Resampling

About: Resampling is a research topic. Over the lifetime, 5428 publications have been published within this topic receiving 242291 citations.

The method of simulated scores for the estimation of LDV models

Abstract: The method of simulated scores (MSS) is presented for estimating limited dependent variables models (LDV) with flexible correlation structure in the unobservables. We propose simulators that are continuous in the unknown parameter vectors, and hence standard optimization methods can be used to compute the MSS estimators that employ these simulators. The first continuous method relies on a recursive conditioning of the multivariate normal density through a Cholesky triangularization of its variance-covariance matrix. The second method combines results about the conditionals of the multivariate normal distribution with Gibbs resampling techniques. We establish consistency and asymptotic normality of the MSS estimators and derive suitable rates at which the number of simulations must rise if biased simulators are used.

A simple resampling method by perturbing the minimand

Abstract: Suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a U-process structure. The covariance matrix of the estimator is generally a function of the underlying density function, which may be difficult to estimate well by conventional methods. In this paper, we present a simple resampling method by perturbing the objective function repeatedly. Inferences of the parameters can then be made based on a large collection of the resulting optimisers. We illustrate our proposal by three examples with a heteroscedastic regression model.

Power spectral density of unevenly sampled data by least-square analysis: performance and application to heart rate signals

Abstract: This work studies the frequency behavior of a least-square method to estimate the power spectral density of unevenly sampled signals. When the uneven sampling can be modeled as uniform sampling plus a stationary random deviation, this spectrum results in a periodic repetition of the original continuous time spectrum at the mean Nyquist frequency, with a low-pass effect affecting upper frequency bands that depends on the sampling dispersion. If the dispersion is small compared with the mean sampling period, the estimation at the base band is unbiased with practically no dispersion. When uneven sampling is modeled by a deterministic sinusoidal variation respect to the uniform sampling the obtained results are in agreement with those obtained for small random deviation. This approximation is usually well satisfied in signals like heart rate (HR) series. The theoretically predicted performance has been tested and corroborated with simulated and real HR signals. The Lomb method has been compared with the classical power spectral density (PSD) estimators that include resampling to get uniform sampling. The authors have found that the Lomb method avoids the major problem of classical methods: the low-pass effect of the resampling. Also only frequencies up to the mean Nyquist frequency should be considered (lower than 0.5 Hz if the HR is lower than 60 bpm). It is concluded that for PSD estimation of unevenly sampled signals the Lomb method is more suitable than fast Fourier transform or autoregressive estimate with linear or cubic interpolation. In extreme situations (low-HR or high-frequency components) the Lomb estimate still introduces high-frequency contamination that suggest further studies of superior performance interpolators. In the case of HR signals the authors have also marked the convenience of selecting a stationary heart rate period to carry out a heart rate variability analysis.

Arguments for Fisher's Permutation Test

Abstract: The problem of statistical comparison of two distributions, continuous as well as discrete, is considered. Very slight and reasonable modifications of traditional parameteric models, e.g. `normal distributions with equal variances', are shown to result in permutation tests, only. Fisher's permutations test is shown to have optimum properties which mean a good merit for its practical use. Further, an accurate method of determining the $p$-value of Fisher's test is proposed.

Quantifying errors in spectral estimates of HRV due to beat replacement and resampling

Abstract: Spectral estimates of heart rate variability (HRV) often involve the use of techniques such as the fast Fourier transform (FFT), which require an evenly sampled time series. HRV is calculated from the variations in the beat-to-beat (RR) interval timing of the cardiac cycle which are inherently irregularly spaced in time. In order to produce an evenly sampled time series prior to FFT-based spectral estimation, linear or cubic spline resampling is usually employed. In this paper, by using a realistic artificial RR interval generator, interpolation and resampling is shown to result in consistent over-estimations of the power spectral density (PSD) compared with the theoretical solution. The Lomb-Scargle (LS) periodogram, a more appropriate spectral estimation technique for unevenly sampled time series that uses only the original data, is shown to provide a superior PSD estimate. Ectopy removal or replacement is shown to be essential regardless of the spectral estimation technique. Resampling and phantom beat replacement is shown to decrease the accuracy of PSD estimation, even at low levels of ectopy or artefact. A linear relationship between the frequency of ectopy/artefact and the error (mean and variance) of the PSD estimate is demonstrated. Comparisons of PSD estimation techniques performed on real RR interval data during minimally active segments (sleep) demonstrate that the LS periodogram provides a less noisy spectral estimate of HRV.