Estimation of the Local Intensity of a Cyclic Poisson Process by Means of Nearest Neighbor Distances

We consider the problem of estimating the local intensity of a cyclic Poisson point process, when we know the period. We suppose that only a single realization of the cyclic Poisson point process is observed within a bounded \u27window\u27, and our aim is to estimate consistently the local intensity at a given point. A nearest neighbor estimator of the local intensity is proposed, and we show that our estimator is weakly and strongly consistent, as the window expands

Comparing Optimism of Error Rate Estimators in Discriminant Analysis by Monte Carlo Simulation on Multivariate Normal Data

The problem considered in this paper is estimation of the error rate in two-group discriminant analysis. Here, performance of 19 existing error rate estimators are compared and contrasted by mean of Monte Carlo simulations under the ideal condition that both parent populations are multivariate normal with common covariance matrix. The criterion used for comparing those error rate estimators is optimism. Five experimental factors are considered for the simulation, they are the number of variables, the sample size relative to the number of variables, the Mahalanobis squared distance between the two populations, dependency factor among variables, and the degree of variation among the elements of the mean vector of the populations. The result of the simulation shows that there is no estimator performing the best for all situations. However, in general, the estimator U¹ proposed by Lachenbruch and Mickey (1968) is the bes

Consistency of a Uniform Kernel Estimator for Intensity of a Periodic Poisson Process with Unknown Period

A uniform kernel estimator for intensity of a periodic Poisson process with unknowm period is presented and a proof of its consistency is discussed. The result presented in this paper is a special case of that in [3]. The aim of discussing a uniform kernel estimator is in order to be able to present a relatively simpler proof of consistency compared to that in [3]. This is a joint work with R. Helmers and R. Zitikis.1991 Mathematics Subject Classi¯cation: 60G55, 62G05, 62G20

Application Of Bootstrap Method On Estimation Of The Error Rates In Discriminant Analysis

This paper is a survey study on applications of boot- strap methods for estimating the probability of misclassifications in two-groups discriminant analysis. Here we use the linear discrimi- nant function as classification rule. Some comparative studies on the performances of the considered estimators are also discussed

Balanced Bootstrap Estimators For The Probability Of Misclassifications In Discriminant Analysis

In this paper we propose new error rate estimators based on balanced bootstrap technique, which are expected to per- form better than the existing estimators. These estimators can be computed by means of separate or mixture resampling methodol- ogy. We consider both of them

Monte Carlo Evaluation of Error Rate Estimators in Discriminant Analysis Under Multivariate Normal Data

This paper is concerned with the problem of estimating the error rate in two-group discriminant analysis. Here, behaviour of 19 existing error rate estimators are compared and contrasted by mean of Monte Carlo simulations under the ideal condition that both parent populations are multivariate normal with common covariance matrix. The criterion used for comparing those error rate estimators is sum squared error (SSE). Five experimental factors are considered for the simulation, they are the number of variables, the sample size relative to the number of variables, the Mahalanobis squared distance between the two populations, dependency factor among variables, and the degree of variation among the elements of the mean vector of the populations. The result of the simulation shows that there is no estimator performing the best for all situations. However, on overall, the Finite Mixture Balanced bootstrap estimator (FMB) proposed by Mangku (2007) is the best estimator

Strong Convergence of a Uniform Kernel Estimator for Intensity of a Periodic Poisson Process with Unknown Period

Strong convergence of a uniform kernel estimator for intensity of a periodic Poisson process with unknowm period is presented and proved. The result presented here is a special case of the one in [3]. The aim of this paper is to present an alternative and a relatively simpler proof of strong convergence compared to the one in [3]. This is a joint work with R. Helmers and R. Zitikis.1991 Mathematics Subject Classication: 60G55, 62G05, 62G20

A Note on Estimation of the Global Intensity of a Cyclic Poisson Process in the Presence of Linear Trend

We construct and investigate a consistent kernel-type nonparametric estimator of the global intensity of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias and variance of the proposed estimator are computed. Bias reduction of the estimator is also proposed.1991 Mathematics Subject Classification: 6

Discriminant Functions And Their Misclassification Errors

This paper is a survey study on discriminant functions and their misclassification errors. Here we consider three groups of discriminant functions, namely discriminant functions for respec- tively multivariate normal variables, multivariate binary variables, and a mixture of multivariate binary and normal variables. Finally we derive their misclassification errors