Relevant bibliographies by topics / Horvitz-Thompson estimator

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Academic literature on the topic 'Horvitz-Thompson estimator'

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Published: 4 June 2021
Last updated: 8 September 2023

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Journal articles on the topic "Horvitz-Thompson estimator"

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Théberge, Alain. "Estimation when the Covariance Structure of the Variable of Interest is Positive Definite." Journal of Official Statistics 33, no. 1 (March 1, 2017): 275–99. http://dx.doi.org/10.1515/jos-2017-0014.

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Abstract Generalized regression (GREG) estimation uses a model that assumes that the values of the variable of interest are not correlated. An extension of the GREG estimator to the case where the vector of interest has a positive definite covariance structure is presented in this article. This extension can be translated to the calibration estimators. The key to this extension lies in a generalization of the Horvitz-Thompson estimator which, in some sense, also assumes that the values of the variable of interest are not correlated. The Godambe-Joshi lower bound is another result which assumes a model with no correlation. This is also generalized to a vector of interest with a positive definite covariance structure, and it is shown that the generalized calibration estimator asymptotically attains this generalized lower bound. Properties of the new estimators are given, and they are compared with the Horvitz-Thompson estimator and the usual calibration estimator. The new estimators are applied to the Canadian Reverse Record Check survey and to the problem of variance estimation.
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Biyani, S. H., and Chand K. Midha. "A Generalized Formula for Variance in Unequal Probability Sampling." Calcutta Statistical Association Bulletin 48, no. 3-4 (September 1998): 241–44. http://dx.doi.org/10.1177/0008068319980312.

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A variance formula is given for a general class of estimators for any fixed sample size design. A formula for an unbiased estimator of the variance is also provided. These results generalize the Yates-Grundy variance formula of the Horvitz-Thompson estimator.
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Zhu, Guangyu, and Liyong Fu. "k-step adaptive cluster sampling with Horvitz–Thompson estimator." International Journal of Biomathematics 11, no. 02 (February 2018): 1850029. http://dx.doi.org/10.1142/s1793524518500298.

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Adaptive cluster sampling (ACS) has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the final sample sizes, in this study, a [Formula: see text]-step ACS based on Horvitz–Thompson (HT) estimator was developed and an unbiased estimator was derived. The [Formula: see text]-step ACS-HT was assessed first using a simulated example and then using a real survey for numbers of plants for three species that were characterized by clustered and patchily spatial distributions. The effectiveness of this sampling design method was assessed in comparison with ACS Hansen–Hurwitz (ACS-HH) and ACS-HT estimators, and [Formula: see text]-step ACS-HT estimator. The effectiveness of using different [Formula: see text]-step sizes was also compared. The results showed that [Formula: see text]-step ACS-HT estimator was most effective and ACS-HH was the least. Moreover, stable sample mean and variance estimates could be obtained after a certain number of steps, but depending on plant species. [Formula: see text]-step ACS without replacement was slightly more effective than that with replacement. In [Formula: see text]-step ACS, the variance estimate of one-step ACS is much larger than other [Formula: see text]-step ACS ([Formula: see text]), but it is smaller than ACS. This implies that [Formula: see text]-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.
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Magnussen, Steen, and Thomas Nord-Larsen. "A Jackknife Estimator of Variance for a Random Tessellated Stratified Sampling Design." Forest Science 65, no. 5 (March 12, 2019): 543–47. http://dx.doi.org/10.1093/forsci/fxy070.

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Abstract Semisystematic sampling designs—in which a population area frame is tessellated into cells, and a randomly located sample is taken from each cell—affords random tessellated stratified (RTS) Horvitz–Thompson-type estimators. Forest inventory applications with RTS estimators are rare, possibly because of computational complexities with the estimation of variance. To reduce this challenge, we propose a jackknife estimator of variance for RTS designs. We demonstrate an application with a model-assisted ratio of totals estimator and data from the Danish National Forest Inventory. RTS estimators of standard error were, as a rule, smaller than comparable estimates obtained under the assumption of simple random sampling. The proposed jackknife estimator performed well.
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Mohd Tajuddin, Razik Ridzuan, Noriszura Ismail, and Kamarulzaman Ibrahim. "On Variance Estimation for the Population Size Estimator under One-Inflated Positive Poisson Distribution." Malaysian Journal of Fundamental and Applied Sciences 18, no. 2 (May 16, 2022): 237–44. http://dx.doi.org/10.11113/mjfas.v18n2.2372.

