Estimation of exploitation rate by combining mark-recapture procedures with a creel survey

Government agencies are usually interested in estimating the annual exploitation rate of a fish population for recreational and commercial fisheries. In this paper, we propose a model-based approach for the estimation of the exploitation rate. Our approach combines mark-recapture procedures with a creel survey (which is a type of angler survey). We consider moment estimation of the exploitation rate. We also consider estimation of the exploitation rate by stratifying the space-time units of the fisheries.     

Estimation of a Difference in Finite Populations with Missing Observations

Sampling strategies for the difference are constructed when missing observations are present. Two different situations are analyzed. One of them is related with a non random device settled by the statistician for reducing costs. The other is a non response problem. An unbiased minimum variance estimator is obtained in the first case and an approximation to it is deduced. The unbiased estimation in the second is associated with subsampling tactics.     

Small Sample Bias and Variance of Lincoln-Petersen and Bailey Estimators

The Lincoln-Petersen and Bailey estimators of an unknown population size were compared in a computer simulation of capture-recapture sampling with replacement from small populations. The Bailey estimator was negatively biased and had smaller variance than the Petersen estimator. The Petersen estimator tended to be positively biased. The Lincoln-Petersen variance estimator tended to be positively biased while the Bailey variance estimator was negatively biased.     

On Use of Distinct Respondents in Randomized Response Surveys

It is well known for direct response surveys (DR), where the responses are obtained from the respondents directly, that the sample mean, based on distinct units of a simple random sample selected with replacement (SRSWR) method, is more efficient than the sample mean based on all the units including repetition. In this paper, it is shown that a linear unbiased estimator based on distinct units is inadmissible for estimating a finite population mean when the sample is selected by an arbitrary with replacement (WR) sampling scheme and the responses are obtained independently by some RR technique. Efficiencies for a few linear unbiased estimators are compared under SRSWR sampling.     

Bayesian analysis for the meiosis I non-disjunction fraction in numerical chromosomal anomalies

The main causes of numerical chromosomal anomalies, including trisomies, arise from an error in the chromosomal segregation during the meiotic process, named a non-disjunction. One of the most used techniques to analyze chromosomal anomalies nowadays is the polymerase chain reaction (PCR), which counts the number of peaks or alleles in a polymorphic microsatellite locus. It was shown in previous works that the number of peaks has a multinomial distribution whose probabilities depend on the non-disjunction fraction F. In this work, we propose a Bayesian approach for estimating the meiosis I non-disjunction fraction F. in the absence of the parental information. Since samples of trisomic patients are, in general, small, the Bayesian approach can be a good alternative for solving this problem. We consider the sampling/importance resampling technique and the Simpson rule to extract information from the posterior distribution of F. Bayes and maximum likelihood estimators are compared through a Monte Carlo simulation, focusing on the influence of different sample sizes and prior specifications in the estimates. We apply the proposed method to estimate F. for patients with trisomy of chromosome 21 providing a sensitivity analysis for the method. The results obtained show that Bayes estimators are better in almost all situations.     

二次等距抽样

本文提出了一种二次等距抽样方法,并提出了总体平均值的一个估计量：拼配部分的比型估计与轮换部分的样本均值的加权平均。当样本量较大时,求出了估计量的方差及最优轮换比．并对特殊情形进行了讨论和数值比较．     

On the Use of Jack‐Knife Techniques in Systematic Sampling

We have proposed two general classes of ratio and product type estimators to estimate an unknown population parameter of a response variable y under systematic sampling strategy. Jack‐Knife technique is employed to make the classes almost/exactly unbiased and sampling variance of the proposed estimators are derived to the first order of approximation. The merits of the proposed estimators over other estimators are discussed in this paper.     

Median estimation of chemical constituents for sampling on two occasions under a log‐normal model

Sampling from a finite population on multiple occasions introduces dependencies between the successive samples when overlap is designed. Such sampling designs lead to efficient statistical estimates, while they allow estimating changes over time for the targeted outcomes. This makes them very popular in real‐world statistical practice. Sampling with partial replacement can also be very efficient in biological and environmental studies where estimation of toxicants and its trends over time is the main interest. Sampling with partial replacement is designed here on two occasions in order to estimate the median concentration of chemical constituents quantified by means of liquid chromatography coupled with tandem mass spectrometry. Such data represent relative peak areas resulting from the chromatographic analysis. They are therefore positive‐valued and skewed data, and are commonly fitted very well by the log‐normal model. A log‐normal model is assumed here for chemical constituents quantified in mainstream cigarette smoke in a real case study. Combining design‐based and model‐based approaches for statistical inference, we seek for the median estimation of chemical constituents by sampling with partial replacement on two time occasions. We also discuss the limitations of extending the proposed approach to other skewed population models. The latter is investigated by means of a Monte Carlo simulation study.     

