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Finite Sample Efficiency and Drawbacks: An Illustration

2011

Historically, finite-sample efficiency was the first notion of optimality introduced and it is still encountered in introductory statistics texts. The definition has several drawbacks however, one being that it is restricted to the class of unbiased estimators. An example is given to illustrate this.

Mathematical optimizationEfficiencyStein's unbiased risk estimateEstimatorSample (statistics)Class (philosophy)U-statisticMathematicsSSRN Electronic Journal

researchProduct

PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
  - PE2_2 Phenomenology of fundamental interactions
  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
  - PE2_12Optics, non-linear optics and nano-optics
  - PE2_13Quantum optics and quantum information
  - PE2_15Thermodynamics
- PE1Mathematics
  - PE1_1Logic and foundations
  - PE1_6Geometry and global analysis
  - PE1_8Analysis
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  - PE1_9Operator algebras and functional analysis
  - PE1_10ODE and dynamical systems
  - PE1_12Mathematical physics
  - PE1_11Theoretical aspects of partial differential equations
  - PE1_13Probability
  - PE1_14Mathematical statistics
  - PE1_15Generic statistical methodology and modelling
  - PE1_4 Algebraic and complex geometry
  - PE1_19Scientific computing and data processing
  - PE1_2Algebra
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  - PE1_21Application of mathematics in sciences
  - PE1_22Application of mathematics in industry and society
  - PE1_5Lie groups, Lie algebras
  - PE1_18Numerical analysis
  - PE1_16Discrete mathematics and combinatorics
  - PE1_17Mathematical aspects of computer science
  - PE1_3Number theory
- PE3Condensed Matter Physics
  - PE3_1Structure of solids, material growth and characterisation
  - PE3_2Mechanical and acoustical properties of condensed matter, lattice dynamics
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  - PE3_13Structure and dynamics of disordered systems, e.g. soft matter (gels, colloids, liquid crystals), granular matter, liquids, glasses, defects
  - PE3_14Fluid dynamics (physics)
  - PE3_15Statistical physics: phase transitions, condensed matter systems, models of complex systems, interdisciplinary applications
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  - PE5_1Structural properties of materials
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  - PE4_8Electrochemistry, electrodialysis, microfluidics, sensors
  - PE4_10Heterogeneous catalysis
  - PE4_9Method development in chemistry
  - PE4_11Physical chemistry of biological systems
  - PE4_15Photochemistry
  - PE4_14Radiation and Nuclear chemistry
  - PE4_16Corrosion
  - PE4_17Characterisation methods of materials
  - PE4_12Chemical reactions: mechanisms, dynamics, kinetics and catalytic reactions
  - PE4_18Environment chemistry
  - PE4_13Theoretical and computational chemistry
- PE6Computer Science and Informatics
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  - PE6_7Artificial intelligence, intelligent systems, natural language processing
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  - PE6_1Computer architecture, embedded systems, operating systems
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  - PE6_6Algorithms and complexity, distributed, parallel and network algorithms, algorithmic game theory
  - PE6_4Theoretical computer science, formal methods, automata
  - PE6_8Computer graphics, computer vision, multimedia, computer games
- PE7Systems and Communication Engineering
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  - PE7_2Electrical engineering: power components and/or systems
  - PE7_7Signal processing
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  - PE7_9Man-machine interfaces
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  - PE8_7Mechanical engineering
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- PE9Universe Sciences
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- PE10Earth System Science
  - PE10_2Meteorology, atmospheric physics and dynamics
  - PE10_7Physics of earth’s interior, seismology, geodynamics
  - PE10_9Biogeochemistry, biogeochemical cycles, environmental chemistry
  - PE10_8Oceanography (physical, chemical, biological, geological)
  - PE10_1Atmospheric chemistry, atmospheric composition, air pollution
  - PE10_4Terrestrial ecology, land cover change
  - PE10_5Geology, tectonics, volcanology
  - PE10_6Palaeoclimatology, palaeoecology
  - PE10_10Mineralogy, petrology, igneous petrology, metamorphic petrology
  - PE10_3Climatology and climate change
  - PE10_16Ozone, upper atmosphere, ionosphere
  - PE10_15Geomagnetism, palaeomagnetism
  - PE10_17Hydrology, hydrogeology, engineering and environmental geology, water and soil pollution
  - PE10_18Cryosphere, dynamics of snow and ice cover, sea ice, permafrosts and ice sheets
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  - PE10_14Earth observations from space/remote sensing
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  - PE10_13Physical geography, geomorphology
