The problem of covariate measurement error with heteroscedastic measurement error variance is considered. Standard regression calibration assumes that the measurement error has a homoscedastic measurement error variance. An estimator is proposed to correct regression coefficients for covariate measurement error with heteroscedastic variance. Point and interval estimates are derived. Validation ...

Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models operates under the assumption that predictors can be replaced by lower dimensional projection without loss of information. It semiparametric forward model-based exhaustive estim...

Consider the estimation of a signal x ∈ R from noisy observations r = x+ z, where the input x is generated by an independent and identically distributed (i.i.d.) Gaussian mixture source, and z is additive white Gaussian noise (AWGN) in parallel Gaussian channels. Typically, the `2-norm error (squared error) is used to quantify the performance of the estimation process. In contrast, we consider ...

Quantile estimation has become increasingly important, particularly in the financial industry, where value at risk (VaR) has emerged as a standard measurement tool for controlling portfolio risk. In this paper, we analyze the probability that a simulation-based quantile estimator fails to lie in a prespecified neighborhood of the true quantile. First, we show that this error probability converg...

Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348–1360] characterizes the optimal behavior of a model selection procedure. However, the least-squares oracle theory breaks down if the error variance is...

For a large class of distributions and large samples, it is shown that estimates of the variance σ2 and of the standard deviation σ are more often Pitman closer to their target than the corresponding shrinkage estimates which improve the mean squared error. Our results indicate that Pitman closeness criterion, despite its controversial nature, should be regarded as a useful and complementary to...

We consider estimation of the common probability density f of i.i.d. random variables Xi that are observed with an additive i.i.d. noise. We assume that the unknown density f belongs to a class A of densities whose characteristic function is described by the exponent exp(−α|u|r) as |u| → ∞, where α > 0, r > 0. The noise density is supposed to be known and such that its characteristic function d...

A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation" completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of t...

We develop and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h-step-ahead forecasts than another, as measured by the difference of approximations to their mean square forecast error. The two statistics differ in the variance estimates used for normalization. Both variance estimates are consistent even when the models considered are in...

In a two-level factorial experiment, we consider construction of parallel-flats designs with two identical parallel flats that allow estimation of a set of specified possibly active effects and the pure error variance. A set of sufficient conditions is presented for the designs to be D-optimal for the specified effects, assuming that the other effects are negligible, over the class of competing...