Estimation of Finite and Closed Population Size: An Inverse Sampling Approach with Unequal Recapture Probability

Based on capture-mark-recapture sampling methods the problem of estimating unknown population size was considered. The sampling started with the assumption that at the beginning of the experiment all the individuals were unmarked, and the unmarked individuals caught in each sample will be marked and returned to the original population before the next sample is drawn. It is also assumed that the population is closed by birth, death, emigration and immigration. Using a general inverse sampling approach, the unknown population size N is estimated by a maximum likelihood estimator (MLE), and a simple form for approximate MLE is obtained. The probability function for S (the minimum number of samples required to be drawn to have L (L ≥ 1) samples, each of which contains at least one marked individual) and the form for E[S] are also obtained. In addition, corrections and improvements of some previous works in this field are given.     

On Combination of Ratio and PPS Estimators

AGARWAL and KUMAR (1980) proposed an estimator, combining ratio and pps estimators of population mean and proved that the proposed estimator would always be better (in minimum mean square error sense) than the pps estimator or the ratio estimator under pps sampling scheme for optimum value of constant k (parameter). The optimum value of k is rarely known in practice, hence the alternative is to replace k from the sample-values. In this paper, an estimator depending on estimated optimum value of k based on sample-values, under pps sampling scheme is proposed and studied.     

The species-area relation II. A second model for continuous sampling

A second mathematical model describing the species-area relation was proposed for continuous expanding of sample area. This model is expressed as S=λ ln(1+x/E) where S is the number of species occurring in an area x, and λ and E are the constants termed specific diversity and elemental area respectively. As a result of testing the validity of the model for several sets of data, it was shown that the above equation would provide an adequate fit to a group of species belonging to a single synusia which exists in an open habitat. The ecological implications of parameters involved were discussed and the characteristic area presented previously (Kobayashi , 1974) was defined in terms of E. The relation between results obtained by discrete sampling and continuous sampling was examined and the possibility of converting one to another was suggested.     

On the potential for illogic with logically defined outcomes

Logically defined outcomes are commonly used in medical diagnoses and epidemiological research. When missing values in the original outcomes exist, the method of handling the missingness can have unintended consequences, even if the original outcomes are missing completely at random. In this note, we consider 2 binary original outcomes, which are missing completely at random. For estimating the prevalence of a logically defined "or" outcome, we discuss the properties of 4 estimators: the complete-case estimator, the available-case estimator, the maximum likelihood estimator (MLE), and a moment-based estimator. With the exception of the available-case case estimator, all the estimators are consistent. The MLE exhibits superior performance and should be generally adopted.     

Development of an optimal sampling protocol for millipedes (Diplopoda)

This study determined a millipede sampling protocol that was efficient, replicable, and thorough, by testing commonly used methods (pitfall trapping, hand collection, and leaf litter collection with Berlese extraction) at sites where the fauna had been intensively sampled, so that the results of different sampling protocols (‘experimental sampling’) could be compared to the previously known fauna of each site (determined by ‘baseline sampling’). Two methods of collecting leaf litter were compared. One method allowed the collector to choose the locations from which to sample leaf litter, while the second method used randomly generated locations. Experimental sampling took place at both an upland site (Swallow Cliff Woods, Cook Co, IL) and a wetland site (Cedarburg Bog, Ozaukee Co, WI) where reliable baseline data was available. The optimal protocol for millipedes was found to consist of a combination of the hand collection and the a priori litter methods. In studies where there are constraints on time or resources devoted to sampling or processing, this protocol can be reduced to the single most effective method, hand collection. Overall, the a priori litter collection method was more effective than the random litter collection method.     

利用多重抽样估计稀有物种的种类数

利用矩估计和二个稳健估计方法（jackknife估计,bootstrap估计）来处理野外生态学工作者的调查数据,在假定已经发现一些稀有物种的情形下,通过统计推断得到那些未被发现的物种的种类数。利用本文所提出的方法调查水稻水稻田的昆虫群落和林地的在面植被群落的稀有种是十分有效的。