Weighted ratio estimation in agricultural surveys

A major problem with satellite-sensed agricultural surveys is loss of data due to cloud cover. The Large Area Crop Inventory Ex¬periment (LACIE) run by three Federal agencies (NASA, NOAA, and USDA) in the years 1974-1977 used a ratioing approach to account for missing data. This approach is found to be reasonable in that it is unbiased with respect to a plausible crop acreage time series model. At the same time, the arbitrary nature of the LACIE proce¬dure's rules for ratioing suggests that improvements to it can be made, thus motivating the discussion of general linear estimators and the development of the 'weighted aggregation' (WAG) procedure. Estimated variances of the LACIE and WAG procedures for an actual LACIE data set indicate that the LACIE procedure, although somewhat heuristic, performs rather well, having an estimated variance 12% higher than that of the WAG, which is theoretically optimal     

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。     

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     

Bias in transition-specific survival and movement probabilities estimated using capture-recapture data

Transition probabilities can be estimated when capture-recapture data are available from each stratum on every capture occasion using a conditional likelihood approach with the Arnason-Schwarz model. To decompose the fundamental transition probabilities into derived parameters, all movement probabilities must sum to 1 and all individuals in stratum r at time i must have the same probability of survival regardless of which stratum the individual is in at time i + 1. If movement occurs among strata at the end of a sampling interval, survival rates of individuals from the same stratum are likely to be equal. However, if movement occurs between sampling periods and survival rates of individuals from the same stratum are not the same, estimates of stratum survival can be confounded with estimates of movement causing both estimates to be biased. Monte Carlo simulations were made of a three-sample model for a population with two strata using SURVIV. When differences were created in transition-specific survival rates for survival rates from the same stratum, relative bias was <2% in estimates of stratum survival and capture rates but relative bias in movement rates was much higher and varied. The magnitude of the relative bias in the movement estimate depended on the relative difference between the transition-specific survival rates and the corresponding stratum survival rate. The direction of the bias in movement rate estimates was opposite to the direction of this difference. Increases in relative bias due to increasing heterogeneity in probabilities of survival, movement and capture were small except when survival and capture probabilities were positively correlated within individuals.     

Using satellite remotely sensed data to estimate crop proportions

A NASA, USDA, and NOAA sponsored experiment called LACIE (Large Area Crop Inventory Experiment) was performed to explore the use of remotely sensed measurements from a satellite-borne sensor to estimate small grains crop acreage. This paper examines the methods used in that experiment to estimate crop proportion in individual areal segments. We discuss the estimators used in LACIE and then consider some possible modifications and extensions which can have smaller bias or variance. Some numerical examples are offered to bring out some interesting features of the estimators and in some cases to make comparisons among estimators     

A note on stratification and gain in precision in estimating diversity from large samples

Several indices of entropy have been suggested in the literature as weighted diversity measures of a population with respect to a classification process. Among them, Shannon's entropy and Havrda -Charvát's non-additive entropies of order a, have been exhaustively used.

When the population is finite but too large to be censused, the diversity with respect to a given classification process must be estimated from a sample.

In this note, on the basis of an asymptotic study of the sample indices in the stratified random sampling, we are going to confirm that when we deal with large samples one can guarantee a gain in precision from stratified random over simple random sampling. This gain becomes considerable when the ‘inaccuracy" (as intended by Kerridge and Rathie and Kannapan) between the frequency vector in each stratum and that in the whole population, varies greatly from stratum to stratum.     

A comparison of alternative variance estimation strategies for estimating the slope of a linear regression in sample surveys

The balanced half-sample, jackknife and linearization methods are used to estimate the variance of the slope of a linear regression under a variety of computer generated situations. The basic sampling design is one in which two PSU's are selected from each of a number of strata . The variance estimation techniques are compared with a Monte Carlo experiment. Results show that variance estimates may be highly biased and variable unless sizeable numbers of observations are available from each stratum. The jackknife and linearization estimates appear superior to the balanced half sample method - particularly when the number of strata or the number of available observations from each stratum is small.     

A Practical Implementation and Bayesian Estimation in Franklin's Randomized Response Procedure

A Bayesian estimator based on Franklin's randomized response procedure is proposed for proportion estimation in surveys dealing with a sensitive character. The method is simple to implement and avoids the usual drawbacks of Franklin's estimator, i.e., the occurrence of negative estimates when the population proportion is small. A simulation study is considered in order to assess the performance of the proposed estimator as well as the corresponding credible interval.     

