop production at the block level. Some scaled estimators are also developed using predicted estimates. An empirical study is also carried out to judge the merits of the proposed estimators.     

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 land equivalent ratios

The estimation of the land equivalent ratios is proposed to be done by the (sum of) ratios of means of intercrop yield to sole crop yield. The bias and standard error of the estimates are obtained for large samples. Comparisons of the cropping systems have been made on the basis of these estimates and illustrated with field data.     

Sampling designs for landsat crop surveys

The problem of designing large scale crop surveys which utilize Landsat data is addressed in this paper. Emphasis is on stratification and sampling approaches designed to achieve preselected precisions while permitting manageable data processing and survey costs. A dynamic area sampling frame which is versatile and highly suited for sampling of Landsat data is discussed along with the use of rotation sampling for incorporating multiple years of information into the area estimation     

Modelling spatial-temporal covariance structures in monocropping barley trials

In long-term trials, not only are individual plot errors correlated over time but there is also a consistent underlying spatial variability in field conditions. The current study sought the most appropriate covariance structure of errors correlated in three dimensions for evaluating the productivity and time-trends in the barley yield data from the monocropping system established in northern Syria. The best spatial-temporal model found reflected the contribution of autocorrelations in spatial and temporal dimensions with estimates varying with the yield variable and location. Compared with a control structure based on independent errors, this covariance structure improved the significance of the fertilizer effect and the interaction with year. Time-trends were estimated in two ways: by accounting the seasonal variable contribution in annual variability (Method 1), which is suitable for detecting significant trends in short data series; and by using the linear component of the orthogonal polynomial on time (year), which is appropriate for long series (Method 2). Method 1 strengthened time-trend detection compared with the method of Jones and Singh [J. Agri. Sci., Cambridge 135 (2000), pp. 251-259] which assumed independence of temporal errors. Most estimates of yield trends over time from fertilizer application were numerically greater than the corresponding linear trends estimated from orthogonal polynomials in time (Method 2), reflecting the effect of accounting for seasonal variables. Grain yield declined over time at the drier site in the absence of nitrogen or phosphorus application, but positive trends were observed fairly generally for straw yield and for grain yield under higher levels of fertilizer inputs. It is suggested that analyses of long-term trials on other crops and cropping systems in other agro-ecological zones could be improved by taking spatial and temporal variability into account in the data evaluation.     

A family of estimators of population variance in two-occasion rotation patterns

Abstract

In this article, we have considered the problem of estimation of population variance on current (second) occasion in two occasion successive (rotation) sampling. A class of estimators of population variance has been proposed and its asymptotic properties have been discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion and the Singh et al. (2013) estimator. Optimum replacement policy is discussed. It has been shown that the suggested estimator is more efficient than the Singh et al. (2013) estimator and a usual unbiased estimator when there is no matching. An empirical study is carried out in support of the present study.     

Incomplete block designs for complete diallel crosses and their analysis

A large number of incomplete block designs for Griffing's complete diallel cross-systems I, II and III, involving from five to 12 lines, are suggested, using two-associate triangular partially balanced incomplete block designs. Analysis of incomplete block designs for complete diallel cross-systems has been carried out assuming the most appropriate model for genetic yield, as advocated by Hinklemnann. This includes estimation of the general combining ability, specific combining ability and reciprocal cross- effects. An illustration of the design for each system is presented.     

Estimating crop yield via Gaussian quadrature

The present study proposes a method to estimate the yield of a crop. The proposed Gaussian quadrature (GQ) method makes it possible to estimate the crop yield from a smaller subsample. Identification of plots and corresponding weights to be assigned to the yield of plots comprising a subsample is done with the help of information about the full sample on certain auxiliary variables relating to biometrical characteristics of the plant. Computational experience reveals that the proposed method leads to about 78% reduction in sample size with absolute percentage error of 2.7%. Performance of the proposed method has been compared with that of random sampling on the basis of the values of average absolute percentage error and standard deviation of yield estimates obtained from 40 samples of comparable size. Interestingly, average absolute percentage error as well as standard deviation is considerably smaller for the GQ estimates than for the random sample estimates. The proposed method is quite general and can be applied for other crops as well-provided information on auxiliary variables relating to yield contributing biometrical characteristics is available.     

