Estimation of a multivariate density

Cacoullos, T.

doi:10.1007/bf02869528

Cited by 573 publications

(231 citation statements)

References 3 publications

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“…The first result in (21) follows from Theorem 3.3 in Cacoullos (1964). By Theorem 3 in Mokkadem et al (2005),…”

Section: A Technical Lemmas and Proofsmentioning

confidence: 92%

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Smooth Plug‐in Inverse Estimators in the Current Status Continuous Mark Model

Groeneboom¹,

Jongbloed²,

Witte³

2011

Scandinavian J Statistics

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ABSTRACT. We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable when the event time is subject to interval censoring case 1 and the continuous mark variable is only observed in case the event occurred before the time of inspection. The nonparametric maximum likelihood estimator in this model is known to be inconsistent. We study two alternative smooth estimators, based on the explicit (inverse) expression of the distribution function of interest in terms of the density of the observable vector. We derive the pointwise asymptotic distribution of both estimators.

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“…The first result in (21) follows from Theorem 3.3 in Cacoullos (1964). By Theorem 3 in Mokkadem et al (2005),…”

Section: A Technical Lemmas and Proofsmentioning

confidence: 92%

“…The results in Cacoullos (1964) and Mokkadem et al (2005) hold for density estimators, whereas the estimatorĥ…”

Section: A Technical Lemmas and Proofsmentioning

confidence: 95%

Smooth Plug‐in Inverse Estimators in the Current Status Continuous Mark Model

Groeneboom¹,

Jongbloed²,

Witte³

2011

Scandinavian J Statistics

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“…To determine the class, the probability density function is estimated by a non-parametric estimation method developed by Parzen [27] and extended afterwards by Cacoulos [28] . The joint probability density function for a set of p variables can be expressed as:…”

Section: Probabilistic Neural Network (Pnn)mentioning

confidence: 99%

Consumer Choice Prediction: Artificial Neural Networks versus Logistic Models

Gan¹,

Limsombunc²,

Clemes³

et al. 2005

J. of Social Sciences

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Conventional econometric models, such as discriminant analysis and logistic regression have been used to predict consumer choice. However, in recent years, there has been a growing interest in applying artificial neural networks (ANN) to analyse consumer behaviour and to model the consumer decision-making process. The purpose of this paper is to empirically compare the predictive power of the probability neural network (PNN), a special class of neural networks and a MLFN with a logistic model on consumers' choices between electronic banking and non-electronic banking. Data for this analysis was obtained through a mail survey sent to 1,960 New Zealand households. The questionnaire gathered information on the factors consumers' use to decide between electronic banking versus non-electronic banking. The factors include service quality dimensions, perceived risk factors, user input factors, price factors, service product characteristics and individual factors. In addition, demographic variables including age, gender, marital status, ethnic background, educational qualification, employment, income and area of residence are considered in the analysis. Empirical results showed that both ANN models (MLFN and PNN) exhibit a higher overall percentage correct on consumer choice predictions than the logistic model. Furthermore, the PNN demonstrates to be the best predictive model since it has the highest overall percentage correct and a very low percentage error on both Type I and Type II errors.

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“…The existing knowledge h i could be obtained from a previous sample or expert opinion and f i (X) is determined by applying an established mathematical foundation (Parzen 1962) to estimate the univariate pdf of a population from its sample, by taking an average sum of suitably chosen kernel (pdf) values for each observation in the sample. Estimation of the multivariate density function, as discussed by Cacoullos (1966), can be achieved by firstly taking the multivariate pdf of an observation as a product of its univariate kernel, then applying Parzen's average sum to estimate the multivariate pdf.…”

Section: Pnn Classificationmentioning

confidence: 99%

Application of probabilistic neural networks in modelling structural deterioration of stormwater pipes

Tran

Perera

et al. 2006

Urban Water Journal

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In Australia, when stormwater systems were first introduced over 100 years ago, they were constructed independently of the sewer systems, and they are normally the responsibility of the third level of government, i.e., local government or city councils. Because of the increasing age of these stormwater systems and their worsening performance, there are serious concerns in a significant number of city councils regarding their deterioration. A study has been conducted on the structural deterioration of concrete pipes that make up the bulk of the stormwater pipe systems in these councils. In an attempt to look for a reliable deterioration model, a probabilistic neural network (PNN) model was developed using the data set supplied from participating councils. The PNN model was validated with snapshot-based sample data, which makes up the data set. The predictive performance of the PNN model was compared with a traditional parametric model using discriminant analysis on the same data set. Structural deterioration was hypothesised to be influenced by a set of explanatory factors, including pipe design and construction factors-such as pipe size, buried depth-and site factorssuch as soil type, moisture index, tree root intrusion, etc. The results show that the PNN model has a better predictive power and uses significantly more input variables (i.e., explanatory factors) than the discriminant model. More importantly, the key factors for prediction in the PNN model are difficult to interpret, suggesting that besides prediction accuracy, model interpretation is an important issue for further investigation.

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Estimation of a multivariate density

Cited by 573 publications

References 3 publications

Smooth Plug‐in Inverse Estimators in the Current Status Continuous Mark Model

Smooth Plug‐in Inverse Estimators in the Current Status Continuous Mark Model

Consumer Choice Prediction: Artificial Neural Networks versus Logistic Models

Application of probabilistic neural networks in modelling structural deterioration of stormwater pipes

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