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Let NO1PPbe the Horvitz-Thompson estimator for the population size with one-inflated positive Poisson distribution as the underlying distribution. We estimate the variance of this estimator using conditional expectation technique and provide some descriptions on the variance and its associated confidence interval based on simulation study and real data applications.
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Bakar, K. S. "Inference on Environmental Population Using Horvitz-Thompson Estimator." Journal of Environmental Informatics 16, no. 1 (September 2010): 27–34. http://dx.doi.org/10.3808/jei.201000175.

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Al-Jararha, J., and Mazen Sulaiman. "Horvitz-Thompson estimator based on the auxiliary variable." Statistics in Transition New Series 21, no. 1 (2020): 37–53. http://dx.doi.org/10.21307/stattrans-2020-003.

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Magnussen, Steen. "A Horvitz-Thompson-type estimator of species richness." Environmetrics 22, no. 7 (May 2, 2011): 901–10. http://dx.doi.org/10.1002/env.1117.

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Stoyan, Dietrich, Helga Stoyan, André Tscheschel, and Torsten Mattfeldt. "ON THE ESTIMATION OF DISTANCE DISTRIBUTION FUNCTIONS FOR POINT PROCESSES AND RANDOM SETS." Image Analysis & Stereology 20, no. 1 (May 3, 2011): 65. http://dx.doi.org/10.5566/ias.v20.p65-69.

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This paper discusses various estimators for the nearest neighbour distance distribution function D of a stationary point process and for the quadratic contact distribution function Hq of a stationary random closed set. It recommends the use of Hanisch's estimator of D, which is of Horvitz-Thompson type, and the minussampling estimator of Hq. This recommendation is based on simulations for Poisson processes and Boolean models.
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Sengupta, S. "A Comparison Between PPSWR and Brewer's ∏PSWOR Procedures." Calcutta Statistical Association Bulletin 35, no. 3-4 (September 1986): 207–10. http://dx.doi.org/10.1177/0008068319860311.

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It is proved that the variance of the Horvitz-Thompson estimator (HTE) of a finite population total based on Brewer's (1975) ∏PSWOR procedure is smaller than the variance or the Hansen-Hurwitz estimator (HHB) based on a PPSWR sample involvioa the same number of draws.
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Dissertations / Theses on the topic "Horvitz-Thompson estimator"

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Shehzad, Muhammad Ahmed. "Pénalisation et réduction de la dimension des variables auxiliaires en théorie des sondages." Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00812880.

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Les enquêtes par sondage sont utiles pour estimer des caractéristiques d'une populationtelles que le total ou la moyenne. Cette thèse s'intéresse à l'étude detechniques permettant de prendre en compte un grand nombre de variables auxiliairespour l'estimation d'un total.Le premier chapitre rappelle quelques définitions et propriétés utiles pour lasuite du manuscrit : l'estimateur de Horvitz-Thompson, qui est présenté commeun estimateur n'utilisant pas l'information auxiliaire ainsi que les techniques decalage qui permettent de modifier les poids de sondage de facon à prendre encompte l'information auxiliaire en restituant exactement dans l'échantillon leurstotaux sur la population.Le deuxième chapitre, qui est une partie d'un article de synthèse accepté pourpublication, présente les méthodes de régression ridge comme un remède possibleau problème de colinéarité des variables auxiliaires, et donc de mauvais conditionnement.Nous étudions les points de vue "model-based" et "model-assisted" dela ridge regression. Cette technique qui fournit de meilleurs résultats en termed'erreur quadratique en comparaison avec les moindres carrés ordinaires peutégalement s'interpréter comme un calage pénalisé. Des simulations permettentd'illustrer l'intérêt de cette technique par compar[a]ison avec l'estimateur de Horvitz-Thompson.Le chapitre trois présente une autre manière de traiter les problèmes de colinéaritévia une réduction de la dimension basée sur les composantes principales. Nousétudions la régression sur composantes principales dans le contexte des sondages.Nous explorons également le calage sur les moments d'ordre deux des composantesprincipales ainsi que le calage partiel et le calage sur les composantes principalesestimées. Une illustration sur des données de l'entreprise Médiamétrie permet deconfirmer l'intérêt des ces techniques basées sur la réduction de la dimension pourl'estimation d'un total en présence d'un grand nombre de variables auxiliaires
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Žakienė, Inesa. "Horvico ir Tompsono įvertinio dispersijos vertinimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120813_131528-29461.

