Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete.
About: This article is published in Biometrika.The article was published on 1963-12-01. It has received 237 citations till now.
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TL;DR: Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable and argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing.
Abstract: Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. HA¤rdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper understanding of the techniques. The methods covered in this text have numerous applications in many areas using statistical analysis. Examples are drawn from economics as well as from other disciplines including medicine and engineering.
1,421 citations
Cites background from "Zeitschrift fur Wahrscheinlichkeits..."
...The special case of Si = Xi has been investigated by Cheng and Lin (1981). A notion of an asymptotic equivalence of the weight sequences {W (2) hi } and {W (3) hi } is deferred to the Exercises....
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...The special case of Si = Xi has been investigated by Cheng and Lin (1981). A notion of an asymptotic equivalence of the weight sequences {W (2) hi } and {W (3) hi } is deferred to the Exercises. Note that {W (1) hi } and {W (2) hi } do not necessarily sum up to one, but {W (3) hi } does. The weights W (3) hi (x) are related to the so-called convolution smoothing as defined by Clark (1980); see Exercise 3....
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TL;DR: In this paper, fast closed form solutions for prices on European stock options were developed in a jump-diffusion model with stochastic volatility and Stochastic interest rates, using the Fourier inversion formula for distribution functions.
Abstract: Fast closed form solutions for prices on European stock options are developed in a jump-diffusion model with stochastic volatility and stochastic interest rates. The probability functions in the solutions are computed by using the Fourier inversion formula for distribution functions. The model is calibrated for the S and P 500 and is used to analyze several effects on option prices, including interest rate variability, the negative correlation between stock returns and volatility, and the negative correlation between stock returns and interest rates.
442 citations
Cites methods from "Zeitschrift fur Wahrscheinlichkeits..."
...In addition to option prices, one can compute derivatives to 2See the analysis in Chesney, Elliott, and Gibson (1993), section 3 and Appendix B, and apply equation (2.k) of Pitman and Yor (1982)....
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01 Jan 2004
TL;DR: This tutorial explains the reasons for using this platform for simulation, discusses why this is frequently an efficient way to build simulation models and execute them, describes how to setup a spreadsheet simulation, and examines some limitations on the use of spreadsheets for simulation.
Abstract: “Spreadsheet simulation” refers to the use of a spreadsheet as a platform for representing simulation models and performing simulation experiments. This tutorial explains the reasons for using this platform for simulation, discusses why this is frequently an efficient way to build simulation models and execute them, describes how to setup a spreadsheet simulation, and finally examines some limitations on the use of spreadsheets for simulation.
407 citations
14 Jun 2012
TL;DR: In this paper, a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments is presented. This easily verifiable condition uses the spectrum of the average weight matrix.
Abstract: We consider the consensus problem for stochastic discrete time linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1.
391 citations
References
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Posted Content•
TL;DR: Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable and argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing.
Abstract: Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. HA¤rdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper understanding of the techniques. The methods covered in this text have numerous applications in many areas using statistical analysis. Examples are drawn from economics as well as from other disciplines including medicine and engineering.
1,421 citations
Book•
01 Jan 1987
TL;DR: In this article, a Unified Asymptotic Theory for Nonlinear Regression with Regression Structure (UATRS) is proposed. But it is not a unified theory for dynamic nonlinear models.
Abstract: Univariate Nonlinear Regression. Univariate Nonlinear Regression: Special Situations. A Unified Asymptotic Theory for Nonlinear Models with Regression Structure. Univariate Nonlinear Regression: Asymptotic Theory. Multivariate Nonlinear Regression. Nonlinear Simultaneous Equations Models. A Unified Asymptotic Theory for Dynamic Nonlinear Models. References. Index.
1,187 citations
01 Jan 2004
TL;DR: This tutorial explains the reasons for using this platform for simulation, discusses why this is frequently an efficient way to build simulation models and execute them, describes how to setup a spreadsheet simulation, and examines some limitations on the use of spreadsheets for simulation.
Abstract: “Spreadsheet simulation” refers to the use of a spreadsheet as a platform for representing simulation models and performing simulation experiments. This tutorial explains the reasons for using this platform for simulation, discusses why this is frequently an efficient way to build simulation models and execute them, describes how to setup a spreadsheet simulation, and finally examines some limitations on the use of spreadsheets for simulation.
407 citations
TL;DR: In this paper, a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments is presented. This easily verifiable condition uses the spectrum of the average weight matrix.
Abstract: We consider the consensus problem for stochastic discrete-time linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1.
398 citations
TL;DR: In this article, a connection between resilience and reactivity is established by introducing two variability-based stability measures, intrinsic, stochastic and deterministic invariability, respectively defined as the inverse of the strongest stationary response to white-noise and to single-frequency perturbations.
114 citations