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If you are working in digital signal processing, control or numerical analysis, you will find this authoritative analysis of quantization noise (roundoff error) invaluable. Do you know where the theory of quantization noise comes from, and under what circumstances it is true? Get answers to these and other important practical questions from expert authors, including the founder of the field and formulator of the theory of quantization noise, Bernard Widrow. The authors describe and analyze uniform quantization, floating-point quantization, and their applications in detail. Key features include: • Analysis of floating point round off • Dither techniques and implementation issues analyzed • Offers heuristic explanations along with rigorous proofs, making it easy to understand 'why' before the mathematical proof is given.
Roundoff errors. --- Roundoff errors --- Error analysis (Mathematics) --- Numerical analysis --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Statistics
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Part of the OXFORD STATISTICAL SCIENCE series describing the use of smoothing techniques in statistics with an emphasis on applications rather than detailed theory, and making extensive reference to S-Plus as a computing environment in which examples can be explored. S-Plus functions and example scripts are provided to implement the techniques.
Smoothing (Statistics) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Kernel functions.
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Methods of kernel estimates represent one of the most effective nonparametric smoothing techniques. These methods are simple to understand and they possess very good statistical properties. This book provides a concise and comprehensive overview of statistical theory and in addition, emphasis is given to the implementation of presented methods in Matlab. All created programs are included in a special toolbox which is an integral part of the book. This toolbox contains many Matlab scripts useful for kernel smoothing of density, cumulative distribution function, regression function, hazard funct
Smoothing (Statistics) --- Kernel functions. --- Functions, Kernel --- Functions of complex variables --- Geometric function theory --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics
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Exponential smoothing methods have been around since the 1950s, and are the most popular forecasting methods used in business and industry. Recently, exponential smoothing has been revolutionized with the introduction of a complete modeling framework incorporating innovations state space models, likelihood calculation, prediction intervals and procedures for model selection. In this book, all of the important results for this framework are brought together in a coherent manner with consistent notation. In addition, many new results and extensions are introduced and several application areas are examined in detail. Rob J. Hyndman is a Professor of Statistics and Director of the Business and Economic Forecasting Unit at Monash University, Australia. He is Editor-in-Chief of the International Journal of Forecasting, author of over 100 research papers in statistical science, and received the 2007 Moran medal from the Australian Academy of Science for his contributions to statistical research. Anne B. Koehler is a Professor of Decision Sciences and the Panuska Professor of Business Administration at Miami University, Ohio. She has numerous publications, many of which are on forecasting models for seasonal time series and exponential smoothing methods. J.Keith Ord is a Professor in the McDonough School of Business, Georgetown University, Washington DC. He has authored over 100 research papers in statistics and its applications and ten books including Kendall's Advanced Theory of Statistics. Ralph D. Snyder is an Associate Professor in the Department of Econometrics and Business Statistics at Monash University, Australia. He has extensive publications on business forecasting and inventory management. He has played a leading role in the establishment of the class of innovations state space models for exponential smoothing.
Business forecasting. --- Smoothing (Statistics) --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Business --- Business forecasts --- Forecasting, Business --- Economic forecasting --- Forecasting --- Distribution (Probability theory. --- Statistics. --- Economic theory. --- Mathematical statistics. --- Probability Theory and Stochastic Processes. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Statistical Theory and Methods. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Economic theory --- Political economy --- Social sciences --- Economic man --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities. --- Statistics . --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.
Interpolation. --- Smoothing (Numerical analysis) --- Smoothing (Statistics) --- Curve fitting. --- Splines. --- Spline theory. --- Spline functions --- Approximation theory --- Interpolation --- Joints (Engineering) --- Mechanical movements --- Harmonic drives --- Fitting, Curve --- Numerical analysis --- Least squares --- Statistics --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Graphic methods --- Accuracy and precision. --- Affine space. --- Affine variety. --- Algorithm. --- Approximation. --- Arbitrarily large. --- B-spline. --- Banach space. --- Bernstein polynomial. --- Bifurcation theory. --- Big O notation. --- Birkhoff interpolation. --- Boundary value problem. --- Bézier curve. --- Chaos theory. --- Computation. --- Computational problem. --- Condition number. --- Constrained optimization. --- Continuous function (set theory). --- Continuous function. --- Control function (econometrics). --- Control theory. --- Controllability. --- Convex optimization. --- Convolution. --- Cubic Hermite spline. --- Data set. --- Derivative. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Directional derivative. --- Discrete mathematics. --- Dynamic programming. --- Equation. --- Estimation. --- Filtering problem (stochastic processes). --- Gaussian quadrature. --- Gradient descent. --- Gramian matrix. --- Growth curve (statistics). --- Hermite interpolation. --- Hermite polynomials. --- Hilbert projection theorem. --- Hilbert space. --- Initial condition. --- Initial value problem. --- Integral equation. --- Iterative method. --- Karush–Kuhn–Tucker conditions. --- Kernel method. --- Lagrange polynomial. --- Law of large numbers. --- Least squares. --- Linear algebra. --- Linear combination. --- Linear filter. --- Linear map. --- Mathematical optimization. --- Mathematics. --- Maxima and minima. --- Monotonic function. --- Nonlinear programming. --- Nonlinear system. --- Normal distribution. --- Numerical analysis. --- Numerical stability. --- Optimal control. --- Optimization problem. --- Ordinary differential equation. --- Orthogonal polynomials. --- Parameter. --- Piecewise. --- Pointwise. --- Polynomial interpolation. --- Polynomial. --- Probability distribution. --- Quadratic programming. --- Random variable. --- Rate of convergence. --- Ratio test. --- Riccati equation. --- Simpson's rule. --- Simultaneous equations. --- Smoothing spline. --- Smoothing. --- Smoothness. --- Special case. --- Spline (mathematics). --- Spline interpolation. --- Statistic. --- Stochastic calculus. --- Stochastic. --- Telemetry. --- Theorem. --- Trapezoidal rule. --- Waypoint. --- Weight function. --- Without loss of generality.
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