Bandwidth Selection In Density Estimation Research Articles

Cosine-based variable bandwidth selection for nonparametric spectral density estimation under long-range dependence

The optimal bandwidth selection in kernel-based nonparametric density estimation is one of the important parts in the spectral density estimation under long-range dependence (LRD). To improve the performance of the nonparametric spectral density estimation (NPSDE) under LRD, we propose a new cosine-based variable bandwidth selection method, which is motivated by variable bandwidth selection for density estimation and spectral density for autoregressive fractionally-integrated moving average models. The performance of the proposed method was illustrated through the simulation studies and data examples. The proposed cosine-based variable bandwidth selection method for NPSDE under LRD provides better performance than any other bandwidth selection method. Our method is robust to any values of the fractional differencing parameters.

Real-time prediction of upcoming respiratory events via machine learning using snoring sound signal.

The aim of the study was to inspect the acoustic properties and sleep characteristics of a preapneic snoring sound. The feasibility of forecasting upcoming respiratory events by snoring sound was also investigated. Participants with habitual snoring or a heavy breathing sound during sleep were recruited consecutively. Polysomnography was conducted, and snoring-related breathing sound was recorded simultaneously. Acoustic features and sleep features were extracted from 30-second samples, and a machine learning algorithm was used to establish 2 prediction models. A total of 74 eligible participants were included. Model 1, tested by 5-fold cross-validation, achieved an accuracy of 0.92 and an area under the curve of 0.94 for respiratory event prediction. Model 2, with acoustic features and sleep information tested by Leave-One-Out cross-validation, had an accuracy of 0.78 and an area under the curve of 0.80. Sleep position was found to be the most important among all sleep features contributing to the performance of the 2 models. Preapneic sound presented unique acoustic characteristics, and snoring-related breathing sound could be deployed as a real-time apneic event predictor. The models, combined with sleep information, serve as a promising tool for an early warning system to forecast apneic events. Wang B, Yi X, Gao J, etal. Real-time prediction of upcoming respiratory events via machine learning using snoring sound signal. J Clin Sleep Med. 2021;17(9):1777-1784.

Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data

A smoothed version of the stationary bootstrap is established for the purpose of bandwidth selection in density estimation for dependent data. An exact expression for the bootstrap version of the mean integrated squared error under dependence is obtained in this context. This is very useful since implementation of the bootstrap selector does not require Monte Carlo approximation. A simulation study is carried out to show the good practical performance of the new bootstrap bandwidth selector with respect to other existing competitors. The method is illustrated by applying it to two real data sets.

Non-asymptotic Bandwidth Selection for Density Estimation of Discrete Data

We propose a new method for density estimation of categorical data. The method implements a non-asymptotic data-driven bandwidth selection rule and provides model sparsity not present in the standard kernel density estimation method. Numerical experiments with a well-known ten-dimensional binary medical data set illustrate the effectiveness of the proposed approach for density estimation, discriminant analysis and classification.

A least-squares cross-validation bandwidth selection approach in pair correlation function estimations

The pair correlation function is a useful tool to analyze spatial point patterns. It is often estimated nonparametrically by a procedure such as kernel smoothing. This article develops a data-driven method for the selection of the bandwidth involved in the estimation. The proposed method uses the idea of least-squares cross-validation which has been often applied for bandwidth selection in density estimation and many other nonparametric estimations. The asymptotic property of the proposed approach will be investigated under an increasing-domain setting in this paper.

Absolute error criteria for bandwidth selection in density estimation from censored data

In Kernel density estimation, a criticism of bandwidth selection techniques which minimize squared error expressions is that they perform poorly when estimating tails of probability density functions. Techniques minimizing absolute error expressions are thought to result in more uniform performance and be potentially superior. An asympotic mean absolute error expression for nonparametric kernel density estimators from right-censored data is developed here. This expression is used to obtain local and global bandwidths that are optimal in the sense that they minimize asymptotic mean absolute error and integrated asymptotic mean absolute error, respectively. These estimators are illustrated fro eight data sets from known distributions. Computer simulation results are discussed, comparing the estimation methods with squared-error-based bandwidth selection for right-censored data.

Bandwidth Selection in Density Estimation with Truncated and Censored Data

A plug-in type bandwidth selector is presented for density estimation with truncated and censored data. It is based on a representation of the MISE function obtained in the paper. Rate of convergence and limit distribution are derived for this selector. A bootstrap method is introduced to estimate the MISE whose minimizer is an alternative bandwidth selector. A simulation study was carried out to assess the behavior with small samples. This methodology is applied to a real-data problem consisting of reporting delay of AIDS cases. The almost sure representation of the product-limit estimator is a key tool in our proofs.

C.440. On data- based bandwidth selection for density estimation from censored samples: a simulation

Click to increase image sizeClick to decrease image sizeKeywords: Random right censorshipkernel density estimationsmoothing parametersurvival analysis

Discussion of the Paper by Hall and Johnstone

Discussion of the Paper by Hall and Johnstone

Lower bounds for bandwidth selection in density estimation

This paper establishes asymptotic lower bounds which specify, in a variety of contexts, how well (in terms of relative rate of convergence) one may select the bandwidth of a kernel density estimator. These results provide important new insights concerning how the bandwidth selection problem should be considered. In particular it is shown that if the error criterion is Integrated Squared Error (ISE) then, even under very strong assumptions on the underlying density, relative error of the selected bandwidth cannot be reduced below ordern −1/10 (as the sample size grows). This very large error indicates that any technique which aims specifically to minimize ISE will be subject to serious practical difficulties arising from sampling fluctuations. Cross-validation exhibits this very slow convergence rate, and does suffer from unacceptably large sampling variation. On the other hand, if the error criterion is Mean Integrated Squared Error (MISE) then relative error of bandwidth selection can be reduced to ordern −1/2, when enough smoothness is assumed. Therefore bandwidth selection techniques which aim to minimize MISE can be much more stable, and less sensitive to small sampling fluctuations, than those which try to minimize ISE. We feel this indicates that performance in minimizing MISE, rather than ISE, should become the benchmark for measuring performance of bandwidth selection methods.

Lower bounds for bandwidth selection in density estimation

Lower bounds for bandwidth selection in density estimation

Bootstrap choice of tuning parameters

Consider the problem of estimating θ=θ(P) based on datax n from an unknown distributionP. Given a family of estimatorsT n, β of θ(P), the goal is to choose β among β∈I so that the resulting estimator is as good as possible. Typically, β can be regarded as a tuning or smoothing parameter, and proper choice of β is essential for good performance ofT n, β . In this paper, we discuss the theory of β being chosen by the bootstrap. Specifically, the bootstrap estimate of β, $$\hat \beta _n$$ , is chosen to minimize an empirical bootstrap estimate of risk. A general theory is presented to establish the consistency and weak convergence properties of these estimators. Confidence intervals for θ(P) based on $$T_{n,\hat \beta _n }$$ , are also asymptotically valid. Several applications of the theory are presented, including optimal choice of trimming proportion, bandwidth selection in density estimation and optimal combinations of estimates.