三维平衡轮换的多水平抽样调查设计研究综述及应用

现行的多水平抽样调查使用的各种形式的轮换模式,在西方各国均得到了广泛应用,但也存在着一系列问题。鉴此,通过对各种形式轮换模式的归纳统一和理论化综述研究,最终归纳出三维平衡多水平轮换模式设计方法,即将多水平轮换模式设计与后续的抽样估计方法研究统一起来,不但能够削减各类轮换偏差的负面影响,还能准确度量轮换样本之间的相关关系,并在多水平调查下得出更加准确的连续性抽样数据。此套设计方法具有极大的推广价值。     

Robust small area estimation

Small area estimation has received considerable attention in recent years because of growing demand for small area statistics. Basic area‐level and unit‐level models have been studied in the literature to obtain empirical best linear unbiased prediction (EBLUP) estimators of small area means. Although this classical method is useful for estimating the small area means efficiently under normality assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for small area estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. To estimate the mean squared errors of the robust estimators of small area means, a parametric bootstrap method is adopted here, which is applicable to models with block diagonal covariance structures. Simulations are carried out to study the behaviour of the proposed robust estimators in the presence of outliers, and these estimators are also compared to the EBLUP estimators. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real data to estimate crop areas for counties in Iowa, using farm‐interview data on crop areas and LANDSAT satellite data as auxiliary information. The Canadian Journal of Statistics 37: 381–399; 2009 © 2009 Statistical Society of Canada     

The Bayesian choice of crop variety and fertilizer dose

Recent contributions to the theory of optimizing fertilizer doses in agricultural crop production have introduced Bayesian ideas to incorporate information on crop yield from several environments and on soil nutrients from a soil test, but they have not used a fully Bayesian formulation. We present such a formulation and demonstrate how the resulting Bayes decision procedure can be evaluated in practice by using Markov chain Monte Carlo methods. The approach incorporates expert knowledge of the crop and of regional and local soil conditions and allows a choice of crop variety as well as of fertilizer level. Alternative dose–response functions are expressed in terms of a common interpretable set of parameters to facilitate model comparisons and the specification of prior distributions. The approach is illustrated with a set of yield data from spring barley nitrogen–response trials and is found to be robust to changes in the dose–response function and the prior distribution for indigenous soil nitrogen.     

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。     

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。     

Regression Estimation of Crop Acreages With Transformed Landsat Data as Auxiliary Variables

Methods are developed for combining data collected by satellite with data collected in an area survey to estimate crop acreages. The basic procedure is that of survey regression estimation. Two methods of transforming the satellite information prior to regression estimation are compared.     

On regression method for estimating a population proportion

In this paper the regression method of estimation has been discussed for the estimation of proportion of the units possessing the given characteristic. An unbiased regression type estimator has also been discussed. An unbiased estimator is given for estimating the common MSE/variance of the estimators discussed. The results have also been extended to deal with the populations of a peculiar nature.     

Analysis of two-phase sampling data with semiparametric additive hazards models

Under the case-cohort design introduced by Prentice (Biometrica 73:1–11, 1986), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.     

Long-term experiments and strip plot designs

In a long-term experiment usually the experimenter needs to know whether the effect of a treatment varies over time. But time usually has both a fixed and a random effects over the output and the difficulty in the analysis depends on the particular design considered and the availability of covariates. Actually, as shown in the paper, the presence of covariates can be very useful to model the random effect of time. In this paper a model to analyze data from a long-term strip plot design with covariates is proposed. Its effectiveness will be tested using both simulated and real data from a crop rotation experiment.     

Exploring spatial dependence in area-level random effect model for disaggregate-level crop yield estimation

This paper describes an application of small area estimation (SAE) techniques under area-level spatial random effect models when only area (or district or aggregated) level data are available. In particular, the SAE approach is applied to produce district-level model-based estimates of crop yield for paddy in the state of Uttar Pradesh in India using the data on crop-cutting experiments supervised under the Improvement of Crop Statistics scheme and the secondary data from the Population Census. The diagnostic measures are illustrated to examine the model assumptions as well as reliability and validity of the generated model-based small area estimates. The results show a considerable gain in precision in model-based estimates produced applying SAE. Furthermore, the model-based estimates obtained by exploiting spatial information are more efficient than the one obtained by ignoring this information. However, both of these model-based estimates are more efficient than the direct survey estimate. In many districts, there is no survey data and therefore it is not possible to produce direct survey estimates for these districts. The model-based estimates generated using SAE are still reliable for such districts. These estimates produced by using SAE will provide invaluable information to policy-analysts and decision-makers.     

Joint coverage probability in a simulation study on continuous-time Markov chain parameter estimation

Parameter dependency within data sets in simulation studies is common, especially in models such as continuous-time Markov chains (CTMCs). Additionally, the literature lacks a comprehensive examination of estimation performance for the likelihood-based general multi-state CTMC. Among studies attempting to assess the estimation, none have accounted for dependency among parameter estimates. The purpose of this research is twofold: (1) to develop a multivariate approach for assessing accuracy and precision for simulation studies (2) to add to the literature a comprehensive examination of the estimation of a general 3-state CTMC model. Simulation studies are conducted to analyze longitudinal data with a trinomial outcome using a CTMC with and without covariates. Measures of performance including bias, component-wise coverage probabilities, and joint coverage probabilities are calculated. An application is presented using Alzheimer's disease caregiver stress levels. Comparisons of joint and component-wise parameter estimates yield conflicting inferential results in simulations from models with and without covariates. In conclusion, caution should be taken when conducting simulation studies aiming to assess performance and choice of inference should properly reflect the purpose of the simulation.