tailieunhanh - Ebook Advanced calculus with applications in statistics (2nd edition): Part 2

(BQ) Part 2 book "Advanced calculus with applications in statistics" has contents: Optimization in statistics, approximation of functions, orthogonal polynomials, fourier series, approximation of integrals. | CHAPTER 8 Optimization in Statistics Optimization is an essential feature in many problems in statistics. This is apparent in almost all fields of statistics. Here are few examples, some of which will be discussed in more detail in this chapter. 1. In the theory of estimation, an estimator of an unknown parameter is sought that satisfies a certain optimality criterion such as minimum variance, maximum likelihood, or minimum average risk Žas in the case of a Bayes estimator Some of these criteria were already discussed in Section . For example, in regression analysis, estimates of the parameters of a fitted model are obtained by minimizing a certain expression that measures the closeness of the fit of the model. One common example of such an expression is the sum of the squared residuals Žthese are deviations of the predicted response values, as specified by the model, from the corresponding observed response values This particular expression is used in the method of ordinary least squares. A more general class of parameter estimators is the class of M-estimators. See Huber Ž1973, 1981 The name ‘‘ M-estimator’’ comes from ‘‘generalized maximum likelihood.’’ They are based on the idea of replacing the squared residuals by another symmetric function of the residuals that has a unique minimum at zero. For example, minimizing the sum of the absolute values of the residuals produces the so-called least absolute ®alues ŽLAV. estimators. 2. Estimates of the variance components associated with random or mixed models are obtained by using several methods. In some of these methods, the estimates are given as solutions to certain optimization problems as in maximum likelihood ŽML. estimation and minimum norm quadratic unbiased estimation ŽMINQUE In the former method, the likelihood function is maximized under the assumption of normally distributed data wsee Hartley and Rao . A completely different approach is used in the latter method, which was proposed .

• Toán học
• Optimization in statistics
• Approximation of functions
• Orthogonal polynomials
• Fourier series
• Approximation of integrals
• Advanced calculus
• Applications in statistics
• Angiographic Stenosis
• Optimization
• Radiation Dose
• Image Quality
• Cardiac Catheterization
• Catheterization Laboratories
• Mathematical statistics
• Mathematical statistics with applications
• Descriptive statistics
• Interval estimation
• Hypothesis testing
• Point estimation
• Even you can learn statistics
• Learn statistics
• Simple linear regression
• Multiple regression
• Sigma applications of statistics
• Linear regression models
• Design of experiments
• Analysis of variance
• Empirical methods
• Some issues in statistical applications
• Nonparametric tests
• An introduction to set theory
• Basic concepts in linear algebra
• Continuity of functions
• Infinite sequences
• Multidimensional calculus
• Basic business statistics
• Multiple regression model building
• Statistical applications
• Analyzing data
• Elementary statistics
• Statistical inferences
• Inferences involving
• Inferences involving two populations
• Applications of chi square
• Linear correlation
• Nonparametric statistics
• Applications of q deformed Fermi Dirac statistics
• Statistical moment
• Thermodynamic properties
• Magnetic properties
• Metallic thin films
• Mathematics as profession
• Definitions of mathematics
• Quantity
• Statistics and other decision sciences
• Managing Statistics
• Oracle XML Applications
• database
• data management
• Oracle XML
• Performance Tuning
• XML Data
• Administration
• Visualizing data
• Basic probability
• Discrete probability distributions
• The normal distribution
• Other continuous distributions
• Conditional Probability
• Probability Function
• Combinatorial Probability
• Hypergeometric Probabilities
• Random variables
• Special distributions
• Types of data
• Business mathematics and statistics
• Business mathematics
• Business equations
• Specialised business applications
• Linear equations
• Linear inequalities
• Statistical techniques
• Statistical techniques in business
• Statistical techniques in economics
• Chi square applications
• Test of hypothesis
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• streamlined presentation
• develops frame theory
• applications
• electrical engineering
• applied mathematics
• statistics and computer science
• Mathematics for engineers
• Applications of integration
• Differential equations
• The Laplace transform
• Statistics and probability
• Partial differentiation
• The Fourier transform
• Statistics for managers using Microsoft excel
• Time series forecasting
• Quality management
• Nonparametric methods