The use of power transformations in small area estimation

Sample surveys are usually designed and analysed to produce estimates for larger areas. Nevertheless, sample sizes are often not large enough to give adequate precision for small area estimates of interest. To overcome such difficulties, borrowing strength from related small areas via modelling becomes essential. In line with this, we propose components of variance models with power transformations for small area estimation. This paper reports the results of a study aimed at incorporating the power transformation in small area estimation for improving the quality of small area predictions. The proposed methods are demonstrated on satellite data in conjunction with survey data to estimate mean acreage under a specified crop for counties in Iowa.     

The effectiveness of coach turnover and the effect on home team advantage,team quality and team ranking

The effectiveness of coach turnover on team performance is widely discussed in the literature due to the indirect impact of a team's performance on a club's revenues. This study examines the effect of coach turnover within a competition season by focusing on the change in team quality and the change in home team advantage under the new coach. The change in team quality or home team advantage can vary according to the team (team specific) or might be an independent quantity (non-team specific). We estimated nine possible regression models, given no change, team-specific change and non-team-specific change in quality or home team advantage. The data are the match results of Belgian male soccer teams playing in the highest national division during seven seasons. Results point to a team-specific effect of a new coach on a team's quality. This article further contributes by evaluating the new coach's success with regard to whether his ability to improve team quality also results in a better position of the team in the final ranking. A new coach will be able to improve the ranking of the team if the improved team quality under the new coach renders a positive team quality.     

An Improved Range Estimator of Sigma for Determining Sample Sizes

The use of a range estimator of the population standard deviation, sigma (σ), for determining sample sizes is discussed in this study. Standardized mean ranges (d_n's), when divided into the ranges of sampling frames, provide estimates of the standard deviation of the population. These estimates can be used for determining sample sizes. The d_n's are provided for seven different distributions for sampling frame sizes that range from 2 to 2000, For each of the seven distributions, functional relationships are developed such that d_n = f(n_SF) where n_SF is the size of the sample frame. From these functions, d_n's can be estimated for sampling frame sizes which are not presented in the study.     

Split Questionnaire Designs: collecting only the data that you need through MCAR and MAR designs

We call a sample design that allows for different patterns, or sets, of data items to be collected from different sample units a Split Questionnaire Design (SQD). SQDs can be thought of as incorporating missing data into survey design. This paper examines the situation where data that are not collected by an SQD can be treated as Missing Completely At Random or Missing At Random, targets are regression coefficients in a generalised linear model fitted to binary variables, and targets are estimated using Maximum Likelihood. A key finding is that it can be easy to measure the relative contribution of a respondent to the accuracy of estimated model parameters before collecting all the respondent's model covariates. We show empirically and theoretically that we could achieve a significant reduction in respondent burden with a negligible impact on the accuracy of estimates by not collecting model covariates from respondents who we identify as contributing little to the accuracy of estimates. We discuss the general implications for SQDs.     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.     

Anderson's classification statistic based on a post-stratified training sample

The performance of Anderson's classification statistic based on a post-stratified random sample is examined. It is assumed that the training sample is a random sample from a stratified population consisting of two strata with unknown stratum weights. The sample is first segregated into the two strata by post-stratification. The unknown parameters for each of the two populations are then estimated and used in the construction of the plug-in discriminant. Under this procedure, it is shown that additional estimation of the stratum weight will not seriously affect the performance of Anderson's classification statistic. Furthermore, our discriminant enjoys a much higher efficiency than the procedure based on an unclassified sample from a mixture of normals investigated by Ganesalingam and McLachlan (1978).     

Estimating bird species richness from capture and count data

We used capture-recapture methods to estimate bird species richness from mist-net and point-count data from a study area in Campeche, Mexico. We estimated species richness separately for each survey technique for two habitats, forest and pasture, in six sampling periods. We then estimated richness based on species' detections by either technique, and estimated the proportion of species detected by each technique that are not part of the population sampled by the other technique. No consistent differences existed between richness estimates from count data and from capture data in the two habitats. In some sampling periods, over 50% of the richness estimate from one survey technique may be species that are not sampled by the other technique, suggesting that one technique may not be adequate to estimate total species richness and that comparing estimates from areas sampled by different techniques may not be valid.     

