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Dissertations / Theses on the topic 'New statistics'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Wang, Yishi. "Some new tests for normality." Diss., Online access via UMI:, 2006.

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2

Lesser, Elizabeth Rochelle. "A New Right Tailed Test of the Ratio of Variances." UNF Digital Commons, 2016. http://digitalcommons.unf.edu/etd/719.

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It is important to be able to compare variances efficiently and accurately regardless of the parent populations. This study proposes a new right tailed test for the ratio of two variances using the Edgeworth’s expansion. To study the Type I error rate and Power performance, simulation was performed on the new test with various combinations of symmetric and skewed distributions. It is found to have more controlled Type I error rates than the existing tests. Additionally, it also has sufficient power. Therefore, the newly derived test provides a good robust alternative to the already existing me

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3

Lochner, Michelle Aileen Anne. "New applications of statistics in astronomy and cosmology." Doctoral thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/12864.

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Includes bibliographical references.<br>Over the last few decades, astronomy and cosmology have become data-driven fields. The parallel increase in computational power has naturally lead to the adoption of more sophisticated statistical techniques for data analysis in these fields, and in particular, Bayesian methods. As the next generation of instruments comes online, this trend should be continued since previously ignored effects must be considered rigorously in order to avoid biases and incorrect scientific conclusions being drawn from the ever-improving data. In the context of supernova co

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4

Liu, Yanping. "NEW APPROACHES TO MULTIPLE TESTING OF GROUPED HYPOTHESES." Diss., Temple University Libraries, 2016. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/376210.

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Statistics<br>Ph.D.<br>Testing multiple hypotheses appearing in non-overlapping groups is a common statistical problem in many modern scientific investigations, with this group formation occurring naturally in many of these investigations. The goal of this dissertation is to explore the current state of knowledge in the area of multiple testing of grouped hypotheses and to present newer and improved statistical methodologies. As the first part of this dissertation, we propose a new Bayesian two-stage multiple testing method controlling false discovery rate (FDR) across all hypotheses. The meth

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5

Taneja, Atrayee. "New approaches to testing a composite null hypothesis for the two sample binomial problem /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487323583622319.

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6

Lee, Baumin. "Three new algorithms for exact D-optimal design problems /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487843688959047.

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7

Melbourne, Davayne A. "A New method for Testing Normality based upon a Characterization of the Normal Distribution." FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1248.

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The purposes of the thesis were to review some of the existing methods for testing normality and to investigate the use of generated data combined with observed to test for normality. The approach to testing for normality is in contrast to the existing methods which are derived from observed data only. The test of normality proposed follows a characterization theorem by Bernstein (1941) and uses a test statistic D*, which is the average of the Hoeffding’s D-Statistic between linear combinations of the observed and generated data to test for normality. Overall, the proposed method showed consid

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8

Florêncio, Dinei Alfonso Ferreira. "A new sampling theory and a framework for nonlinear filter banks." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/15792.

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9

Ma, Zhengbo. "A New Jackknife Empirical Likelihood Method for U-Statistics." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/97.

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U-statistics generalizes the concept of mean of independent identically distributed (i.i.d.) random variables and is widely utilized in many estimating and testing problems. The standard empirical likelihood (EL) for U-statistics is computationally expensive because of its onlinear constraint. The jackknife empirical likelihood method largely relieves computation burden by circumventing the construction of the nonlinear constraint. In this thesis, we adopt a new jackknife empirical likelihood method to make inference for the general volume under the ROC surface (VUS), which is one typical kind

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10

Lo, Wing Sze. "Statistics-based Chinese word segmentation and new word detection /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?ELEC%202002%20LOW.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002.<br>Includes bibliographical references (leaves 83-86). Also available in electronic version. Access restricted to campus users.

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11

Felus, Yaron A. "New methods for spatial statistics in geographic information systems /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486400446373917.

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12

Attia, N. F. "New methods of constrained optimization using penalty functions." Thesis, University of Essex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356044.

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13

Roualdes, Edward A. "New Results in ell_1 Penalized Regression." UKnowledge, 2015. http://uknowledge.uky.edu/statistics_etds/13.

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Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate

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14

Smith, Andrew Korb. "New results in dimension reduction and model selection." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22586.

