Related papers: Optimal Data-based Kernel Estimation of Evolutiona…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square…
We consider kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise. The expected estimation error consists of two terms. The systematic bias error grows as the kernel halfwidth increases while the…
In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…
This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…
We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multiple taper estimate. This procedure reduces the expected mean…
Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM),…
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…
Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel…
Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…
Phase retrieval refers to the problem of recovering a signal $\mathbf{x}_{\star}\in\mathbb{C}^n$ from its phaseless measurements $y_i=|\mathbf{a}_i^{\mathrm{H}}\mathbf{x}_{\star}|$, where $\{\mathbf{a}_i\}_{i=1}^m$ are the measurement…
Behavior of neural networks is irremediably determined by the specific loss and data used during training. However it is often desirable to tune the model at inference time based on external factors such as preferences of the user or…