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221.
Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers
holds if the class
has an envelope function that is μ-integrable, or if
is bounded in L
p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of
the class
in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion
local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE)
and to prove consistency for a class of simple M-estimators.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
222.
A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R
d
is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L
p
-properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit. 相似文献
223.
Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous Bézout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous Bézout number. As with any other local search method, it may give a local minimum rather than the minimum over all possible homogenizations. Numerical examples show the efficiency of this local search method.
224.
If (Xi, i
) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H0: {f=f0}, where f0 is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between fn, a kernel estimator of f, and f0, or between fn and its expected value computed under H0. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071–1095). 相似文献
225.
The problem of estimating of the law
(in the space
of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure
with probability 1 converges weakly in
to
.(2) The empirical measure
corresponding to the path
, converges a.s. when T in total variation to the marginal law if and only if the local time for X exists. (3) The L
p-convergence of the empirical densities f
T to the marginal one is studied.(4) A version of the CLT for empirical densities f
T provided both the mixing properties and the local time of the underlying process are good enough is given. 相似文献
226.
Probability Density Function Estimation Using Gamma Kernels 总被引:6,自引:0,他引:6
Song Xi Chen 《Annals of the Institute of Statistical Mathematics》2000,52(3):471-480
We consider estimating density functions which have support on [0, ) using some gamma probability densities as kernels to replace the fixed and symmetric kernel used in the standard kernel density estimator. The gamma kernels are non-negative and have naturally varying shape. The gamma kernel estimators are free of boundary bias, non-negative and achieve the optimal rate of convergence for the mean integrated squared error. The variance of the gamma kernel estimators at a distance x away from the origin is O(n
–4/5
x
–1/2) indicating a smaller variance as x increases. Finite sample comparisons with other boundary bias free kernel estimators are made via simulation to evaluate the performance of the gamma kernel estimators. 相似文献
227.
B. B. Bhattacharyya X. Li M. Pensky G. D. Richardson 《Annals of the Institute of Statistical Mathematics》2000,52(1):71-83
The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model st= s-1,t+s,t-1- s-1,t-1+st. Moreover, for the sequence
n
= e
c/n
,
n
= e
d/n
of local Pitman-type alternatives, the limiting distribution of the normalized periodogram ordinate is shown to be a linear combination of two independent chi-square random variables whose coefficients depend on c and d. This result is used to tabulate the asymptotic power of a test for various values of c and d. A comparison is made between the periodogram test and a spatial domain test. 相似文献
228.
In this paper we determine the possible Hilbert functions ofa CohenMacaulay local ring of dimension d and multiplicitye, in the case where the embedding dimension v satisfies v =e + d 3 and the CohenMacaulay type is less thanor equal to e 3. 1991 Mathematics Subject Classification:primary 13D40; secondary 13P99. 相似文献
229.
Tim Haslett Simon Moss Charles Osborne Paul Ramm 《Nonlinear dynamics, psychology, and life sciences》2000,4(1):67-86
This paper examines the imposition of local rules in five mail delivery centres of Australia Post. Local rules are patterns of behaviour used by subunits of an organization to optimise their payoff. These local rules may ultimately benefit the total organization. Fitness landscapes are used to examine the emergence of local rules in this workplace. This research examined the relationship between the time taken to sort the mail and the volume of this mail. Work rates show a clear catastrophe shift; that is, work rates suddenly drop when the volume of mail exceeds a certain level, as Postal Delivery Officers apply local rules to maximise gains inherent in the pay structures. Such behaviour is close to that predicted by Kauffman (1995) in computer simulations of lattices and may be indicative of the application of local rules in organizations. The implications of the use of local rules are that behaviour in social systems may be dictated by systemic and emergent processes which are outside immediate management control. A further implication is that organizations may be structured to a significant extent by such local rules. 相似文献
230.
Robert Blackburn 《Journal of Theoretical Probability》2000,13(3):825-842
For X(t) a real-valued symmetric Lévy process, its characteristic function is E(e
iX(t))=exp(–t()). Assume that is regularly varying at infinity with index 1<2. Let L
x
t
denote the local time of X(t) and L*
t
=sup
xR
L
x
t
. Estimates are obtained for P(L
0
t
y) and P(L*
t
y) as y and t fixed. 相似文献