Central limit theorem for integrated square error of kernel estimators of spherical density

LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions.

Integrated Square Error of Hazard Rate Estimation for Survival Data with Missing Censoring Indicators

The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.

Histogram-kernel Error and Its Application for Bin Width Selection in Histograms

Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. 3ust as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott＇s optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.

Reactive power compensation of an isolated hybrid power system with load interaction using ANFIS tuned STATCOM

This paper presents an adaptive neuro fuzzy interference system （ANFIS） based approach to tune the parameters of the static synchronous compensator （STAT- COM） with frequent disturbances in load model and power input of a wind-diesel based isolated hybrid power system （IHPS）. In literature, proportional integral （PI） based controller constants are optimized for voltage stability in hybrid systems due to the interaction of load disturbances and input power disturbances. These conventional controlling techniques use the integral square error （ISE） criterion with an open loop load model. An ANFIS tuned constants of a STATCOM controller for controlling the reactive power requirement to stabilize the voltage variation is proposed in the paper. Moreover, the interaction between the load and the isolated power system is developed in terms of closed loop load interaction with the system. Furthermore, a comparison of transient responses of IHPS is also presented when the system has only the STATCOM and the static compensation requirement of the induction generator is fulfilled by the fixed capacitor, dynamic compensation requirement, meanwhile, is fulfilled by STATCOM. The model is tested for a 1% step increase in reactive power load demand at t = 0 s and then a sudden change of 3% from the 1% at t = 0.01 s for a 1% step increase in power input at variable wind speed model.

The abstract of doctoral dissertation‘nonlinear wavelet density estimation and hazard rate estimation with data missing at random’

In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.

A new recursive method for the analysis of linear time invariant dynamic systems via double-term triangular functions (DTTF) in state space environment

This paper presents a new recursive method for system analysis via double-term triangular functions （DTTF） in state space environment. The proposed method uses orthogonal triangular function sets and proves to be more accurate as compared to single term Walsh series （STWS） method with respect to mean integral square error （MISE）. This has been established theoretically and comparison of error with respect to MISE is presented for clarity. A numerical example is treated to establish the proposed method. Relevant curves for the solutions of states of the dynamic system are also presented with plots of percentage error for DTTF-based analysis.