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Mohammad Jafari Jozani - One of the best experts on this subject based on the ideXlab platform.

  • an improved procedure for estimation of malignant breast cancer prevalence using partially rank Ordered Set samples with multiple concomitants
    Statistical Methods in Medical Research, 2017
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani
    Abstract:

    Rank-based sampling designs are widely used in situations where measuring the variable of interest is costly but a small number of sampling units (Set) can be easily ranked prior to taking the final measurements on them and this can be done at little cost. When the variable of interest is binary, a common approach for ranking the sampling units is to estimate the probabilities of success through a logistic regression model. However, this requires training samples for model fitting. Also, in this approach once a sampling unit has been measured, the extra rank information obtained in the ranking process is not used further in the estimation process. To address these issues, in this paper, we propose to use the partially rank-Ordered Set sampling design with multiple concomitants. In this approach, instead of fitting a logistic regression model, a soft ranking technique is employed to obtain a vector of weights for each measured unit that represents the probability or the degree of belief associated with its...

  • information content of partially rank Ordered Set samples
    AStA Advances in Statistical Analysis, 2017
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani
    Abstract:

    Abstract Partially rank-Ordered Set (PROS) sampling is a generalization of ranked Set sampling in which rankers are not required to fully rank the sampling units in each Set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked Set sampling and simple random sampling for estimating the population mean. We study Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked Set sample (RSS) counterparts of the same size from the underlying population. We study uncertainty structure in terms of the Shannon entropy, Renyi entropy and Kullback–Leibler (KL) discrimination measures.

  • mixture model analysis of partially rank Ordered Set samples age groups of fish from length frequency data
    Scandinavian Journal of Statistics, 2015
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani, Omer Ozturk
    Abstract:

    type="main" xml:id="sjos12140-abs-0001"> 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.

  • information content of partially rank Ordered Set samples
    arXiv: Statistics Theory, 2015
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani
    Abstract:

    Partially rank-Ordered Set (PROS) sampling is a generalization of ranked Set sampling in which rankers are not required to fully rank the sampling units in each Set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked Set sampling and simple random sampling for estimating the population mean. In this paper, we study the Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked Set sample (RSS) counterparts of the same size from the underlying population. We study the uncertainty structure in terms of the Shannon entropy, Renyi entropy and Kullback-Leibler (KL) discrimination measures. Several examples including the FI of PROS samples from the location-scale family of distributions as well as a regression model are discussed.

  • inclusion probabilities in partially rank Ordered Set sampling
    Computational Statistics & Data Analysis, 2014
    Co-Authors: Omer Ozturk, Mohammad Jafari Jozani
    Abstract:

    In a finite population Setting, this paper considers a partially rank Ordered Set (PROS) sampling design. The PROS design selects a simple random sample (SRS) of M units without replacement from a finite population and creates a partially rank Ordered judgment subSets by dividing the units in SRS into subSets of a pre-specified size. The subSetting process creates a partial ordering among units in which each unit in subSet h is considered to be smaller than every unit in subSet h^' for h^'>h. The PROS design then selects a unit for full measurement from one of these subSets. Remaining units are returned to the population based on three replacement policies. For each replacement policy, we compute the first and second order inclusion probabilities and use them to construct the Horvitz-Thompson estimator and its variance for the estimation of the population total and mean. It is shown that the replacement policy that does not return any of the M units, prior to selection of the next unit for full measurement, outperforms all other replacement policies.

Omer Ozturk - One of the best experts on this subject based on the ideXlab platform.

  • mixture model analysis of partially rank Ordered Set samples age groups of fish from length frequency data
    Scandinavian Journal of Statistics, 2015
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani, Omer Ozturk
    Abstract:

    type="main" xml:id="sjos12140-abs-0001"> 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.