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Šiame magistro diplominiame darbe, naudojant skirtingas atstumo funkcijas ir kalibravimo lygtis, išvedami Horvico ir Tompsono įvertinio dispersijos įvertinių svoriai. Tokiu būdu, sukonstruojami aštuoni nauji Horvico ir Tompsono įvertinio dispersijos įvertiniai. Naudojant Teiloro ištiesinimo metodą pateikiamos sukonstruotų įvertinių apytikslės dispersijos ir pasiūlyti šių dispersijų įvertiniai. Be to, darbe atliekamas matematinis modeliavimas, kurio eksperimentai atlikti naudojant darbo autorės sukurtas MATLAB programas. Matematinio modeliavimo tikslas - naujus įvertinius palyginti tarpusavyje ir su standartiniu įvertiniu. Tiriama, kaip įvertinių tikslumas priklauso nuo pasirinkto imties plano.
In this master's graduation work, the weights of estimators of Horvitz & Thompson estimator of variance are defined by using some different distance function and calibration equations. In such a way, the new eight estimators of Horvitz & Thompson estimator of variance were constructed. Using the Taylor linearization method the approximate variances of the constructed estimators were derived. The estimators of the variances of these estimators are proposed as well. Also we perform here a mathematical modeling using MATLAB program. The aim of this mathematical modeling is to compare the new estimators with each other and with a standard one. We analyze also how the accuracy of estimators depends of selected sampling design.
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Santos, Thuany de Aguiar. "Intervalo de confiança para o parâmetro estimado pelo estimador de Horvitz-Thompson." reponame:Repositório Institucional da UnB, 2016. http://repositorio.unb.br/handle/10482/20880.

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Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Estatística, 2016.
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Em um problema de amostragem sem reposição com probabilidades desiguais de seleção, Horvitz e Thompson (1952) propuseram um estimador não viesado capaz de estimar o total, a média de uma variável de interesse ou o tamanho populacional. Além dos estimadores pontuais, pode-se estimar intervalos de possíveis estimativas do parâmetro estudado por meio de estimadores intervalares. Portanto, este trabalho visa apresentar uma revisão da metodologia utilizada para calcular os Intervalos de Confiança (IC) baseados no estimador de Horvitz-Thompson. Verificou-se que o intervalo de confiança clássico, baseado na distribuição normal, é o mais utilizado na literatura. Este IC necessita da variância populacional para ser calculado, por isso, utilizou-se também o IC baseado na distribuição t-student, devido a variância ser estimada e comparou-se o desempenho de diferentes estimadores da variância apresentados na literatura com relação ao tamanho amostral. Verificou-se que nem sempre os IC baseados na distribuição normal atingiram a cobertura nominal e que os estimadores da variância, que independem da probabilidade de seleção conjunta, tiveram desempenho parecido ao estimador proposto por Yates e Grundy (1953) e Sem (1953), em populações pequenas. ________________________________________________________________________________________________ ABSTRACT
In a problem of sampling without replacement with unequal probability of selection, Horvitz e Thompson (1952) have given an estimator without bias capable of estimates the total, the mean of a variable or the population size. Besides the point estimators, it is possible to estimate the ranges of possibles estimates of the parameter analyzed, by the intervals estimators. Therefore, this research has the main purpose to show an overview about the methodologies used to compute the con dence interval based on the Horviz-Thompson estimator. It was found that the classic con dence interval, based on the normal distribution, it is the most used in the literature. This interval needs that the population variance must be calculated, that is why, it was also used the con dence interval based on the t-student distribution, because the variance is estimated and then it was compared the performance of the di erent estimators of variance showed in the literature with relation to the sample size. It was concluded that not always the con dence interval based on the normal distribution reached the nominal cover and that the estimators of variance that are independent of the joint probability of selection had similar performance to the estimator given by Yates e Grundy (1953) and Sen (1953) in small populations.
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Lardin, Pauline. "Estimation de synchrones de consommation électrique par sondage et prise en compte d'information auxiliaire." Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00842199.

