Deviation of order p for estimators of the variance in first-order stochastic differential equation (SDE)

In this work, we consider a non-parametric estimator of the variance in one-dimensional diffusion models or, more generally, in Itô processes with a deterministic diffusion term and a general non-anticipative drift. The estimation is based on the quadratic variation of discrete time observations over a finite interval. In particular, a central limit theorem (CLT) is proved for the deviation in L ^p norm (p≥; 1) between the variance and this estimator. The method of the proof consists in writing the L ^p norm of the deviation, when the drift term is equal to zero, as a sum of 4-dependent random variables. The moments are then computed by means of a Gaussian approximation and a CLT for m-dependent random variables is applied. The convergence is stable in law, this allows the result for processes with general drifts to be obtained, by using Girsanov's formula.     

On the euclidean distance between biased estimators

The purpose of this paper is to extend the results achieved by Hsuan (1981) to a wide class of biased estimators. It is shown that in the case of multicollinearity ridge and Iteration estimator can be made very close to the principal component estimator whereas the shrunken estimator does not have this property.     

Robust estimation of the mean vector for high-dimensional data set using robust clustering

The first step in statistical analysis is the parameter estimation. In multivariate analysis, one of the parameters of interest to be estimated is the mean vector. In multivariate statistical analysis, it is usually assumed that the data come from a multivariate normal distribution. In this situation, the maximum likelihood estimator (MLE), that is, the sample mean vector, is the best estimator. However, when outliers exist in the data, the use of sample mean vector will result in poor estimation. So, other estimators which are robust to the existence of outliers should be used. The most popular robust multivariate estimator for estimating the mean vector is S-estimator with desirable properties. However, computing this estimator requires the use of a robust estimate of mean vector as a starting point. Usually minimum volume ellipsoid (MVE) is used as a starting point in computing S-estimator. For high-dimensional data computing, the MVE takes too much time. In some cases, this time is so large that the existing computers cannot perform the computation. In addition to the computation time, for high-dimensional data set the MVE method is not precise. In this paper, a robust starting point for S-estimator based on robust clustering is proposed which could be used for estimating the mean vector of the high-dimensional data. The performance of the proposed estimator in the presence of outliers is studied and the results indicate that the proposed estimator performs precisely and much better than some of the existing robust estimators for high-dimensional data.     

Efficiency and productivity of the cement industry: Pakistani experience of deregulation and privatisation

This study evaluates the impact of privatisation on efficiency and productivity of the Pakistani cement industry. To address some of the serious concerns about the problem of dimension and outlier, we use a newly developed unconditional hyperbolic α-quantile estimator of Wheelock and Wilson to estimate efficiency (Wheelock DC, Wilson PW. Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations. Journal of Econometrics; 2008: 209–25). Subsequently, we use these efficiency estimates to calculate the Malmquist productivity growth and its components. The results show that deregulation and privatisation had the desired positive effect on productivity growth due to technological progress. We conclude that this improvement in the post reform period could be linked to political stability, improved economic conditions and a competitive industry.     

Validation of qualitative microbiological test methods

This paper considers a statistical model for the detection mechanism of qualitative microbiological test methods with a parameter for the detection proportion (the probability to detect a single organism) and a parameter for the false positive rate. It is demonstrated that the detection proportion and the bacterial density cannot be estimated separately, not even in a multiple dilution experiment. Only the product can be estimated, changing the interpretation of the most probable number estimator. The asymptotic power of the likelihood ratio statistic for comparing an alternative method with the compendial method, is optimal for a single dilution experiment. The bacterial density should either be close to two CFUs per test unit or equal to zero, depending on differences in the model parameters between the two test methods. The proposed strategy for method validation is to use these two dilutions and test for differences in the two model parameters, addressing the validation parameters specificity and accuracy. Robustness of these two parameters might still be required, but all other validation parameters can be omitted. A confidence interval‐based approach for the ratio of the detection proportions for the two methods is recommended, since it is most informative and close to the power of the likelihood ratio test. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficiency of the generalized difference-based Liu estimators in semiparametric regression models with correlated errors

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β in the semiparametric regression model. Under the linear nonstochastic constraint Rβ=r, the generalized restricted difference-based Liu estimator is given. The risk function for the β?_GRD(η) associated with weighted balanced loss function is presented. The performance of the proposed estimators is evaluated by a simulated data set.     

Statistical Estimation for a Class of Self‐Regulating Processes

Self‐regulating processes are stochastic processes whose local regularity, as measured by the pointwise Hölder exponent, is a function of amplitude. They seem to provide relevant models for various signals arising for example in geophysics or biomedicine. We propose in this work an estimator of the self‐regulating function (that is, the function relating amplitude and Hölder regularity) of the self‐regulating midpoint displacement process and study some of its properties. We prove that it is almost surely convergent and obtain a central limit theorem. Numerical simulations show that the estimator behaves well in practice.