A Bayesian approach is used to estimate a nonparametric regression model. The main features of the procedure are, first, the functional form of the curve is approximated by a mixture of local polynomials by Bayesian Model Averaging (BMA); second, the model weights are approximated by the BIC criterion, and third, a robust estimation procedure is incorporated to improve the smoothness of the est...

The receiver operating characteristic (ROC) curve is used for classification between two populations. Usually two independent random samples from the populations with absolutely continuous cumulative distribution functions (CDF) F and G are considered. Then the ROC curve is defined as ROC(t) = 1−G(F−1(1− t)) for 0 < t < 1 if the inverse F−1 exists. Classical ROC curve estimator is based on empi...

among different models for runoff estimation in watershed management, the soil conservation services-curve number (scs-cn) method along with its modifications have been widely applied to ungauged watersheds because of quickly and more accurate estimation of surface runoff. this approach has been widely accepted by hydrologists, water resources planners, foresters, and engineers, as well. theref...

A Bayesian method of estimating an unknown regression curve by a polynomial of random order is proposed. A joint distribution is assigned over both the set of possible orders of the polynomial and the polynomial coeecients. 1995) are used to compute required posteriors. The methodology is extended to polynomials of random order with discontinuties and to piecewise poly-nomials of random order. ...

A maximum likelihood procedure is presented for the estimation of the parameters in a survival curve which is used in the quantitative investigation of cytological damage resulting from ionizing radiation. This estimation procedure is developed under the assumption that the observations are distributed as independent Poisson random variables. In addition, a weighted least squares procedure, whi...

In many applications, observed signals are contaminated by both random noise and blur. This paper proposes a blind deconvolution procedure for estimating a regression function with possible jumps preserved, by removing both noise and blur when recovering the signals. Our procedure is based on three local linear kernel estimates of the regression function, constructed from observations in a left...

Receiver operating characteristic (ROC) curve has been widely used in medical science for its ability to measure the accuracy of diagnostic tests under the gold standard. However, in a complicated medical practice, a gold standard test can be invasive, expensive, and its result may not always be available for all the subjects under study. Thus, a gold standard test is implemented only when it i...

• This document describes how I used mathematical methods for the estimation of implied volatility curve, a crucial engineering problem raised in our High Frequency Trading (HFT) strategy. I apologize for using many of jargons and unformatted figures. This is because the materials were not prepared for an academic purpose, but just for internal usage. • All data used in this document are about ...

where f is an unknown function, and the ei's are noise. Our goal is to recover f using wavelet methods. We shall assume that n = 2 is an integer power of 2, and consider both the cases of independent and correlated noise. Let f = (f0; : : : ; fn 1) T , y = (y0; : : : ; yn 1) T and W be the discrete wavelet transform (DWT) matrix (e.g., see Donoho & Johnstone 1994). A wavelet{based estimate f̂ of...