Related papers: Fourier Analytic Approach to Phase Estimation
In this article, by using composite asymmetric least squares (CALS) and empirical likelihood, we propose a two-step procedure to estimate the conditional value at risk (VaR) and conditional expected shortfall (ES) for the GARCH series.…
This paper explains existing results for the application of special functions to phase estimation, which is a fundamental topic in quantum information. We focus on two special functions. One is prolate spheroidal wave function, which…
In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ($\alpha N$) and sampled under two different random times. Based on…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
In this paper, we propose a statistical theory on measurement and estimation of Rayleigh fading channels in wireless communications and provide complete solutions to the fundamental problems: What is the optimum estimator for the…
Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these…
We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…
This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different…
In this paper phase of a signal has been viewed from a different angle. According to this view a signal can have countably infinitely many phases, one associated with each Fourier component. In other words each frequency has a phase…
We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index alpha<2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape…
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram)…
For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the…