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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: Huo, Xiaoming; Committee Member: Serban, Nicoleta; Committee Member: Shapiro, Alexander; Committee Member: Yuan, Ming; Committee Member: Zha, Hongyuan.

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15

Svensson, Depraetere Xavier. "Application of new particle-based solutions to the Simultaneous Localization and Mapping (SLAM) problem." Thesis, KTH, Matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-212999.

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In this thesis, we explore novel solutions to the Simultaneous Localization and Mapping (SLAM) problem based on particle filtering and smoothing methods. In essence, the SLAM problem constitutes of two interdependent tasks: map building and tracking. Three solution methods utilizing different smoothing techniques are explored. The smoothing methods used are fixed lag smoothing (FLS), forward-only forward-filtering backward-smoothing (forward-only FFBSm) and the particle-based, rapid incremental smoother (PaRIS). In conjunction with these smoothing techniques the well-established Expectation-Ma

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16

Wang, Chunnan. "Analysis of a new bivariate distribution in reliability theory." Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/284128.

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Freund [1961] introduced a bivariate extension of the exponential distribution that provides a model in which the exponential residual lifetime of one component depends on the working status of another component. We define and study an extension of the Freund distribution in this dissertation. In the first chapter we define some basic concepts that are needed for later developments. We give the definition of the multivariate conditional hazard rate functions of a nonnegative absolutely continuous random vector and study a characterization of these functions in Section 1.1. Then we study some n

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17

Biazi, Elenice. "Some aspects of influence analysis and a new approach." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275289.

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18

Li, Dingjun. "On the sequential test per MIL-STD-781 and new, more efficient test plans." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185264.

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The sequential probability ratio test is an efficient test procedure compared to the fixed sample size test procedure in the sense that it minimizes the average sample size needed for terminating the experiment at the two specified hypotheses, i.e., at H₀: θ = θ₀ and H₁: θ = θ₁. However, this optimum property does not hold for the values of the testing parameter other than these two hypotheses, especially for those with values between these two. Also the estimation following a sequential test is considered to be difficult, and the usual maximum likelihood estimate is in general biased. The seq

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19

Shi, Pucheng. "Study of new models for insider trading and impulse control." Thesis, London School of Economics and Political Science (University of London), 2013. http://etheses.lse.ac.uk/3156/.

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This thesis presents the development and study of two stochastic models. The first one is an equilibrium model for a market involving risk-averse insider trading. In particular, the static information model is considered under new assumptions: a) the insider is risk-averse, b) the signal received by the insider is not necessarily Gaussian, and c) the price set by the market maker is a function of a weighted signal that is not necessarily Gaussian either. Conditions on the weighting and pricing functions ensuring the existence of equilibrium are discussed. Equilibrium pricing and weighting func

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20

Zheng, Shuo. "New Hierarchical Nonlinear Modeling for Count Data: Estimation and Testing in The Presence of Overdispersion." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/132533.

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Statistics<br>Ph.D.<br>In studies of traffic accidents, disease occurrence, mismatches in genetic code and impact of pollution on ecological communities the key observational variable is often a count. For example, daily counts of accidents on a segment of highway will vary with weather and other traffic conditions: highway engineers seek to relate accident counts to these roadway conditions. Formal statistical analysis of this kind of data is critically dependent on using the correct model for the random count data. However, statistical analysis packages use only those random count models tha

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21

Ren, Sheng. "New Methods of Variable Selection and Inference on High Dimensional Data." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511883302569683.

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22

Jennings, Paul Anthony. "New applications of statistics within automotive EMC and pass-by noise." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343798.

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23

Kallus, Nathan. "From data to decisions through new interfaces between optimization and statistics." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/98570.

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Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 283-293).<br>The growing availability of data is creating opportunities for making better decisions, but in many circumstances it is yet unknown how to correctly leverage this data in systematic and optimal ways. In this thesis,

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24

Emmanouilides, Christos J. "Micro-level modelling of new product adoption in the presence of social interactions." Thesis, Lancaster University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310507.

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25

Weale, Michael Edmund. "Degrees of visible polymorphism and new methods measuring frequency-dependent selection by preditors." Thesis, University of Southampton, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385257.