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Dans cette thèse, nous nous intéressons à l'estimation de la synchrone de consommation électrique (courbe moyenne). Etant donné que les variables étudiées sont fonctionnelles et que les capacités de stockage sont limitées et les coûts de transmission élevés, nous nous sommes intéressés à des méthodes d'estimation par sondage, alternatives intéressantes aux techniques de compression du signal. Nous étendons au cadre fonctionnel des méthodes d'estimation qui prennent en compte l'information auxiliaire disponible afin d'améliorer la précision de l'estimateur de Horvitz-Thompson de la courbe moyenne de consommation électrique. La première méthode fait intervenir l'information auxiliaire au niveau de l'estimation, la courbe moyenne est estimée à l'aide d'un estimateur basé sur un modèle de régression fonctionnelle. La deuxième l'utilise au niveau du plan de sondage, nous utilisons un plan à probabilités inégales à forte entropie puis l'estimateur de Horvitz-Thompson fonctionnel. Une estimation de la fonction de covariance est donnée par l'extension au cadre fonctionnel de l'approximation de la covariance donnée par Hájek. Nous justifions de manière rigoureuse leur utilisation par une étude asymptotique. Pour chacune de ces méthodes, nous donnons, sous de faibles hypothèses sur les probabilités d'inclusion et sur la régularité des trajectoires, les propriétés de convergence de l'estimateur de la courbe moyenne ainsi que de sa fonction de covariance. Nous établissons également un théorème central limite fonctionnel. Afin de contrôler la qualité de nos estimateurs, nous comparons deux méthodes de construction de bande de confiance sur un jeu de données de courbes de charge réelles. La première repose sur la simulation de processus gaussiens. Une justification asymptotique de cette méthode sera donnée pour chacun des estimateurs proposés. La deuxième utilise des techniques de bootstrap qui ont été adaptées afin de tenir compte du caractère fonctionnel des données
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Butkuvienė, Rita. "Baigtinės populiacijos parametrų įvertinių tikslumo tyrimas modeliuojant." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2013~D_20130617_111757-43302.

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Baigiamajame magistro darbe nagrinėjamas nuoseklusis ėmimas, priklausantis pozicinių imties planų su fiksuota rikiuojančio skirstinio forma klasei. Šio imties plano atveju gautos imties plano ir populiacijos elementų priklausymo imčiai tikimybių analizinės išraiškos. Remiantis entropija, nuoseklusis ėmimas yra lyginamas su tai pačiai klasei priklausančiais Pareto ir nuosekliuoju Puasono ėmimu. Nagrinėjamas ir dviejų fazių imties planas sluoksniavimui, taikant pirmosios fazės nuoseklųjį ėmimą. Baigtinėje populiacijoje apibrėžto tyrimo kintamojo reikšmių suma vertinama kvazi Horvico ir Tompsono įvertiniu. Modeliuojant tiriama, ar sumažėja įvertinio dispersija dėl antrosios fazės sluoksniavimo. Šiame tyrime naudojami Lietuvos gyventojų užimtumo statistinio tyrimo duomenys, vertinamas užimtųjų ir bedarbių skaičius, nedarbo lygis.
The successive sampling design, belonging to the class of order sampling designs with fixed order distribution shape, is studied. Analytical expressions for design probability and element inclusion probability are obtained. Entropy is used to compare successive, Pareto and sequential Poisson sampling designs, belonging to the same class. Two-phase sampling design for stratification with the first-phase order sampling is also studied. The total of the study variable values, defined on a finite population, is estimated by a quasi-Horwitz-Thompson estimator. The behaviour of the variance estimator influenced by the second phase stratification is investigated by simulation. The study is carried out for estimates of the number of employed, unemployed and the unemployment rate using the Lithuanian Labor Force Survey data.
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Grafström, Anton. "On unequal probability sampling designs." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-33701.

