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    Wyświetlanie 1-7 z 7
    Tytuł:
    Searching for an optimal AUC estimation method : a never-ending task?
    Autorzy:
    Jawień, Wojciech
    Opis:
    An effective method of construction of a linear estimator of AUC in the finite interval, optimal in the minimax sense, is developed and demonstrated for five PK models. The models may be given as an explicit $C_{t}$ relationship or defined by differential equations. For high variability and rich sampling the optimal method is only moderately advantageous over optimal trapezoid or standard numerical approaches (Gauss-Legendre or Clenshaw- Curtis quadratures). The difference between the optimal estimator and other methods becomes more pronounced with a decrease in sample size or decrease in the variability. The described estimation method may appear useful in development of limited-sampling strategies for AUC determination, as an alternative to the widely used regression-based approach. It is indicated that many alternative approaches are also possible.
    Dostawca treści:
    Repozytorium Uniwersytetu Jagiellońskiego
    Artykuł
    Tytuł:
    Estimation of stability index for symmetric $\alpha$-stable distribution using quantile conditional variance ratios
    Autorzy:
    Pączek, Kewin
    Wyłomańska, Agnieszka
    Pitera, Marcin
    Jelito, Damian
    Opis:
    The class of $\alpha$-stable distributions is widely used in various applications, especially for modeling heavy-tailed data. Although the $\alpha$-stable distributions have been used in practice for many years, new methods for identification, testing, and estimation are still being refined and new approaches are being proposed. The constant development of new statistical methods is related to the low efficiency of existing algorithms, especially when the underlying sample is small or the distribution is close to Gaussian. In this paper, we propose a new estimation algorithm for the stability index, for samples from the symmetric $\alpha$-stable distribution. The proposed approach is based on a quantile conditional variance ratio. We study the statistical properties of the proposed estimation procedure and show empirically that our methodology often outperforms other commonly used estimation algorithms. Moreover, we show that our statistic extracts unique sample characteristics that can be combined with other methods to refine existing methodologies via ensemble methods. Although our focus is set on the symmetric $\alpha$-stable case, we demonstrate that the considered statistic is insensitive to the skewness parameter change, so our method could be also used in a more generic framework. For completeness, we also show how to apply our method to real data linked to financial market and plasma physics.
    Dostawca treści:
    Repozytorium Uniwersytetu Jagiellońskiego
    Artykuł
    Tytuł:
    Comparing the performance of various estimators using large model communities
    Estimating species numbers by extrapolation. 1
    Estimating species numbers by extrapolation. 1, Comparing the performance of various estimators using large model communities
    Autorzy:
    Ulrich, Werner
    Współwytwórcy:
    Polish Academy of Sciences. Institute of Ecology
    Wydawca:
    Polish Academy of Sciences. Institute of Ecology. Publishing Office
    Powiązania:
    Smith E. P., van Belle G. 1984 - Nonparametric estimation of species richness - Biometrics, 40: 119-129.
    Kobayashi S., Kimura K. 1994 - The number of species occurring in a sample of a biotic community and its connections with species-abundance relationships and spatial distribution - Ecol. Res. 9: 281-294.
    Heltshe J., Forrester N. E. 1983 - Estimating species richness using the jackknife procedurę - Biometrics 39: 1-11.
    Coddington J. A., Young L. H., Coyle F. A. 1996 - Estimating spider species richness in a Southern Appalachian cove hardwood forest - J. Arachnology, 24: 111-128.
    Mingoti S. A., Meeden G. 1992 - Estimating the total number of distinct species using presence and absence data - Biometrics, 48: 863-875.
    Preston F. W. 1962 - The canonical distribution of commonness and rarity. Part I – Ecology 43: 185-215.
    Baltanas A. 1992 - On the use of some methods for the estimation of species richness - Oikos, 65: 484-492.
    Keating K. A. 1998 - Estimating species richness: the Michaelis-Menten model revisited - Oikos, 81: 411-416.
    Longino J. T., Colwell R. K. 1997 - Biodiversity assessment using structured inventory: capturing the ant fauna of a tropical rain forest - Ecol. Appl. 7: 1263-1277.
    Ulrich W. 1999a - Estimating species numbers by extrapolation II: determining the minimum sample size to obtain a certain fraction of species in a community - Pol. J. Ecol. 47: 293-305.
    Slocomb J., Dickson K. L. 1978 - Estimating the total number of species in a biological community (In: Biological data in water pollution assessment: quantitative and statistical analyses, Eds.: K. L. Dickson, J. Cairns Jr., R. J. Livingston) - Philadelphia, pp. 38-52.