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26

Jung, Yoonsuh. "Regularization of Case Specific Parameters: A New Approach for Improving Robustness and/or Efficiency of Statistical Methods." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1275115372.

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27

Zhao, Anqi. "`Time for a New Angle!': Unravel the Mystery of Split-Plot Designs via the Potential Outcomes Prism." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493320.

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This manuscript investigates two different approaches, namely the Neymanian randomization based (Neyman, 1923) method and the Bayesian model based (Rubin, 1978) method, towards the causal inference for 2-by-2 split-plot designs (Jones and Nachtsheim, 2009), both under the potential outcomes framework (Neyman, 1923; Rubin, 1974, 1978, 2005). Chapter 1 -- Chapter 5. Given two 2-level factors of interest, a 2-by-2 split-plot design (a) takes each of the 2-by-2 = 4 possible factorial combinations as a treatment, (b) identifies one factor as 'whole-plot,' (c) divides the experimental units into bl

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28

Sepehrifar, Mohammad. "MODELING AND CHARACTERIZATIONS OF NEW NOTIONS IN LIFE TESTING WITH STATISTICAL APPLICATIONS." Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3599.

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Knowing the class to which a life distribution belongs gives us an idea about the aging of the device or system the life distribution represents, and enables us to compare the aging properties of different systems. This research intends to establish several new nonparametric classes of life distributions defined by the concept of inactivity time of a unit with a guaranteed minimum life length. These classes play an important role in the study of reliability theory, survival analysis, maintenance policies, economics, actuarial sciences and many other applied areas.<br>Ph.D.<br>Department of Sta

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29

Pond, Eric L. "An analysis of the relationship of military affiliation to demographics, new sailor survey responses, and boot camp success." Thesis, Monterey, Calif. : Naval Postgraduate School, 2008. http://handle.dtic.mil/100.2/ADA483498.

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Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2008.<br>Thesis Advisor(s): Buttrey, Samuel E. "June 2008." Description based on title screen as viewed on August 26, 2008. Includes bibliographical references (p. 139-140). Also available in print.

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30

Mehrabian, Amanollah. "The leverage effect in stochastic volatility: new models, Bayesian inference, and model selection." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107636.

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A striking empirical feature of many financial time series is that when the price drops, the future volatility increases. This negative correlation between the financial return and future volatility processes was initially addressed in Black 76 and explained based on financial leverage, or a firm's debt-to-equity ratio: when the price drops, financial leverage increases, the firm becomes riskier, and hence, the future expected volatility increases. The phenomenon is, therefore, traditionally been named the leverage effect. In a discrete time Stochastic Volatility (SV) model framework, the leve

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31

Moodie, Felicity Zoe. "A new framework for nonparametric estimation of the bivariate survivor function /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/9535.

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32

Safonov, Taras Aleksandrovich. "A New Measure of Quality of Life and Its Application in the Regions of the Russian Federation." Thesis, Western Illinois University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1597385.

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<p> The search for a reliable measure of the quality of life (QOL) has long been a heavily discussed issue for many a researcher and a policy analyst. Despite much debate in theoretical and practical circles, there is still no consensus on either what exactly constitutes QOL or on the universal formula to quantify this concept. For instance, the United Nations’ Human Development Index is arguably one of the most well-known indicators of people’s welfare that allows one to compare QOL across countries and regional blocs. </p><p> However, the practice of regional policy developmen

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33

Savarese, Paul Tenzing. "New design comparison criteria in Taguchi's robust parameter design." Diss., This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-06062008-171200/.

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34

Chebikin, Denis. "Polytopes, generating functions, and new statistics related to descents and inversions in permutations." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43793.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>Includes bibliographical references (p. 75-76).<br>We study new statistics on permutations that are variations on the descent and the inversion statistics. In particular, we consider the alternating descent set of a permutation [sigma] = [sigma] 1 [sigma] 2 an defined as the set of indices i such that either i is odd and ai > ui+l, or i is even and au < au+l. We show that this statistic is equidistributed with the 3-descent set statistic on permutations [sigma] = [sigma] 1 [sigma] 2 ... [sigma] n+1 with al =

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35

Julien, Marilyse. "Development of a new disease activity index for Systemic Sclerosis using traditional and machine learning techniques." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22023.