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The main objective in sampling is to select a sample from a population in order to estimate some unknown population parameter, usually a total or a mean of some interesting variable. When the units in the population do not have the same probability of being included in a sample, it is called unequal probability sampling. The inclusion probabilities are usually chosen to be proportional to some auxiliary variable that is known for all units in the population. When unequal probability sampling is applicable, it generally gives much better estimates than sampling with equal probabilities. This thesis consists of six papers that treat unequal probability sampling from a finite population of units. A random sample is selected according to some specified random mechanism called the sampling design. For unequal probability sampling there exist many different sampling designs. The choice of sampling design is important since it determines the properties of the estimator that is used. The main focus of this thesis is on evaluating and comparing different designs. Often it is preferable to select samples of a fixed size and hence the focus is on such designs. It is also important that a design has a simple and efficient implementation in order to be used in practice by statisticians. Some effort has been made to improve the implementation of some designs. In Paper II, two new implementations are presented for the Sampford design. In general a sampling design should also have a high level of randomization. A measure of the level of randomization is entropy. In Paper IV, eight designs are compared with respect to their entropy. A design called adjusted conditional Poisson has maximum entropy, but it is shown that several other designs are very close in terms of entropy. A specific situation called real time sampling is treated in Paper III, where a new design called correlated Poisson sampling is evaluated. In real time sampling the units pass the sampler one by one. Since each unit only passes once, the sampler must directly decide for each unit whether or not it should be sampled. The correlated Poisson design is shown to have much better properties than traditional methods such as Poisson sampling and systematic sampling.
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Smith, Christina D. "Estimation of treatment effects under combined sampling and experimental designs." Diss., Manhattan, Kan. : Kansas State University, 2007. http://hdl.handle.net/2097/282.

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Henderson, Tamie, and Tamie Anakotta. "Estimating the variance of the Horvitz-Thompson estimator." Thesis, 2006. http://hdl.handle.net/1885/10608.

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Unequal probability sampling was introduced by Hansen and Hurwitz (1943) as a means of reducing the mean squared errors of survey estimators. For simplicity they used sampling with replacement only. Horvitz and Thompson (1952) extended this methodology to sampling without replacement, however the knowledge of the joint inclusion probabilities of all pairs of sample units was required for the variance estimation process. The calculation of these probabilities is typically problematic. Sen (1953) and Yates and Grundy (1953) independently suggested the use fixed, but this estimator again involved the calculation of the joint inclusion probabilities. This requirement has proved to be a substantial disincentive to its use. More recently, efforts have been made to find useful approximations to this fixed-size sample variance, which would avoid the need to evaluate the joint inclusion probabilities. These approximate variance estimators have been shown to perform well under high entropy sampling designs, however, there is now an ongoing dispute in the literature regarding the preferred approximate estimator. This thesis examines in detail nine of these approximate estimators, and their empirical performances under two high entropy sampling designs, namely Conditional Poisson Sampling and Randomised Systematic Sampling. These nine approximate estimators were separated into two families based on their variance formulae. It was hypothesised, due to the derivation of these variance estimators, that one family would perform better under Randomised Systematic Sampling and the other under Conditional Poisson Sampling. The two families of approximate variance estimators showed within group similarities, and they usually performed better under their respective sampling designs. Recently algorithms have been derived to efficiently determine the exact joint inclusion probabilities under Conditional Poisson Sampling. As a result, this study compared the Sen-Yates-Grundy variance estimator to the other approximate estimators to determine whether the knowledge of these probabilities could improve the estimation process. This estimator was found to avoid serious inaccuracies more consistently than the nine approximate estimators, but perhaps not to the extent that would justify its routine use, as it also produced estimates of variance with consistently higher mean squared errors than the approximate variance estimators. The results of the more recent published papers, Matei and Till´e (2005), have been shown to be largely misleading. This study also shows that the relationship between the variance and the entropy of the sampling design is more complex than was originally supposed by Brewer and Donadio (2003). Finally, the search for a best all-round variance estimator has been somewhat inconclusive, but it has been possible to indicate which estimators are likely to perform well in certain definable circumstances.
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Hanek, Petr. "Výběrové metody v lesnictví." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-320999.

