For the problems of nonparametric estimation of nonincreasing and symmetric unimodal density functions with bounded supports we determine the projections of estimates onto the convex families of possible parent densities with respect to the weighted integrated squared error. We also describe the...

We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT β + g(T) when the T's are measured with additive error. We derive an estimator of β by modification local-likelihood method. The resulting estimator of β is shown to be asymptotically...

Considering partially linear single-index errors-in-variables model which can be described as Y = n(X T a) + ZT ßo + e when the Z' s are measured with additive errors. The general estimators established in literature are biased when ignoring the measurement errors. We proposed two estimators in...

Motivated by an example in nutritional epidemiology, we investigate some design and analysis aspects of linear measurement error models with missing surrogate data. The specific problem investigated consists of an initial large sample in which the response (a food frequency questionnaire, FFQ)...

In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric techniques, regression splines and kernel...

In this paper we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Consistent parameter estimates and their associated standard errors are derived. Two general methods are considered, with the methods differing in their assumptions...

In many problems one wants to model the relationship between a response Y and a covariate X. Sometimes it is difficult, expensive, or even impossible to observe X directly, but one can instead observe a substitute variable W which is easier to obtain. By far the most common model for the...

Let a process SI , ... ,ST obey the conditionally heteroskedastic equation St = Vt Et whcrc Et is a random noise and Vt is the volatility coefficient which in turn obeys an autoregression type equation log v t = w + a S t- l + nt with an additional noise nt. We consider the situation which the...

The Normal Inverse Gaussian (NIG) distribution recently introduced by Barndorff-Nielsen (1997) is a promising alternative for modelling financial data exhibiting skewness and fat tails. In this paper we explore the Bayesian estimation of NIG-parameters by Markov Chain Monte Carlo Methods. --...