    Tackaberry R., Brokaw N., Kellman M., Mallory E. 1997 - Estimating species richness in tropical forest: the missing species extrapolation technique - J. Trop. Ecol. 13: 449-458.
    Scharf S. F., Juanes F., Sutherland M. 1998 - Inferring ecological relationships from the edges of scatter diagrams: comparisons of regression techniques - Ecology, 79: 448-460.
    Chao A. 1984 - Non-parametric estimation of the number of classes in a population - Scand. J. Stat. 11: 265-270.
    Lee S. M., Chao A. 1994 - Estimating population size via sample coverage for closed capture-recapture models - Biometrics 50: 88-97.
    Miller R. I., Wiegert R. G. 1989 - Documenting completeness, species-area relations, and the species abundance distribution of a regional flora - Ecology, 70: 16-22.
    Lawton J. H. 1990 - Species richness and population dynamics of animal assemblages. Patterns in body-size: abundance space - Phil. Tans. R. Soc. Lond. B 330: 283-291.
    Brainerd B. 1972 - On the relation between types and tokens in literary text - J. Appl. Prob. 9: 507-518.
    Tokeshi M. 1996 - Power fraction: a new explanation of relative abundance patterns in species-rich assemblages - Oikos, 75: 543-550.
    Lauga J., Joachim J. 1987 - L'echantillonnage des populations d'oiseaux par la methode des E.F.P.: interet d'une etude mathemathique de la courbe de richesse cumulee - Acta Oecol. Oecol. Gen. 8: 117-124.
    Ulrich W. l999b - The density - size and the biomass - weight distribution is generated by the species - size distribution together with Density Fluctuations: Evidence from Model Species Distributions in the Hymenoptera - Pol. J. Ecol. 47: 87-101.
    Bunge J., Fitzpatrick M. 1993 - Estimating the number of species: a review - J. Am. Stat. Assoc. 88: 364-373.
    Tokeshi M. 1993 - Species, abundance patterns and community structure - Adv. Ecol. Res. 24: 111-186.
    De Caprariis P., Lindemann R. H., Collins C. 1976 - A method for determining optimum sample size in species diversity studies - Math. Geol. 8: 575-581.
    Hilpert H. 1989 - Zur Hautfluglerfauna eines sudbadischen Eichen-Hainbuchenmischwaldes - Spixiana, 12: 57-90.
    Pielou E. C. 1977 - Mathematical Ecology - New York, 1-385.
    Palmer M. W. 1990 - The estimation of species richness by extrapolation - Ecology, 71: 1195-1198.
    Morris J. G. 1976 - Physikalische Chemie fur Biologen – Weinheim, New York, 1-345.
    Chao A., Lee S. M., Jeng S. L. 1992 - Estimation of population size for capture-recapture data when capture probabilities vary by time and individual animal - Biometrics, 48: 201-216.
    Hodkinson I. D., Hodkinson E. 1993 - Pondering the imponderable: a probability based approach to estimating insect diversity from repeat faunal samples - Ecol. Entomol. 18: 91-92.
    Walther B. A., Morand S. 1998 - Comparative performance of species richness estimation methods - Parasitology, 116: 395-405.
    McArdle B. H., Gaston K. J., Lawton J. H. 1990 - Variation in the size of animal populations: patterns, problems and artefacts - J. Anim. Ecol. 59: 439-454.
    Schaefer M. 1996 - Die Bodenfauna von Waldern: Biodiversitat in einem okologischen System - Abh. Math.-Naturw. Klasse 1996, 2, Stuttgart.
    Palmer M. W. 1991 - The estimation of species richness: the second-order jackknife reconsidered - Ecology. 72: 1512-1513.
    Chao A., Lee S. M. 1992 - Estimating the number of classes via sample coverage - J. Am. Sta. Assoc. 87: 210-217.
    Boulinier Th., Nichols J. D., Sauer J. R., Hines J. E., Pollock K. H. 1998 - Estimating species richness: the importance of heterogeneity in species detectability - Ecology, 79: 1018-1028.
    Currie D. J. 1993 - What shape is the relationship between body mass and population density - Oikos, 66: 353.
    Colwell R. K., Coddington J. A. 1994 - Estimating terrestrial biodiversity through extrapolation - Phil. Trans. R. Soc. Lond. B: 345: 101-118.
    Burnham K. P., Overton W. S. 1979 - Robust estimation of population size when capture probabilities vary among animals - Ecology. 60: 927-936.