  • inclusion probabilities in partially rank Ordered Set sampling
    Computational Statistics & Data Analysis, 2014
    Co-Authors: Omer Ozturk, Mohammad Jafari Jozani
    Abstract:

    In a finite population Setting, this paper considers a partially rank Ordered Set (PROS) sampling design. The PROS design selects a simple random sample (SRS) of M units without replacement from a finite population and creates a partially rank Ordered judgment subSets by dividing the units in SRS into subSets of a pre-specified size. The subSetting process creates a partial ordering among units in which each unit in subSet h is considered to be smaller than every unit in subSet h^' for h^'>h. The PROS design then selects a unit for full measurement from one of these subSets. Remaining units are returned to the population based on three replacement policies. For each replacement policy, we compute the first and second order inclusion probabilities and use them to construct the Horvitz-Thompson estimator and its variance for the estimation of the population total and mean. It is shown that the replacement policy that does not return any of the M units, prior to selection of the next unit for full measurement, outperforms all other replacement policies.

  • quantile inference based on partially rank Ordered Set samples
    Journal of Statistical Planning and Inference, 2012
    Co-Authors: Omer Ozturk
    Abstract:

    Abstract This paper develops statistical inference for population quantiles based on a partially rank-Ordered Set (PROS) sample design. A PROS sample design is similar to a ranked Set sample with some clear differences. This design first creates partially rank-Ordered subSets by allowing ties whenever the units in a Set cannot be ranked with high confidence. It then selects a unit for full measurement at random from one of these partially rank-Ordered subSets. The paper develops a point estimator, confidence interval and hypothesis testing procedure for the population quantile of order p. Exact, as well as asymptotic, distribution of the test statistic is derived. It is shown that the null distribution of the test statistic is distribution-free, and statistical inference is reasonably robust against possible ranking errors in ranking process.

  • two sample distribution free inference based on partially rank Ordered Set samples
    Statistics & Probability Letters, 2012
    Co-Authors: Jinguo Gao, Omer Ozturk
    Abstract:

    This paper develops distribution-free inference for a location shift model based on a partially rank-Ordered Set (PROS) sample. In a PROS sample, a small Set of experimental units is judgment ranked without measurement by allowing ties whenever the units cannot be ranked with high confidence. These tied units are replaced in partially Ordered judgment subSets from which a unit is selected at random for a full measurement. Based on this sampling design, we construct an estimator, a test and a confidence interval for the location shift parameter. It is shown that the new sampling design is robust against any possible ranking error and has higher efficiency than competitor designs in the literature.

Armin Hatefi - One of the best experts on this subject based on the ideXlab platform.

  • an improved procedure for estimation of malignant breast cancer prevalence using partially rank Ordered Set samples with multiple concomitants
    Statistical Methods in Medical Research, 2017
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani
    Abstract:

    Rank-based sampling designs are widely used in situations where measuring the variable of interest is costly but a small number of sampling units (Set) can be easily ranked prior to taking the final measurements on them and this can be done at little cost. When the variable of interest is binary, a common approach for ranking the sampling units is to estimate the probabilities of success through a logistic regression model. However, this requires training samples for model fitting. Also, in this approach once a sampling unit has been measured, the extra rank information obtained in the ranking process is not used further in the estimation process. To address these issues, in this paper, we propose to use the partially rank-Ordered Set sampling design with multiple concomitants. In this approach, instead of fitting a logistic regression model, a soft ranking technique is employed to obtain a vector of weights for each measured unit that represents the probability or the degree of belief associated with its...

  • information content of partially rank Ordered Set samples
    AStA Advances in Statistical Analysis, 2017
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani
    Abstract:

    Abstract Partially rank-Ordered Set (PROS) sampling is a generalization of ranked Set sampling in which rankers are not required to fully rank the sampling units in each Set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked Set sampling and simple random sampling for estimating the population mean. We study Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked Set sample (RSS) counterparts of the same size from the underlying population. We study uncertainty structure in terms of the Shannon entropy, Renyi entropy and Kullback–Leibler (KL) discrimination measures.