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This diploma thesis is devoted to the sampling strategies in forestry. It describes their theoretical aspects and their applications on a real landscape. The sampling methods in forestry are of particular importance in forest inven- tory. The aim of sampling methods is to estimate population characteristics based on the knowledge of sample. Two basic approaches can be distinguished according to the size of population, we speak about discrete or continuous population. Several types of sampling designs and corresponding estimators of target values are described for both approaches. Besides estimates of po- pulation total or average, we mention the formulas for computing variance of these estimates and the methods for their estimation for different sampling designs. The thesis also contains the comparison of studied methods based on computer simulations.
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Šedová, Michaela. "Odhad parametru při dvoufázovém stratifikovaném a skupinovém výběru." Doctoral thesis, 2011. http://www.nusl.cz/ntk/nusl-299533.

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Title: Parameter Estimation under Two-phase Stratified and Cluster Sampling Author: Mgr. Michaela Šedová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Mgr. Michal Kulich, Ph.D. Abstract: In this thesis we present methods of parameter estimation under two-phase stratified and cluster sampling. In contrast to classical sampling theory, we do not deal with finite population parameters, but focus on model parameter inference, where the ob- servations in a population are considered to be realisations of a random variable. However, we consider the sampling schemes used, and thus we incorporate much of survey sampling theory. Therefore, the presented methods of the parameter estimation can be understood as a combination of the two approaches. For both sampling schemes, we deal with the concept where the population is considered to be the first-phase sample, from which a sub- sample is drawn in the second phase. The target variable is then observed only for the subsampled subjects. We present the mean value estimation, including the statistical prop- erties of the estimator, and show how this estimation can be improved if some auxiliary information, correlated with the target variable, is observed for the whole population. We extend the method to the regression problem....
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Books on the topic "Horvitz-Thompson estimator"

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Ouyang, Zhao. Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. Fort Collins, Colo: U.S. Dept. of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station, 1997.

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T, Schreuder Hans, Boes Duane C, and Rocky Mountain Forest and Range Experiment Station (Fort Collins, Colo.), eds. Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. Fort Collins, Colo. (3825 E. Mulberry St., Fort Collins 80524): U.S. Dept. of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station, 1997.

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T, Schreuder Hans, Boes Duane C, and Rocky Mountain Forest and Range Experiment Station (Fort Collins, Colo.), eds. Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. Fort Collins, Colo. (3825 E. Mulberry St., Fort Collins 80524): U.S. Dept. of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station, 1997.

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Ouyang, Z. Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. 1997.

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Hankin, David, Michael S. Mohr, and Kenneth B. Newman. Sampling Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198815792.001.0001.

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We present a rigorous but understandable introduction to the field of sampling theory for ecologists and natural resource scientists. Sampling theory concerns itself with development of procedures for random selection of a subset of units, a sample, from a larger finite population, and with how to best use sample data to make scientifically and statistically sound inferences about the population as a whole. The inferences fall into two broad categories: (a) estimation of simple descriptive population parameters, such as means, totals, or proportions, for variables of interest, and (b) estimation of uncertainty associated with estimated parameter values. Although the targets of estimation are few and simple, estimates of means, totals, or proportions see important and often controversial uses in management of natural resources and in fundamental ecological research, but few ecologists or natural resource scientists have formal training in sampling theory. We emphasize the classical design-based approach to sampling in which variable values associated with units are regarded as fixed and uncertainty of estimation arises via various randomization strategies that may be used to select samples. In addition to covering standard topics such as simple random, systematic, cluster, unequal probability (stressing the generality of Horvitz–Thompson estimation), multi-stage, and multi-phase sampling, we also consider adaptive sampling, spatially balanced sampling, and sampling through time, three areas of special importance for ecologists and natural resource scientists. The text is directed to undergraduate seniors, graduate students, and practicing professionals. Problems emphasize application of the theory and R programming in ecological and natural resource settings.
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Book chapters on the topic "Horvitz-Thompson estimator"

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Maiti, Tapabrata. "Horvitz–Thompson Estimator." In International Encyclopedia of Statistical Science, 637–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_291.

