Nonparametric Estimation of Probability Distribution Density Using Sign Quantization

A developed digital algorithm is used to obtain analytical expressions characterizing the error due to the bias and variance in a proposed estimate of a probability distribution density. The results of experimental investigations are presented which demonstrate the efficiency of the proposed algorithm.     

Nonparametric Estimation of the Quadratic Functional of a Multimodal Probability Density

Measurement Techniques - A nonparametric method for estimating the mean square functional of a multimodal probability density of a one-dimensional random variable is examined. The proposed method...     

Series Estimation of a Probability Density Function

A class of nonparametric estimators of f(x) based on a set of n observations has been proved by Parzen [l] to be consistent and asymptotically normal subject to certain conditions. Although quite useful for a wide variety of practical problems, these estimators have two serious disadvantages when n is large: 1. All n observations must be stored in rapid-access storage.

2. Evaluation of f(x) for a particular value of x requires a long computation involving each of the observations.

The Parzen estimator, which has n terms, can be replaced by a series approximation which has a number of terms determined by the accuracy required in the estimate rather than by the number of observations in the sample. The summation over all of the observations is performed only to establish the value of the coefficients in the series.

Although no member of the class of estimators has been proved “best” for estimating an unknown density from a finite sample, a power series expansion for a particular member of the class was singled out because of computational simplicity. A comparison is made between the proposed estimator and the Gram–Charlier Series of Type A. A multidimensional counterpart of the proposed estimator has also been derived.     

Estimation of a Nonlinear Functional of Probability Density when Optimizing Nonparametric Decision Functions

Measurement Techniques - We propose a method for estimating the nonlinear functional of the probability density of a two-dimensional random variable. The technique applies to the implementation of...     

Nonparametric Profile Monitoring using Dynamic Probability Control Limits

This article focuses on monitoring nonparametric profile with time‐varying sample sizes and random predictors. Traditional profile monitoring schemes, whose control limits are often determined before the monitoring initiates, are constructed based on perfect knowledge of profile sample sizes and predictors. In practice, however, our foreknowledge about future random sample sizes and predictors is seldom available. An inappropriate assumption or estimation of the sample sizes model and/or predictors distribution function may lead to unexpected performance of traditional control charts. To overcome this problem, we propose a kernel‐based nonparametric profile monitoring scheme which integrates the multivariate exponentially weighted moving average procedure with the probability control limits. The success of the proposed chart lies in the use of dynamic control limits which are determined online, essentially aiming at guaranteeing the conditional probability that the charting statistic exceeds the control limit at present given that there is no alarm before the current time point to meet a pre‐specified false alarm rate. The simulation studies show that the proposed control scheme has good in‐control and out‐of‐control performances under various scenarios of time‐varying sample sizes and random predictors. Copyright © 2016 John Wiley & Sons, Ltd.     

非参数核密度估计视频目标空域定位技术研究

针对智能视频监控场合对视频运动目标定位的需求,本文提出了一种基于非参数核密度估计的视频运动目标空域定位技术.该技术先对代表视频运动目标的前景样本点进行非参数核密度估计,选择具有最高密度指标的样本点为第一个目标中心,然后通过修正样本点的密度估计值,逐步实现对视频运动目标的空域定位.本文的方法是减法聚类视频运动目标定位技术的进一步推广.推广后的定位方法,可根据具体的目标定位场合,灵活选择核函数对样本点进行核密度估计.实验表明,本文方法具有良好定位效果,同时,在样本点的密度估计上更具灵活性.     

Bootstrap Confidence Limits for Short-Run Capability Indices

The capability indices are widely used by quality professionals as an estimate of process capability. Recently, techniques and tables were developed to construct confidence limits for each index. These techniques are based on the assumption that the underlying process is normally distributed. In industries it may not be possible to get large samples, and, hence, the normality assumption is often violated. For the short-run production processes where sample size is small, appropriate indices can be developed. In this article, the capability indices such as C_p, C_pk, and C_pm are modified, and appropriate capability indices are constructed. A further bootstrap technique is used to define the confidence intervals. A simulation using two distributions (one normal and the other nonnormal) is conducted, and a comparison is made to show the performances of the three nonparametric confidence intervals.     

雨流循环均值-幅值二维联合概率密度的实用算法

在实际工程结构疲劳损伤计算中，经常忽略雨流循环均值，而只考虑幅值的影响。这对计算结果会带来一定的误差，尤其是那些对均值影响比较敏感的材料来说更是如此。若考虑雨流循环均值的影响，在时域计算中可以很方便地实现，但在频域中则必须得到雨流循环均值-幅值二维联合概率密度。本文针对工程中常常遇到的平稳Gauss随机过程，提出由结构响应的PSD得到雨流循环均值-幅值条件概率的简便计算公式，进而结合Dirlik经验公式直接计算出雨流循环均值-幅值二维联合概率密度函数的实用方法。     

APProximate Confidence Limits for the Reliability of Series and Parallel Systems

Suppose a complex mechanism, e.g., a missile, is built up from a number of different types of components, where the reliability of each of the components has been estimated by means of separate tests on each of the components. This paper gives a method for combining such data to determine approximate confidence limits for the reliability of the complete mechanism. More precisely, a method of determining approximate confidence limits for the reliability of “series,” “parallel,” and “seriesparallel” systems is given, based on observed failures of the individual components. It is assumed that the failures are independent, and that failures of a given component follow a binomial distribution with unknown parameter, the component reliability. The large-sample properties of the likelihood-ratio test are then used to construct the appropriate confidence limits for the system reliability.     

噪声为厚尾过程的非参数函数变点的小波估计

本文给出了随机设计下非参数回归模型中噪声为无穷方差过程的小波检测和估计方法。利用基于经验小波系数的检验统计量,在原假设成立的条件下,推导出任意尺度上检验的临界值,证明了检验的一致性;在备择假设成立的条件下,得到变点个数、变点位置的相合估计与收敛速度。数值模拟以及IBM股票数据实例分析的结果均表明方法是有效的。     

Autocorrelation Central Hole in Clipped Photon-counting Detection Estimation from the Zero-count Probability Density

Abstract

In this paper we develop a procedure to avoid the autocorrelation central hole that appears in clipped photon-counting detection. This method can be understood as a higher order approximation than the Hofmann procedure. It can be applied in combination with any of the alternative methods to evaluate the autocorrelation function in clipped conditions proposed up until the present. We especially analyse that based on the zero-count probability measurement. Fairly good autocorrelation estimates are obtained for low intensity signals.     

Optimization of the Kernel Probability Density Estimation of a Two-Dimensional Random Variable with Independent Components

Measurement Techniques - The paper studies the problem associated with the optimization of nonparametric probability density estimates, whose relevance is attributed to the lower efficiency of...