论文检索

核密度估计的自动带宽选择器AI 解读

To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross-validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. It is proposed to select the cut-off frequency by a generalization…

核密度估计的自动带宽选择器AI 解读

To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross-validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. It is proposed to select the cut-off frequency by a generalization…

核密度估计的带宽选择AI 解读

The problem of automatic bandwidth selection for a kernel density estimator is considered. It is well recognized that the bandwidth estimate selected by the least squares cross-validation is subject to large sample variation. This difficulty limits the application of the cross-validation estimate. Based on characteristic functions, an important expression for the cross-validation bandwidth estimate is obtained. The expression clearly points out the source of variation. To…

非参数回归中的稳定化带宽选择方法AI 解读

The problem of bandwidth selection for nonparametric kernel regression is considered. It is well recognized that the classical bandwidth selectors are subject to large sample variation. Due to the large variation, these selectors might not be very useful in practice. Based on the frequency-domain representation of the residual sum of squares (RSS), the source of the variation is pointed out. The observation leads to consideration of a procedure which stabilizes the RSS by…

离散化误差对核密度估计带宽选择的影响AI 解读

It is well known that the cross-validation score function of discretized data often tends to -∞ as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions,…

离散化误差对核密度估计带宽选择的影响AI 解读

It is well known that the cross-validation score function of discretized data often tends to -∞ as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions,…

带宽估计量的渐近分布AI 解读

The problem of automatic bandwidth selection for a kernel regression estimate is studied. Since the bandwidth considerably affects the features of the estimated curve, it is important to understand the behavior of bandwidth selection procedures. The bandwidth estimate considered here is the minimizer of Mallows' criterion. Though it was established that the bandwidth estimate is asymptotically normal, it is well recognized that the rate of convergence is extremely slow. In…

带宽选择器为何倾向于选择较小带宽及其修正方法AI 解读

This note is concerned with the problem of automatic data-driven bandwidth selectors for nonparametric regression. Though some selectors were shown to be consistent and asymptotically unbiased by Rice (1984) and Hãrdle, Hall & Marron (1988), it is often observed in simulation studies that most selectors are biased toward undersmoothing. An explanation for this is given. The source of the large sample variation in the bandwidth estimates is also pointed out. This leads to the…

白高斯时间序列中周期成分的检测AI 解读

SUMMARY A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to a trimmed mean of the periodograms. The asymptotic distributions of the statistics are obtained. It is shown that the proposed test and Fisher's test have the same asymptotic powers against the alternative of a sinusoidal wave at a non-zero Fourier frequency. The simulation results suggest…

时间序列参数的频域加权最小二乘估计AI 解读

A procedure for estimating the parameters of a time series is proposed. The estimate minimizes a criterion function which is the weighted sum of squares of the distances between the periodogram and the spectrum of the series. Under regularity conditions, the estimate is shown to be strongly consistent. The asymptotic distribution of the estimate is also obtained. It is shown that, for a Gaussian process, an asymptotically efficient estimate can be obtained by using an…

利用传感器阵列数据估计移动信号源参数AI 解读

This paper is concerned with the problem of estimating the variable time delays of a signal arriving at an array of sensors. A procedure to estimate the parameters of a linear time delay model is proposed. The procedure compares the Fourier transforms at different frequencies (thereby taking the Doppler effect into consideration). Under regularity conditions, the estimate obtained is shown to be consistent and asymptotically normal. Simulations were carried out and the…