Second-order approximation to the characteristic function of certain point-process integrals

1987 ◽  
Vol 19 (3) ◽  
pp. 546-559 ◽  
Author(s):  
Steven P. Ellis
Keyword(s):  
Characteristic Function ◽  
Point Process ◽  
Order Approximation ◽  
Poisson Approximation ◽  
Characteristic Functions ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Kernel Estimates ◽  
Spatial Point ◽  
Better Than

A general way to look at kernel estimates of densities is to regard them as stochastic integrals with respect to a spatial point process. Under regularity conditions these behave asymptotically as if the point process were Poisson. However, this Poisson approximation may not work well if the data exhibits a lot of clustering. In this paper a more refined approximation to the characteristic functions of the integrals is developed. For clustered data, a ‘Gauss–Poisson’ approximation works better than the Poisson.

Second-order approximation to the characteristic function of certain point-process integrals

1987 ◽  
Vol 19 (03) ◽  
pp. 546-559
Author(s):  
Steven P. Ellis
Keyword(s):  
Characteristic Function ◽  
Point Process ◽  
Order Approximation ◽  
Poisson Approximation ◽  
Characteristic Functions ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Kernel Estimates ◽  
Spatial Point ◽  
Better Than

A general way to look at kernel estimates of densities is to regard them as stochastic integrals with respect to a spatial point process. Under regularity conditions these behave asymptotically as if the point process were Poisson. However, this Poisson approximation may not work well if the data exhibits a lot of clustering. In this paper a more refined approximation to the characteristic functions of the integrals is developed. For clustered data, a ‘Gauss–Poisson’ approximation works better than the Poisson.

scholarly journals Three State Estimation Fusion Methods Based on the Characteristic Function Filtering

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1440
Author(s):  
Yiran Yuan ◽  
Chenglin Wen ◽  
Yiting Qiu ◽  
Xiaohui Sun
Keyword(s):  
Characteristic Function ◽  
State Estimation ◽  
Packet Loss ◽  
Estimation Accuracy ◽  
Measurement Systems ◽  
Fusion Methods ◽  
Estimation Fusion ◽  
Parallel Filter ◽  
Sequential Filter ◽  
Better Than

There are three state estimation fusion methods for a class of strong nonlinear measurement systems, based on the characteristic function filter, namely the centralized filter, parallel filter, and sequential filter. Under ideal communication conditions, the centralized filter can obtain the best state estimation accuracy, and the parallel filter can simplify centralized calculation complexity and improve feasibility; in addition, the performance of the sequential filter is very close to that of the centralized filter and far better than that of the parallel filter. However, the sequential filter can tolerate non-ideal conditions, such as delay and packet loss, and the first two filters cannot operate normally online for delay and will be invalid for packet loss. The performance of the three designed fusion filters is illustrated by three typical cases, which are all better than that of the most popular Extended Kalman Filter (EKF) performance.

SOME EXTENSIONS OF A LEMMA OF KOTLARSKI

2012 ◽  
Vol 28 (4) ◽  
pp. 925-932 ◽  
Author(s):  
Kirill Evdokimov ◽  
Halbert White
Keyword(s):  
Characteristic Function ◽  
Characteristic Functions ◽  
Real Zeros ◽  
Number Of Zeros ◽  
Weaker Conditions

This note demonstrates that the conditions of Kotlarski’s (1967, Pacific Journal of Mathematics 20(1), 69–76) lemma can be substantially relaxed. In particular, the condition that the characteristic functions of M, U1, and U2 are nonvanishing can be replaced with much weaker conditions: The characteristic function of U1 can be allowed to have real zeros, as long as the derivative of its characteristic function at those points is not also zero; that of U2 can have an isolated number of zeros; and that of M need satisfy no restrictions on its zeros. We also show that Kotlarski’s lemma holds when the tails of U1 are no thicker than exponential, regardless of the zeros of the characteristic functions of U1, U2, or M.

Certain Fourier Transforms of Distributions: II

1954 ◽  
Vol 6 ◽  
pp. 186-189 ◽  
Author(s):  
Eugene Lukacs ◽  
Otto Szász
Keyword(s):  
Characteristic Function ◽  
Fourier Transforms ◽  
Necessary Conditions ◽  
Laplace Transforms ◽  
Characteristic Functions ◽  
Necessary Condition ◽  
Multiple Roots ◽  
Not Given ◽  
Class Of Functions

In an earlier paper (1), published in this journal, a necessary condition was given which the reciprocal of a polynomial without multiple roots must satisfy in order to be a characteristic function. This condition is, however, valid for a wider class of functions since it can be shown (2, theorem 2 and corollary to theorem 3) that it holds for all analytic characteristic functions. The proof given in (1) is elementary and has some methodological interest since it avoids the use of theorems on singularities of Laplace transforms. Moreover the method used in (1) yields some additional necessary conditions which were not given in (1) and which do not seem to follow easily from the properties of analytic characteristic functions.

scholarly journals CHARACTERIZING FORAGING PATTERNS AMONG CATTLE AND BONDED AND NON-BONDED SMALL RUMINANTS USING SPATIAL POINT PROCESS TECHNIQUES

2010 ◽  
Author(s):  
D. M. Anderson ◽  
L. W. Murray ◽  
P. Sun ◽  
E. L. Fredrickson ◽  
R. E. Estell ◽  
...  
Keyword(s):  
Point Process ◽  
Small Ruminants ◽  
Spatial Point Process ◽  
Foraging Patterns ◽  
Spatial Point

scholarly journals COMPARISON OF CHARACTERISTIC DISTANCES BETWEEN AIR VOIDS EVALUATED BY THE LINEAR TRAVERSE PROCEDURE AND THE SPATIAL POINT PROCESS METHOD

2019 ◽  
Vol 72 (1) ◽  
pp. 158-165
Author(s):  
Takuma MUROTANI ◽  
Shin-ichi IGARASHI ◽  
Yusuke TERASAWA
Keyword(s):  
Point Process ◽  
Spatial Point Process ◽  
Air Voids ◽  
Spatial Point ◽  
Process Method
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