  • mixture model analysis of partially rank Ordered Set samples age groups of fish from length frequency data
    Scandinavian Journal of Statistics, 2015
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani, Omer Ozturk
    Abstract:

    type="main" xml:id="sjos12140-abs-0001"> 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.

  • information content of partially rank Ordered Set samples
    arXiv: Statistics Theory, 2015
    Co-Authors: Armin Hatefi, Mohammad Jafari Jozani
    Abstract:

    Partially rank-Ordered Set (PROS) sampling is a generalization of ranked Set sampling in which rankers are not required to fully rank the sampling units in each Set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked Set sampling and simple random sampling for estimating the population mean. In this paper, we study the Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked Set sample (RSS) counterparts of the same size from the underlying population. We study the uncertainty structure in terms of the Shannon entropy, Renyi entropy and Kullback-Leibler (KL) discrimination measures. Several examples including the FI of PROS samples from the location-scale family of distributions as well as a regression model are discussed.

Bernd S. W. Schröder - One of the best experts on this subject based on the ideXlab platform.

  • The Fixed Point Property for Ordered Sets of Interval Dimension 2
    Order, 2016
    Co-Authors: Bernd S. W. Schröder
    Abstract:

    We provide a polynomial time algorithm that identifies if a given finite Ordered Set is in the class of d2-collapsible Ordered Sets. For a d2-collapsible Ordered Set, the algorithm also determines if the Ordered Set is connectedly collapsible. Because finite Ordered Sets of interval dimension 2 are d2-collapsible, in particular, the algorithm determines in polynomial time if a given finite Ordered Set of interval dimension 2 has the fixed point property. This result is also a first step in investigating the complexity status of the question whether a given collapsible Ordered Set has the fixed point property.

  • Examples on Ordered Set Reconstruction
    Order, 2002
    Co-Authors: Bernd S. W. Schröder
    Abstract:

    We prove that Ordered Sets are not reconstructible from the maximal deck and the minimal deck together. The construction also produces classes of more than two pairwise nonisomorphic Ordered Sets that have the same maximal deck and the same minimal deck.

  • Uniqueness of the Core for Chain-Complete Ordered Sets
    Order, 2000
    Co-Authors: Bernd S. W. Schröder
    Abstract:

    It is proved that the C -core of a chain-complete Ordered Set is unique up to isomorphism if it exists. We also give an example that shows that the ( U C ∪ L C )-core of an Ordered Set need not be unique. This is related to a question, which asks if the P -core is unique if it exists.

  • Reconstruction of the Neighborhood Deck of an Ordered Set
    Order, 2000
    Co-Authors: Bernd S. W. Schröder
    Abstract:

    We show that the neighborhood deck of an Ordered Set can be reconstructed from the deck of one point deleted subSets. As a consequence of the above results we reconstruct some maximal cards and present short new proofs of the reconstructibility of Ordered Sets of width 2 and of the recognizability of N-free Ordered Sets. We also reconstruct the maximal cards of N-free Ordered Sets.

Siu Oyoung - One of the best experts on this subject based on the ideXlab platform.

  • a totally Ordered Set of discrete abstractions for a given hybrid continuous system
    Lecture Notes in Computer Science, 1997
    Co-Authors: Jorg Raisch, Siu Oyoung
    Abstract:

    This contribution proposes a hierarchy of discrete abstractions for a given hybrid or continuous system with quantized measurements and symbolic control inputs. The continuous (or hybrid) base system and its discrete abstractions form a totally Ordered Set of models; ordering is in the sense of Set inclusion of model behaviours or, equivalently, in terms of approximation accuracy. The ordering is shown to be invariant under feedback; this provides theoretical justification for designing feedback control for the underlying hybrid system on the basis of a discrete abstraction. Also, within this Ordered Set, the notion of a “least accurate” (and therefore least complex) model which allows a given Set of specifications to be met makes sense. The discrete abstractions are realized as nondeterministic automata; they are in observer-canonical form and hence, by construction, observable. Non-reachable states are also “weeded out” by construction, leaving a minimal state Set for each approximating automaton.