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Scleroderma is an auto-immune disease characterized by thickened and hardened skin. Similarly to other rheumatic diseases such as Lupus, disease activity in Scleroderma greatly fluctuates over time. Developing a new disease activity index for Scleroderma is a necessary step before undertaking clinical trials to test different treatments and would provide a conceptual structure to approach this poorly-defined disease. In this thesis, we first apply statistical methods traditionally used to develop disease activity indices such as Factor Analysis, Principal Component Analysis and Multiple Line

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36

Li, Yingzhen. "Approximate inference : new visions." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277549.

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Nowadays machine learning (especially deep learning) techniques are being incorporated to many intelligent systems affecting the quality of human life. The ultimate purpose of these systems is to perform automated decision making, and in order to achieve this, predictive systems need to return estimates of their confidence. Powered by the rules of probability, Bayesian inference is the gold standard method to perform coherent reasoning under uncertainty. It is generally believed that intelligent systems following the Bayesian approach can better incorporate uncertainty information for reliable

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37

Botana, Alcalde Adolfo. "New methods in mixture analysis." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/new-methods-in-mixture-analysis(3e15a837-6576-4252-b060-587eb10cc25a).html.

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The quest for a complete understanding of mixtures is a challenge which has stimulated the development of several techniques. One of the most powerful NMR-based techniques is known as Diffusion-Ordered SpectroscopY (DOSY), in which it is possible to distinguish the NMR spectra of chemical species with different hydrodynamic radii, i.e. with different self-diffusion coefficients. It allows the study of intact mixtures, providing information on the interactions within the mixture and saving time and money compared to other techniques. Unfortunately, DOSY is not very effective when signals overla

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38

Pechoutre, Jean-Baptiste. "Optimization of calculation models of maintenance offers for new civil engines." Thesis, KTH, Flygdynamik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-77621.

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The sales support department performs calculations concerning maintenance offerings for civil engines based on the use of complex tools. This report describes the missions conducted during my Master's thesis: firstly, the establishment of a monitoring and security tool in the process of calculating maintenance costs. The second achievement is the creation of a tool for decision support in order to estimate and compare some of the maintenance costs associated with the use of the new commercial engine and those associated with its competitor. The goal is to estimate offers configurations giving

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39

Huakau, John Tupou. "New methods for analysis of epidemiological data using capture-recapture methods." Thesis, University of Auckland, 2002. http://wwwlib.umi.com/dissertations/fullcit/3085723.

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Capture-recapture methods take their origins from animal abundance estimation, where they were used to estimate the unknown size of the animal population under study. In the late 1940s and again in the late 1960s and early 1970s these same capture-recapture methods were modified and applied to epidemiological list data. Since then through their continued use, in particular in the 1990s, these methods have become popular for the estimation of the completeness of disease registries and for the estimation of the unknown total size of human disease populations. In this thesis we investigate new

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40

Ritchie, Felix. "Accessing the New Earnings Survey Panel Dataset : efficient techniques and applications." Thesis, University of Stirling, 1996. http://hdl.handle.net/1893/21519.

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The New Earnings Survey Panel Dataset is one of the largest datasets of its kind in the world. Its size and confidentiality restrictions present considerable difficulties for analysis using standard econometric packages. This thesis presents a number of methods for accessing the information held within the panel relatively efficiently, based upon the use of cross-product matrices and on data compression techniques. These methods allow, for the first time, the panel aspect of the dataset to be used in analysis. The techniques described here are then employed to produce an overview of changes in

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41

Zhang, Chian-fan. "Applying spatial theory to new democracies : a model for analyzing aggregate election data /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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42

Mikolai, Julia. "Partnership dynamics and the transition to first birth in Europe and the United States : new insights from a multi-state approach." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/378648/.

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43

Canter, Brandi N. "Modeling Antibiotic Resistance when Adding a New Antibiotic to a Hospital Setting." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/honors/30.

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As of now, not many pharmaceutical companies are producing new categories of antibiotics to fight bacterial infections. Therefore, bacteria are building up a resistance to the medications commonly used. Often, antibiotic resistance begins within a hospital. To combat resistance, researchers completed several studies using cycling of the medications that are already in place, but they found either no improvement or the resistance increased with this type of setting. In addition, although preventative infection control measures have been shown to decrease antibiotic resistance for some antibiot

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Wang, Yu-Xiang. "New Paradigms and Optimality Guarantees in Statistical Learning and Estimation." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/1113.