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Ghosh, J. K. "The Horvitz-Thompson Estimate and Basu’s Circus Revisited." In Bayesian Analysis in Statistics and Econometrics, 225–28. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2944-5_14.

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Singh, Sarjinder, Stephen A. Sedory, Maria del Mar Rueda, Antonio Arcos, and Raghunath Arnab. "Tuning of the Horvitz–Thompson estimator." In A New Concept for Tuning Design Weights in Survey Sampling, 199–218. Elsevier, 2016. http://dx.doi.org/10.1016/b978-0-08-100594-1.00007-3.

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Hankin, David G., Michael S. Mohr, and Ken B. Newman. "Spatially balanced sampling." In Sampling Theory, 240–68. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198815792.003.0012.

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In many ecological and natural resource settings, there may be a high degree of spatial structure or pattern to the distribution of target variable values across the landscape. For example, the number of trees per hectare killed by a bark beetle infestation may be exceptionally high in one region of a national forest and near zero elsewhere. In such circumstances it may be highly desirable or even required that a sample survey directed at estimation of total tree mortality across a forest be based on selection of random locations that have good spatial balance, i.e., locations are well spread over the landscape with relatively even distances between them. A simple random sample cannot guarantee good spatial balance. We present two methods that have been proposed for selection of spatially balanced samples: GRTS (Generalized Random Tessellation Stratified Sampling) and BAS (Balanced Acceptance Sampling). Selection of samples using the GRTS approach involves a complicated series of sequential steps that allows generation of spatially balanced samples selected from finite populations or from infinite study areas. Selection of samples using BAS relies on the Halton sequence, is conceptually simpler, and produces samples that generally have better spatial balance than those produced by GRTS. Both approaches rely on use of software that is available in the R statistical/programming environment. Estimation relies on the Horvitz–Thompson estimator. Illustrative examples of running the SPSURVEY software package (used for GRTS) and links to the SDraw package (used for BAS) are provided at http://global.oup.com/uk/companion/hankin.
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Hankin, David G., Michael S. Mohr, and Ken B. Newman. "Unequal probability sampling." In Sampling Theory, 140–72. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198815792.003.0008.

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Equal probability selection is a special case of the general theory of probability sampling in which population units may be selected with unequal probabilities. Unequal selection probabilities are often based on auxiliary variable values which are measures of the sizes of population units, thus leading to the acronym (PPS)—“Probability Proportional to Size”. The Horvitz–Thompson (1953) theorem provides a unifying framework for design-based sampling theory. A sampling design specifies the sample space (set of all possible samples) and associated first and second order inclusion probabilities (probabilities that unit i, or units i and j, respectively, are included in a sample of size n selected from N according to some selection method). A valid probability sampling scheme must have all first order inclusion probabilities > 00 (i.e., every population unit must have a chance of being in the sample). Unbiased variance estimation is possible only for those schemes that guarantee that all second order inclusion probabilities exceed zero, thus providing theoretical justification for the absence of unbiased estimators of sampling variance in systematic sampling and other schemes for which some second order inclusion probabilities are zero. Numerous generalized Horvitz–Thompson (HT) estimators can be formed and all are consistent estimators because they are functions of consistent HT estimators. Unequal probability systematic sampling and Poisson sampling (the unequal probability counterpart to Bernoulli sampling for which sample size is a random variable) are also considered. Several R programs for selecting unequal probability samples and for calculating first and second order inclusion probabilities are posted at http://global.oup.com/uk/companion/hankin.
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Conference papers on the topic "Horvitz-Thompson estimator"

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Clemencon, Stephan, Patrice Bertail, and Emilie Chautru. "Scaling up M-estimation via sampling designs: The Horvitz-Thompson stochastic gradient descent." In 2014 IEEE International Conference on Big Data (Big Data). IEEE, 2014. http://dx.doi.org/10.1109/bigdata.2014.7004208.

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