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空间点过程二阶强度加权积分的估计AI 解读

SUMMARY This paper considers the nonparametric estimation of the integral J=∫0Ttλ2(t)φ(t)dt where λ2(t) is the unknown second-order intensity function of a two-dimensional stationary isotropic point process observed in some region and φ(t) is known for t ϵ [0, T]. An unbiased estimator of J is derived, and a computationally fast approximation to it is proposed. The estimator is then used to obtain a kernel method for smoothing point process data, a new estimator of the…

Jacobi 定理及其推广AI 解读

A theorem of Jacobi (1841), which shows how the ordinary least-squares estimator from a linear regression can be represented as the weighted sum of ‘elementary’ estimators of the parameters, is extended to the generalized least-squares estimator. The generalization is applied to a problem in microwave engineering.

Jacobi 定理及其推广AI 解读

A theorem of Jacobi (1841), which shows how the ordinary least-squares estimator from a linear regression can be represented as the weighted sum of ‘elementary’ estimators of the parameters, is extended to the generalized least-squares estimator. The generalization is applied to a problem in microwave engineering.

圆心与半径若干最小二乘估计量的统计性质AI 解读

SUMMARY This paper examines the statistical behaviour of some least squares estimators of the centre and radius of a circle. Two error models are used. The asymptotic consistency of the estimators is investigated. Where asymptotic consistency is established, asymptotic covariance matrices are obtained. A small sample simulation study gives results showing the same pattern as those of the asymptotic theory.

非齐次与调制 Gamma 过程AI 解读

Two classes of point processes, the inhomogeneous and modulated gamma processes, are defined. Asymptotic test statistics of stationarity are derived for modulated gamma processes. Some examples are studied in detail and applied to two sets of data.

非齐次与调制伽马过程AI 解读

Two classes of point processes, the inhomogeneous and modulated gamma processes, are defined. Asymptotic test statistics of stationarity are derived for modulated gamma processes. Some examples are studied in detail and applied to two sets of data.