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Machine learning (ML) has become one of the most powerful classes of tools for artificial intelligence, personalized web services and data science problems across fields. Within the field of machine learning itself, there had been quite a number of paradigm shifts caused by the explosion of data size, computing power, modeling tools, and the new ways people collect, share, and make use of data sets. Data privacy, for instance, was much less of a problem before the availability of personal information online that could be used to identify users in anonymized data sets. Images, videos, as well a

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45

Sun, Xin. "Statistical methods for diagnostic testing: an illustration using a new method for cancer detection." Kansas State University, 2013. http://hdl.handle.net/2097/16679.

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Master of Science<br>Department of Statistics<br>Gary Gadbury<br>This report illustrates how to use two statistic methods to investigate the performance of a new technique to detect breast cancer and lung cancer at early stages. The two methods include logistic regression and classification and regression tree (CART). It is found that the technique is effective in detecting breast cancer and lung cancer, with both sensitivity and specificity close to 0.9. But the ability of this technique to predict the actual stages of cancer is low. The age variable improves the ability of logistic regressio

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46

Zhang, Yongxu. "ON TWO NEW ESTIMATORS FOR THE CMS THROUGH EXTENSIONS OF OLS." Diss., Temple University Libraries, 2017. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/449833.

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Statistics<br>Ph.D.<br>As a useful tool for multivariate analysis, sufficient dimension reduction (SDR) aims to reduce the predictor dimensionality while simultaneously keeping the full regression information, or some specific aspects of the regression information, between the response and the predictor. When the goal is to retain the information about the regression mean, the target of the inference is known as the central mean space (CMS). Ordinary least squares (OLS) is a popular estimator of the CMS, but it has the limitation that it can recover at most one direction in the CMS. In this di

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47

Barrett, Tyson S. "Marginal Mediation Analysis: A New Framework for Interpretable Mediated Effects." DigitalCommons@USU, 2018. https://digitalcommons.usu.edu/etd/6963.

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Mediation analysis is built to answer not only if one variable affects another, but how the effect takes place. However, it lacks interpretable effect size estimates in situations where the mediator (an intermediate variable) and/or the outcome is categorical or otherwise non-normally distributed. By integrating a powerful approach known as average marginal effects within mediation analysis—termed Marginal Mediation Analysis (MMA)—the issues regarding categorical mediators and/or outcomes are, in large part, resolved. This new approach allows the estimation of the indirect effects (those effec

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48

Fan, Yiying. "Covariance estimation and application to building a new control chart." Case Western Reserve University School of Graduate Studies / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=case1291406214.

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49

Johnson, Andrew, of Western Sydney Hawkesbury University, Faculty of Social Inquiry, and School of Ecology. "Crime, governance and numbers : a genealogy of counting crime in New South Wales." THESIS_FSI_SEL_Johnson_A.xml, 2000. http://handle.uws.edu.au:8081/1959.7/535.

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This thesis is an intellectual genealogy of counting crime in New South Wales. It is a history of a system of thought which is one of the contemporary foundations of the way we interpret the nature and extent of crime today. It argues that the incitement to annually record crime statistics in New South Wales, and internationally, is immediately connected with a will to govern crime. This thesis traces this bonding of the technology of crime statistics with mentalities of government, and maintains that although the connection of these two discourses has been highly effective, it has not been on

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50

Liu, Fang. "New Results on the False Discovery Rate." Diss., Temple University Libraries, 2010. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/96718.

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Statistics<br>Ph.D.<br>The false discovery rate (FDR) introduced by Benjamini and Hochberg (1995) is perhaps the most standard error controlling measure being used in a wide variety of applications involving multiple hypothesis testing. There are two approaches to control the FDR - the fixed error rate approach of Benjamini and Hochberg (BH, 1995) where a rejection region is determined with the FDR below a fixed level and the estimation based approach of Storey (2002) where the FDR is estimated for a fixed rejection region before it is controlled. In this proposal, we concentrate on both these

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