This note studies the bias arises from the MLE estimate of the rate parameter and the mean parameter of an exponential distribution. 1 Motivation Although maximum likelihood estimation (MLE) methods provide estimates that are useful, the estimates themselves are not guaranteed to be unbiased. Nevertheless, MLE methods are still highly regarded in practice due to several of their properties, not...

Within the class of non-homogeneous Poisson process (NHPP) models and as a result of the simplicity of the mathematical computations of the Power Law Process (PLP) model and the attractive physical explanation of its parameters, this model has found considerable attention in repairable systems literature. In this article, we conduct the investigation of new estimation approach, the regression e...

This paper presents an algorithm for predicting the arrival time of transit vehicles using a combination of both AVL and historical data. The algorithm is presented in its two components: tracking (using a Kalman filter framework) and prediction (using statistical estimation). The algorithm produces an estimate of the predicted arrival time for a given transit vehicle and provides a measure of ...

Abstract: Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are established. Kernel estimators of the noise’s density and its derivatives are defined and shown to be uniformly consistent. A simulation experiment conduct...

We consider the problem of estimating the remaining useful life (RUL) of a system or a machine from sensor data. Many approaches for RUL estimation based on sensor data make assumptions about how machines degrade. Additionally, sensor data from machines is noisy and o‰en su‚ers from missing values in many practical seŠings. We propose Embed-RUL: a novel approach for RUL estimation from sensor d...

Both descriptive and normative arguments claim that the discount rate to be applied to public projects should be elicited from individual intertemporal preferences. We present a methodology to analyze data from experimental surveys on intertemporal preferences. Focusing on the exponential and the hyperbolic discounting models, we model the experimental data published by Thaler (1981) by means o...

Continuous-time models are important for investigating interest rate term structure and pricing fixed income derivatives. Economic theory often provides little guidance on the choice of the form of continuous-time models, and existing one-factor and multi-factor continuous-time interest rate models often assume a linear drift, among other things. Some studies, based smoothed nonparametric kerne...

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimat...

The maximum entropy spectral estimator is widely used because of its high spectral resolution, but it lacks an easy procedure for evaluating the statistical significance of the spectral estimates. We implemented the non-parametric computer intensive permutation test in order to evaluate the statistical significance of the maximum entropy spectral estimates. There is the possibility of choosing ...

In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation difficult, so it should be robust against them. Moreover for coding purposes I will show that it is desired the residual of auto-regression be sparse. To these ...