    Burnham K. P., Overton W. S. 1978 - Estimation of the size of a closed population when capture probabilities vary among animals - Biometrika, 65: 623-633.
    Slocomb J., Stauffer B., Dickson K. L. 1977 - On fitting the truncated lognormal distribution to species abundance data using maximum likelihood estimation - Ecology. 58: 693-696.
    Soberon M. J., Llorente B. J. 1993 - The use of species accumulation functions for the prediction of species richness - Cons. Biol. 7: 480-488.
    Hughes R. G. 1986 - Theories and models of species abundance - Am. Nat. 128: 879-899.
    Chao L. 1987 - Estimating the population size for capture - recapture data with unequal catchability - Biometrics, 43: 783-791.
    Stout J., Vandermeer J. 1975 - Comparison of species richness for stream-inhabiting insects in tropical and midlatitude streams - Am. Nat. 109: 263-280.
    Norris J. L., Pollock K. H. 1996 - Nonparametric MLE under two closed capture-recapture models with heterogeneity - Biometrics, 52: 639-649.
    Ulrich W. 1999c - Abundance, biomass and density boundaries in the Hymenoptera: analysis of the abundance - body size relationship and differences between forest and open landscape habitats - Pol. J. Ecol. 47: 73-86.
    Edwards L. E. 1997 - A useful procedure for estimating the species richness of spiders - J. Arachnology, 25: 99-105.
    Ulrich W. 1998 - The parasitic Hymenoptera in a beech forest on limestone I: Species composition, species turnover, abundance and biomass - Pol. J. Ecol. 46: 261-289.
    Hurvich C. M., Tsai C. 1989 - Regression and time series model selection in small samples - Biometrika, 76: 297-307.
    Schaefer M. 1991 - Fauna of the European temperate deciduous forest (In: Temperate deciduous forests. Eds. E. Rohrig, B. Ulrich) - Ecosystems of the world 7. Amsterdam. pp. 503-525.
    Polish Journal of Ecology
    Solow A. R. 1994 - On the Bayesian estimation of the number of species in a community - Ecology 75: 2139-2142.
    Gaston K. J. 1993 - Comparing animals and automobiles: a vehicle for understanding body size and abundance relationships in species assemblages? - Oikos, 66: 172-179.
    Winklehner R., Winkler H., Kampichler C. 1997 - Estimating local species richness of epigeic Collembola in temperate dry grassland - Pedobiologia, 41: 154-158.
    Sugihara G. 1980 - Minimal community structure: an explanation of species abundance patterns - Am. Nat. 116: 770-787.
    Opis:
    Bibliographical references (pages 289-291)
    Bibliografia na stronach 289-291
    Pages 271-291 : illustrations ; 27 cm
    Strony 271-291 : ilustracje ; 27 cm
    A computer program was constructed that simulates large species assemblages (28 to 997 species) with various species-rank order distributions and degrees of aggregation of the species. From these model assemblages random samples were taken to study the performance of 14 estimators of species diversity. For 6 of the estimators correction factors are developed. In sufficiently large samples (more than 2/3 of the true species number (TS) sampled) a corrected second order jackknife estimator gave the best results. 18% of the estimates ranged outside TS ± 10%. If fewer species are represented in the sample (but more than 1/3 TS) two newly developed data analytical estimators performed better. Between 23 and 24%, respectively, of their estimates ranged outside TS ± 20%. Crucial to the performance of all of the estimators is the sample size. The minimum sample size for an estimator to work has to contain at least 1/3 of the total species number.
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Arithmetic or Logarithmic Rate of Return? The Impact of the Choice Made on the Distribution Modelling Results
    Autorzy:
    Czyżycki, Rafał
    Wydawca:
    Kartprint
    Cytata wydawnicza:
    Czyżycki, R., (2015), Arithmetic or Logarithmic Rate of Return? The Impact of the Choice Made on the Distribution Modelling Results, [in:] Contemporary Socio-economic Issues and Problems Management – Processes, Bratislava 2016, ss. 19-29
    Opis:
    The objective of this work is to examine the impact of selection of the type of the rate of return, the distribution and estimation horizon applied on the results of modelling of rates of return. For this purpose, normal and logarithmic rate of return will be used, and the following distributions will be taken into account: skewed normal, skewed t-Student, skewed GED and stable distribution. In addition, in order to specify the significance of maturity of the capital market on the quality of the models obtained, the rate of return from S&P500 and WIG will be subject to modelling.
    Dostawca treści:
    Repozytorium Centrum Otwartej Nauki
    Inne
      Wyświetlanie 1-7 z 7

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