Mixture Model Analysis of Partially Rank‐Ordered Set Samples: Age Groups of Fish from Length‐Frequency Data |
| |
Authors: | Armin Hatefi Mohammad Jafari Jozani Omer Ozturk |
| |
Institution: | 1. Department of Statistical SciencesUniversity of Toronto and Fields Institute;2. Department of StatisticsUniversity of Manitoba;3. Department of StatisticsThe Ohio State University |
| |
Abstract: | We present a novel methodology for estimating the parameters of a finite mixture model (FMM) based on partially rank‐ordered set (PROS) sampling and use it in a fishery application. A PROS sampling design first selects a simple random sample of fish and creates partially rank‐ordered judgement subsets by dividing units into subsets of prespecified sizes. The final measurements are then obtained from these partially ordered judgement subsets. The traditional expectation–maximization algorithm is not directly applicable for these observations. We propose a suitable expectation–maximization algorithm to estimate the parameters of the FMMs based on PROS samples. We also study the problem of classification of the PROS sample into the components of the FMM. We show that the maximum likelihood estimators based on PROS samples perform substantially better than their simple random sample counterparts even with small samples. The results are used to classify a fish population using the length‐frequency data. |
| |
Keywords: | EM algorithm finite mixture model imperfect ranking length‐frequency data maximum likelihood estimation misplacement probability matrix ranked set sampling |
|