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I W. MANGKU

Bogor Agricultural University

Author-ID : 2817569

Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Mathematics

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WEAK AND STRONG CONVERGENCE OF A KERNEL-TYPE ESTIMATOR FOR THE INTENSITY OF A PERIODIC POISSON PROCESSS I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 5 No. 1 (2006): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

In this paper we survey some results on weak and strong convergence of kernel type estimators for the intensity of a periodic Poisson process. We consider the situation when the period is known in order to be able to present simple proofs of the results. For the more general results, which includes the case when the period is unknown, we refer to [15], [16].1991 Mathematics Subject Classiﬁcation: 60G55, 62G05, 62G20.

ASYMPTOTIC NORMALITY OF A KERNEL-TYPE ESTIMATOR FOR THE INTENSITY OF A PERIODIC POISSON PROCESS I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 5 No. 2 (2006): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

In this paper we prove asymptotic normality of a kernel type estimator for the intensity of a periodic Poisson process. This paper is a continuation of [10]. As in [10], we consider the situation when the period is known in order to be able to present simple proofs of the results.1991 Mathematics Subject Classiﬁcation: 60G55, 62G05, 62G20.

BALANCED BOOTSTRAP ESTIMATORS FOR THE PROBABILITY OF MISCLASSIFICATIONS IN DISCRIMINANT ANALYSIS I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 6 No. 1 (2007): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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.

CONSISTENCY OF KERNEL-TYPE ESTIMATORS FOR THE FIRST AND SECOND DERIVATIVES OF A PERIODIC POISSON INTENSITY FUNCTION I W. MANGKU; S. SYAMSURI; H. HERNIWAT
MILANG Journal of Mathematics and Its Applications Vol. 6 No. 2 (2007): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

We construct and investigate consistent kernel-type estimators for the ﬁrst and second derivatives of a periodic Poisson intensity function when the period is known. We do not assume any particular parametric form for the intensity function. More- over, we consider the situation when only a single realization of the Poisson process is available, and only observed in a bounded interval. We prove that the proposed estimators are consistent when the length of the interval goes to inﬁnity. We also prove that the mean-squared error of the estimators converge to zero when the length of the interval goes to inﬁnity.1991 Mathematics Subject Classiﬁcation: 60G55, 62G05, 62G20.

CONSISTENCY OF A UNIFORM KERNEL ESTIMATOR FOR INTENSITY OF A PERIODIC POISSON PROCESS WITH UNKNOWN PERIOD I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 7 No. 2 (2008): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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.

STRONG CONVERGENCE OF A UNIFORM KERNEL ESTIMATOR FOR INTENSITY OF A PERIODIC POISSON PROCESS WITH UNKNOWN PERIOD I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 8 No. 1 (2009): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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.

CONVERGENCE OF MSE OF A UNIFORM KERNEL ESTIMATOR FOR INTENSITY OF A PERIODIC POISSON PROCESS WITH UNKNOWN PERIOD I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 8 No. 2 (2009): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Convergence of MSE (Mean-Squared-Error) 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 convergence for the MSE of the estimator compared to the one in [3]. This is a joint work with R. Helmers and R. Zitikis.

MONTE CARLO EVALUATION OF ERROR RATE ESTIMATORS IN DISCRIMINANT ANALYSIS UNDER MULTIVARIATE NORMAL DATA I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 9 No. 1 (2010): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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.

COMPARING OPTIMISM OF ERROR RATE ESTIMATORS IN DISCRIMINANT ANALYSIS BY MONTE CARLO SIMULATION ON MULTIVARIATE NORMAL DATA I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 9 No. 2 (2010): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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 best

PENDUGAAN KOMPONEN PERIODIK FUNGSI INTENSITAS BERBENTUK FUNGSI PERIODIK KALI TREN KUADRATIK SUATU PROSES POISSON NONHOMOGEN P. RAMDANI; I W. MANGKU; R. BUDIARTI
MILANG Journal of Mathematics and Its Applications Vol. 9 No. 2 (2010): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Pada tulisan ini dibahas pendugaan komponen periodik fungsi intensitas berbentuk fungsi periodik kali tren kuadratik suatu proses Poisson non-homogen. Diperhatikan keadaan terburuk, hanya terdapat realisasi tunggal dari proses Poisson dengan fungsi intensitas yang terdiri atas komponen periodik dikalikan dengan komponen tren kuadratik yang diamati pada interval [0,n]. Diasumsikan bahwa periode dari komponen periodik diketahui. Penduga komponen periodik dari fungsi intensitas tersebut telah disusun dan Mean Square Error (MSE) penduga telah dibuktikan konvergen menuju nol untuk n  . Selain itu, juga telah diformulasikan aproksimasi asimtotik bagi bias, ragam, dan Mean Square Error (MSE) dari penduga yang dikaji. Ditentukan juga bandwidth optimal asimtotik bagi penduga tersebut

Co-Authors A. RAMADHANI Awatif H. HERNIWAT H. SUMARNO I Gusti Putu Purnaba I. WIDIYASTUTI P. RAMDANI R. BUDIARTI S. K. NASIB S. SYAMSURI SISWANDI, S. W. ISMAYULIA

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