Journal ArticleDOI
Probability density estimation from sampled data
TLDR
The consistency and asymptotic expressions for the bias and covariance of discrete-time estimates f_{n}(x) for the marginal probability density function f(X) of continuous-time processes X(t) are established.Abstract:
For broad classes of deterministic and random sampling schemes \{t_{k}\} we establish the consistency and asymptotic expressions for the bias and covariance of discrete-time estimates f_{n}(x) for the marginal probability density function f(x) of continuous-time processes X(t) . The effect of the sampling scheme and the sampling rate on the performance of the estimates is studied. The results are established for continuous-time processes X(t) satisfying various asymptotic independence-uncorrelatedness conditions.read more
Citations
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Journal ArticleDOI
Kernel density estimation on random fields
TL;DR: In this paper, the asymptotic normality of kernel estimators of the multivariate density of stationary random fields indexed by ZN is established and appropriate choices of the bandwiths are found.
Journal ArticleDOI
On smoothed probability density estimation for stationary processes
J.V. Castellana,M. R. Leadbetter +1 more
TL;DR: In this paper, a class of smoothed function estimators including those of kernel type, under various decay of dependence conditions for the process were used to obtain consistency and asymptotic distributional results.
Journal ArticleDOI
Recursive probability density estimation for weakly dependent stationary processes
TL;DR: Recursive estimation of the univariate probability density function f(x) for stationary processes \{X_{j}\} is considered and Quadratic-mean convergence and asymptotic normality for density estimators f_{n}( x) are established for strong mixing and for asymPTotically uncorrelated processes.
Journal ArticleDOI
Strong convergence of sums of α-mixing random variables with applications to density estimation
TL;DR: In this article, the strong convergence of sums of random variables belonging to a triangular array is studied and general results on the convergence of kernel density estimators are derived. But they assume that this array satisfies an α-mixing condition.
Journal ArticleDOI
Local linear spatial regression
TL;DR: In this paper, a local linear kernel estimator of the regression function x → g(x) is proposed and investigated under mild regularity assumptions, asymptotic normality of the estimators of g (x) and its derivatives is established.
References
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Journal ArticleDOI
On Estimation of a Probability Density Function and Mode
TL;DR: In this paper, the problem of the estimation of a probability density function and of determining the mode of the probability function is discussed. Only estimates which are consistent and asymptotically normal are constructed.
Journal ArticleDOI
Remarks on Some Nonparametric Estimates of a Density Function
TL;DR: In this article, some aspects of the estimation of the density function of a univariate probability distribution are discussed, and the asymptotic mean square error of a particular class of estimates is evaluated.
Journal ArticleDOI
The estimation of the gradient of a density function, with applications in pattern recognition
K. Fukunaga,L. Hostetler +1 more
TL;DR: Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.
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A central limit theorem and a strong mixing condition.
TL;DR: This paper focuses on the analysis of the Fouriersche Integrate polynomial, which is a very simple and straightforward way to solve the inequality of the following type: For α ≥ 1, β ≥ 1 using LaSalle's inequality.
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On Strong Mixing Conditions for Stationary Gaussian Processes
A. N. Kolmogorov,Yu. A. Rozanov +1 more
TL;DR: In this article, conditions for strong mixing of stationary random Gaussian processes were considered and it was shown that strong mixing occurs when the spectral density of the process is continuous and positive.