  - PE10_12Sedimentology, soil science, palaeontology, earth evolution
- PE11Materials Engineering
  - PE11_2Engineering of metals and alloys
  - PE11_1Engineering of biomaterials, biomimetic, bioinspired and bio-enabled materials
  - PE11_3Engineering of ceramics and glasses
  - PE11_4Engineering of polymers and plastics
  - PE11_5Engineering of composites and hybrid materials
  - PE11_6Engineering of carbon materials
  - PE11_7Engineering of metal oxides
  - PE11_8Engineering of alternative established or emergent materials
  - PE11_9Nanomaterials engineering, e.g. nanoparticles, nanoporous materials, 1D & 2D nanomaterials
  - PE11_10Soft materials engineering, e.g. gels, foams, colloids
  - PE11_11Porous materials engineering, e.g. covalent-organic, metal-organic, porous aromatic frameworks
  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
- LS1Molecules of Life: Biological Mechanisms, Structures and Functions
  - LS1_2Biochemistry
  - LS1_1Macromolecular complexes including interactions involving nucleic acids, proteins, lipids and carbohydrates
  - LS1_3DNA and RNA biology
  - LS1_4Protein biology
  - LS1_5Lipid biology
  - LS1_6Glycobiology
  - LS1_11Chemical biology
  - LS1_12Protein design
  - LS1_13Early translational research and drug design
  - LS1_14Innovative methods and modelling in molecular, structural and synthetic biology
  - LS1_10Synthetic biology
  - LS1_8Structural biology
  - LS1_9Molecular mechanisms of signalling processes
  - LS1_7Molecular biophysics, biomechanics, bioenergetics
- LS2Integrative Biology: from Genes and Genomes to Systems
  - LS2_1Genetics
  - LS2_3Epigenetics
  - LS2_2Gene editing
  - LS2_4Gene regulation
  - LS2_5Genomics
  - LS2_6Metagenomics
  - LS2_7Transcriptomics
  - LS2_8Proteomics
  - LS2_9Metabolomics
  - LS2_10Glycomics/Lipidomics
  - LS2_11Bioinformatics and computational biology
  - LS2_12Biostatistics
  - LS2_14Genetic diseases
  - LS2_16Innovative methods and modelling in integrative biology
  - LS2_13Systems biology
  - LS2_15Integrative biology for personalised medicine
- LS4Physiology in Health, Disease and Ageing
  - LS4_1Organ and tissue physiology and pathophysiology
  - LS4_4Endocrinology
  - LS4_3Physiology of ageing
  - LS4_2Comparative physiology
  - LS4_5Non-hormonal mechanisms of inter-organ and tissue communication
  - LS4_6Microbiome and host physiology
  - LS4_7Nutrition and exercise physiology
  - LS4_8Impact of stress (including environmental stress) on physiology
  - LS4_9Metabolism and metabolic disorders, including diabetes and obesity
  - LS4_10The cardiovascular system and cardiovascular diseases
  - LS4_11Haematopoiesis and blood diseases
  - LS4_12Cancer
  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
- LS3Cell Biology, Development, Stem Cells and Regeneration
  - LS3_4Cell junctions, cell adhesion, the extracellular matrix, cell communication
  - LS3_5Cell signalling and signal transduction, exosome biology
  - LS3_6Organelle biology and trafficking
  - LS3_7Mechanobiology of cells, tissues and organs
  - LS3_8Embryogenesis, pattern formation, morphogenesis
  - LS3_9Cell differentiation, formation of tissues and organs
  - LS3_10Developmental genetics
  - LS3_11Evolution of developmental strategies
  - LS3_12Organoids
  - LS3_3Cell behaviour, including control of cell shape, cell migration
  - LS3_13Stem cells
  - LS3_14Regeneration
  - LS3_15Development of cell-based therapeutic approaches for tissue regeneration
  - LS3_17Theoretical modelling in cellular, developmental and regenerative biology
  - LS3_16Functional imaging of cells and tissues
  - LS3_1Cell cycle, cell division and growth
  - LS3_2Cell senescence, cell death, autophagy, cell ageing
- LS5Neuroscience and Disorders of the Nervous System
  - LS5_1Neuronal cells
  - LS5_3Neural development and related disorders
  - LS5_5Neural networks and plasticity
  - LS5_10Ageing of the nervous system
  - LS5_11Neurological and neurodegenerative disorders
  - LS5_12Mental disorders
  - LS5_7Sensory systems, sensation and perception, including pain
  - LS5_13Nervous system injuries and trauma, stroke
  - LS5_14Repair and regeneration of the nervous system
  - LS5_15Neuroimmunology, neuroinflammation
  - LS5_16Systems and computational neuroscience (e.g. modelling, simulation, brain oscillations, connectomics)
  - LS5_18Innovative methods and tools for neuroscience
  - LS5_17Imaging in neuroscience
  - LS5_9Neural basis of cognition (e.g. learning, memory, attention, emotions, speech)
  - LS5_6Neurovascular biology and blood-brain barrier
  - LS5_8Neural basis of behaviour (e.g. sleep, consciousness, addiction)
  - LS5_4Neural stem cells
  - LS5_2Glial cells and neuronal-glial communication
- LS6Immunity, Infection and Immunotherapy
  - LS6_1Innate immunity
  - LS6_2Adaptive immunity
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  - LS6_5Biology of pathogens (e.g. bacteria, viruses, parasites, fungi)
  - LS6_7Mechanisms of infection
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  - LS6_8Biological basis of prevention and treatment of infection
