scholarly journals A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods

Stats ◽  
2020 ◽  
Vol 3 (4) ◽  
pp. 475-483
Author(s):  
Salim Bouzebda ◽  
Christophe Chesneau
Keyword(s):  
Nonparametric Estimation ◽  
Estimation Method ◽  
Almost Sure Convergence ◽  
Wavelet Estimation ◽  
Wavelet Estimator ◽  
Statistical Framework ◽  
Conditional Mode ◽  
Wavelet Methods ◽  
Compact Subsets

The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of Rd. A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.

scholarly journals Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

2020 ◽  
Vol 13 (12) ◽  
pp. 298
Author(s):  
Yuan Gao ◽  
Lingju Chen ◽  
Jiancheng Jiang ◽  
Honglong You
Keyword(s):  
Nonparametric Estimation ◽  
Ruin Probability ◽  
Risk Model ◽  
Estimation Method ◽  
Asymptotic Distributions ◽  
Classical Risk Model ◽  
Compound Poisson Risk Model ◽  
The Fourier Transform ◽  
The Classical Risk Model ◽  
Asymptotic Variances

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

scholarly journals Nonparametric estimation of a quantile density function by wavelet methods

2016 ◽  
Vol 94 ◽  
pp. 161-174 ◽  
Author(s):  
Christophe Chesneau ◽  
Isha Dewan ◽  
Hassan Doosti
Keyword(s):  
Density Function ◽  
Nonparametric Estimation ◽  
Wavelet Methods

Wavelet estimation for a multidimensional acoustic or elastic earth

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 902-913 ◽  
Author(s):  
Arthur B. Weglein ◽  
Bruce G. Secrest
Keyword(s):  
Estimation Method ◽  
Normal Derivative ◽  
Source Spectrum ◽  
Earth Model ◽  
Far Field ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Array Pattern ◽  
The Earth ◽  
Source Array

A new and general wave theoretical wavelet estimation method is derived. Knowing the seismic wavelet is important both for processing seismic data and for modeling the seismic response. To obtain the wavelet, both statistical (e.g., Wiener‐Levinson) and deterministic (matching surface seismic to well‐log data) methods are generally used. In the marine case, a far‐field signature is often obtained with a deep‐towed hydrophone. The statistical methods do not allow obtaining the phase of the wavelet, whereas the deterministic method obviously requires data from a well. The deep‐towed hydrophone requires that the water be deep enough for the hydrophone to be in the far field and in addition that the reflections from the water bottom and structure do not corrupt the measured wavelet. None of the methods address the source array pattern, which is important for amplitude‐versus‐offset (AVO) studies. This paper presents a method of calculating the total wavelet, including the phase and source‐array pattern. When the source locations are specified, the method predicts the source spectrum. When the source is completely unknown (discrete and/or continuously distributed) the method predicts the wavefield due to this source. The method is in principle exact and yet no information about the properties of the earth is required. In addition, the theory allows either an acoustic wavelet (marine) or an elastic wavelet (land), so the wavelet is consistent with the earth model to be used in processing the data. To accomplish this, the method requires a new data collection procedure. It requires that the field and its normal derivative be measured on a surface. The procedure allows the multidimensional earth properties to be arbitrary and acts like a filter to eliminate the scattered energy from the wavelet calculation. The elastic wavelet estimation theory applied in this method may allow a true land wavelet to be obtained. Along with the derivation of the procedure, we present analytic and synthetic examples.

How reliable is statistical wavelet estimation?

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. V59-V68 ◽  
Author(s):  
Jonathan A. Edgar ◽  
Mirko van der Baan
Keyword(s):  
Statistical Method ◽  
Estimation Method ◽  
Ground Truth ◽  
Well Logs ◽  
Deterministic Method ◽  
Wavelet Estimation ◽  
Phase Rotation ◽  
Phase Corrections ◽  
Kurtosis Maximization ◽  
Rate Criterion

Well logs often are used for the estimation of seismic wavelets. The phase is obtained by forcing a well-derived synthetic seismogram to match the seismic, thus assuming the well log provides ground truth. However, well logs are not always available and can predict different phase corrections at nearby locations. Thus, a wavelet-estimation method that reliably can predict phase from the seismic alone is required. Three statistical wavelet-estimation techniques were tested against the deterministic method of seismic-to-well ties. How the choice of method influences the estimated wavelet phase was explored, with the aim of finding a statistical method which consistently predicts a phase in agreement with well logs. It was shown that the statistical method of kurtosis maximization by constant phase rotation consistently is able to extract a phase in agreement with seismic-to-well ties. A statistical method based on a modified mutual-information-rate criterion was demonstrated to provide frequency-dependent phase wavelets where the deterministic method could not. Time-varying statistical wavelets also were estimated with good results — a challenge for deterministic approaches because of the short logging sequence. It was concluded that statistical techniques can be used as quality control tools for the deterministic methods, as a way of extrapolating phase away from wells, or to act as standalone tools in the absence of wells.

Wavelet thresholding estimation of density derivatives from a negatively associated size-biased sample

2020 ◽  
Vol 18 (03) ◽  
pp. 2050016
Author(s):  
Junlian Xu
Keyword(s):  
Convergence Rate ◽  
Upper Bounds ◽  
Wavelet Thresholding ◽  
Wavelet Estimation ◽  
Wavelet Estimator ◽  
Negatively Associated ◽  
Better Than

This paper considers wavelet estimation for density derivatives based on negatively associated and size-biased data. We provide upper bounds of nonlinear wavelet estimator on [Formula: see text] risk. It turns out that the convergence rate of the nonlinear estimator is better than that of the linear one.

Evaluation of the nonparametric estimation method in NONMEM VI

2009 ◽  
Vol 37 (1) ◽  
pp. 27-35 ◽  
Author(s):  
Radojka M. Savic ◽  
Maria C. Kjellsson ◽  
Mats O. Karlsson
Keyword(s):  
Nonparametric Estimation ◽  
Estimation Method

Wavelet Estimation Method for Short-Term Prediction of Deep Pit Settlement

2012 ◽  
Vol 594-597 ◽  
pp. 2876-2879
Author(s):  
Jian Guo ◽  
Neng Hui Lin ◽  
Qi Mei Yang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Influencing Factor ◽  
Estimation Method ◽  
Short Term ◽  
Wavelet Estimation ◽  
Deep Pit ◽  
Actual Settlement ◽  
Artificial Neural Network Ann ◽  
Short Term Prediction

A wavelet estimation method is presented herein to estimate deep pit settlement. In this method, the pit settlement is decomposed into the trend settlement and the stochastic settlement by using Wavelet Analysis based on the characteristic of influencing factor. The model identifier is established by using artificial neural network (ANN), and trained to approximate the trend settlement. Then, the prediction controller developed could be applied for estimating the actual settlement. Finally, the verification examples show that the WIAN is an effective tool for predicting the pit settlement dynamically , high precision could be expected and achieved.

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