Approximate bayes estimation for mixtures of two weibull distributions under type-2 censoring

The main object of this paper is the approximate Bayes estimation of the five dimensional vector of parameters and the reliability function of a mixture of two Weibull distributions under Type-2 censoring. Under Type-2 censoring, the posterior distribution is complicated, and the integrals involved cannot be obtained in a simple closed form. In this work, Lindley's (1980) approximate form of Bayes estimation is used in the case of a mixture of two Weibull distributions under Type-2 censoring. Through Monte Carlo simulation, the root mean squared errors (RMSE's) of the Bayes estimates are computed and compared with the corresponding estimated RMSE's of the maximum likelihood estimates.     

On maximum likelihood estimation of the semi-parametric Cox model with time-varying covariates

Including time-varying covariates is a popular extension to the Cox model and a suitable approach for dealing with non-proportional hazards. However, partial likelihood (PL) estimation of this model has three shortcomings: (i) estimated regression coefficients can be less accurate in small samples with heavy censoring; (ii) the baseline hazard is not directly estimated and (iii) a covariance matrix for both the regression coefficients and the baseline hazard is not easily produced.We address these by developing a maximum likelihood (ML) approach to jointly estimate regression coefficients and baseline hazard using a constrained optimisation ensuring the latter''s non-negativity. We demonstrate asymptotic properties of these estimates and show via simulation their increased accuracy compared to PL estimates in small samples and show our method produces smoother baseline hazard estimates than the Breslow estimator.Finally, we apply our method to two examples, including an important real-world financial example to estimate time to default for retail home loans. We demonstrate using our ML estimate for the baseline hazard can give much clearer corroboratory evidence of the ‘humped hazard’, whereby the risk of loan default rises to a peak and then later falls.     

THE ANALYSIS OF MULTISTRATA DESIGNED EXPERIMENTS WITH INCOMPLETE DATA

Building upon early work of E. A. Cornish we show that G. N. Wilkinson's version of Yates' approach to the analysis of designed experiments with a single error stratum carries over completely to designs with an arbitrary non-singular covariance matrix, initially assumed known. We show that the equations, corrections, adjustments and algorithms all have their more general analogues and that these can be solved, computed or executed quite readily if the design has orthogonal block structure and satisfies Nelder's condition of general balance. The results are illustrated with a split-plot and a simple (square) lattice design.     

A new sports ratings system: The tiddlywinks world ratings

A system for calculating relative playing strengths of tiddlywinks players is described. The method can also be used for other sports. It is specifically designed to handle cases where the number of games played in a season varies greatly between players, and thus the confidence that one can have in an assigned rating also varies greatly between players. In addition, the method is designed to handle situations in which some games in the tournament are played as individuals ("singles'), while others are played with a partner ("pairs'). These factors make application of some statistical treatments, such as the Elo rating system used in chess, difficult to apply. The new method characterizes each player's ability by a numerical rating together with an associated uncertainty in that player's rating. After each tournament, a "tournament rating' is calculated for each player based on how many points the player achieved and the relative strength of partner(s) and opponent(s). Statistical analysis is then used to estimate the likely error in the calculated tournament rating. Both the tournament rating and its estimated error are used in the calculation of new ratings. The method has been applied to calculate tiddlywinks world ratings based on over 13 r 000 national tournament games in Britain and the USA going back to 1985.     

Maximum likelihood estimation for mixtures of two gompertz distributions when censoring occurs

In estimating the proportion ‘cured’ after adjuvant treatment, a population of cancer patients can be assumed to be a mixture of two Gompertz subpopulations, those who will die of other causes with no evidence of disease relapse and those who will die of their primary cancer. Estimates of the parameters of the component dying of other causes can be obtained from census data, whereas maximum likelihood estimates for the proportion cured and for the parameters of the component of patients dying of cancer can be obtained from follow-up data.

This paper examines, through simulation of follow-up data, the feasibility of maximum likelihood estimation of a mixture of two Gompertz distributions when censoring occurs. Means, variances and mean square error of the maximum likelihood estimates and the estimated asymptotic variance-covariance matrix is obtained from the simulated samples. The relationship of these variances with sample size, proportion censored, mixing proportion and population parameters are considered.

Moderate sample size typical of cooperative trials yield clinically acceptable estimates. Both increasing sample size and decreasing proportion of censored data decreases variance and covariance of the unknown parameters. Useful results can be obtained with data which are as much as 50% censored. Moreover, if the sample size is sufficiently large, survival data which are as much as 70% censored can yield satisfactory results.