  - LS6_9Antimicrobials, antimicrobial resistance
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- LS7Prevention, Diagnosis and Treatment of Human Diseases
  - LS7_2Medical technologies and tools (including genetic tools and biomarkers) for prevention, diagnosis, monitoring and treatment of diseases
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  - LS7_8Effectiveness of interventions, including resistance to therapies
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  - LS7_14Digital medicine, e-medicine, medical applications of artificial intelligence
  - LS7_15Medical ethics
  - LS7_13Palliative medicine
  - LS7_11Environmental health, occupational medicine
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- LS8Environmental Biology, Ecology and Evolution
  - LS8_2Biodiversity
  - LS8_3Conservation biology
  - LS8_4Population biology, population dynamics, population genetics
  - LS8_5Biological aspects of environmental change, including climate change
  - LS8_6Evolutionary ecology
  - LS8_1Ecosystem and community ecology, macroecology
  - LS8_7Evolutionary genetics
  - LS8_8Phylogenetics, systematics, comparative biology
  - LS8_11Behavioural ecology and evolution
  - LS8_9Macroevolution and paleobiology
  - LS8_10Ecology and evolution of species interactions
  - LS8_12Microbial ecology and evolution
  - LS8_13Marine biology and ecology
  - LS8_14Ecophysiology, from organisms to ecosystems
  - LS8_15Theoretical developments and modelling in environmental biology, ecology, and evolution
- LS9Biotechnology and Biosystems Engineering
  - LS9_3Bioengineering of cells, tissues, organs and organisms
  - LS9_2Applied genetics, gene editing and transgenic organisms
  - LS9_4Microbial biotechnology and bioengineering
  - LS9_5Food biotechnology and bioengineering
  - LS9_6Marine biotechnology and bioengineering
  - LS9_7Environmental biotechnology and bioengineering
  - LS9_8Applied plant sciences, plant breeding, agroecology and soil biology
  - LS9_10Veterinary and applied animal sciences
  - LS9_9Plant pathology and pest resistance
  - LS9_11Biomass production and utilisation, biofuels
  - LS9_12Ecotoxicology, biohazards and biosafety
  - LS9_1Bioengineering for synthetic and chemical biology
SHSocial Sciences and Humanities
- SH2Institutions, Governance and Legal Systems
  - SH2_1Political systems, governance
  - SH2_2Democratisation and social movements
  - SH2_3Conflict resolution, war, peace building
  - SH2_4Legal studies, comparative law, law and economics
  - SH2_5Constitutions, human rights, international law
  - SH2_6International relations, global and transnational governance
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  - SH2_9Digital approaches to political science and law
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  - SH1_7Accounting, asset prices, auditing
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- SH3The Social World and Its Interactions
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  - SH4_8Language learning and processing (first and second languages)
  - SH4_11Pragmatics, sociolinguistics, linguistic anthropology, discourse analysis
  - SH4_9Theoretical linguistics; computational linguistics
  - SH4_10Language typology; historical linguistics
- SH6The Study of the Human Past
  - SH6_1Archaeological methods and theory, history of archaeology
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- SH5Texts and Concepts
  - SH5_4Philology; text and image studies
  - SH5_1Classics, ancient literature
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  - SH5_3Book studies
  - SH5_6Philosophy of mind, philosophy of language
  - SH5_7Philosophy of science, epistemology, logic
  - SH5_8Metaphysics, philosophical anthropology; aesthetics
  - SH5_9Ethics and its applications; social philosophy
  - SH5_10History of philosophy
  - SH5_11Digital humanities; digital approaches to literary studies and philosophy
  - SH5_2Theory and history of literature, comparative literature
- SH7Human Mobility, Environment, and Space
  - SH7_2Migration
  - SH7_1Human, economic and social geography
  - SH7_3Population dynamics: households, family and fertility
  - SH7_5Sustainability sciences, environment and resources, ecosystem services
  - SH7_4Social aspects of health, ageing and society
  - SH7_6Environmental and climate change, societal impact and policy
  - SH7_7Cities; urban, regional and rural studies
  - SH7_8Land use and planning
  - SH7_10GIS, spatial analysis; digital geography
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- SH8Studies of Cultures and Arts
  - SH8_1Kinship; diversity and identities, gender, interethnic relations
  - SH8_2Religious studies, ritual; symbolic representation
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  - SH8_4Museums, exhibitions, conservation and restoration
  - SH8_5History of art and of architecture
  - SH8_6Architecture, design, craft, creative industries
  - SH8_7Music and musicology; history of music
  - SH8_8Visual and performing arts, screen, arts-based research
  - SH8_9Digital approaches to anthropology, cultural studies and art