Almost unbiased product-type estimator

In sample survey methods the use of product estimators was suggested byMurthy [1964] andSrivastava [1966] and were found to serve good purpose provided the two variables viz. the main variable under study and the auxiliary variable have a very high negative correlation between them. The product estimators suggested by them are biased. In the present paper the author has obtained unbiased product estimators (to the first degree of approximation) with the help of the technique developed byQuenouille [1956] and has established that this new estimator is better than the other product estimator in the mean square error sense.     

Shrinkage estimation of semiparametric multiplicative error models

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data or the recently proposed Focused Information Criterion. We illustrate such a methodology using a semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into their dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that, from the forecasting perspective, an appropriate shrinkage strategy can significantly improve on the baseline maximum likelihood estimation.     

Sufficiency and unbiased estimation

Summary The aim of this paper is to give criteria of the sufficiency of certain complete -algebras occurring in the theory of unbiased estimation by means of minimal unbiased estimators. The class ofYoung-functions is used to construct a large class of convex loss functions and a theorem ofBahadur based on quadratic loss is generalized to this general class of loss functions.     

Computing median unbiased estimates in macroeconometric models

A stochastic simulation procedure is proposed in this paper for obtaining median unbiased (MU) estimates in macroeconometric models. MU estimates are computed for lagged dependent variable (LDV) coefficients in 18 equations of a macroeconometric model. The 2SLS bias for a coefficient, defined as the difference between the 2SLS estimate and the MU estimate, is on average smaller in absolute value than would be expected from Andrews exact results for an equation with only a constant term, time trend, and LDV. The results also show that in a practical sense the estimated biases are not very large because they have little effect on the overall predictive accuracy of the model and on its multiplier properties.     

Efficient estimation of a multivariate multiplicative volatility model

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series. We find that the univariate model of Engle and Rangel (2008) appears to be violated in the data whereas our multivariate model is more consistent with the data.     

Stratification,midzuno-sen strategy and nonnegative unbiased variance estimation

When the ratio method is appropriate for estimating the population total one is faced with the problem of nonavailability of uniformly nonnegative unbiased variance estimators (nnuve). Here we highlight the twofold role of stratification in that it not only improves the efficiency of the ratio method of estimation but it also enhances the chances of getting uniformly nonnegative unbiased variance estimators.     

Admissible unbiased variance estimation in finite population sampling under randomized response

LetP be the proportion of units in a finite population possessing a sensitive attribute. We prove the admissibility of (i) an unbiased estimator of the variance of a general homogeneous linear unbiased estimator ofP and (ii) an unbiased estimator of the population varianceP(1−P), based on an arbitrary but fixed sampling design, under the randomized response plans due to Warner (1965) and Eriksson (1973). Admissibility of an unbiased strategy for estimating the population variance is also established.     

Note on unbiased estimation of the squared multiple correlation coefficient

Zoals bekend is het kwadraat van de correlatie-coëfficiënt bij regressie-analyse een onzuivere schatting van zijn tegenhanger in de populatie. Deze onzuiverheid wordt afgeleid tot op de orde 1/T, waarbij T het aantal waarnemingen is. Door een schatting van deze onzuiverheid van het kwadraat van de gewone correlatie-coëfficiënt af te trekken wordt een nieuwe schatting van de correlatie in de populatie verkregen, die zuiver is tot op de orde 1/T, hetgeen van de op de gebruikelgke wijzen gecorrigeerde correlatie-coëfficiënten niet gezegd kan worden.     

Logarithmic calibration for multiplicative distortion measurement errors regression models

In this article, we propose a new identifiability condition by using the logarithmic calibration for the distortion measurement error models, where neither the response variable nor the covariates can be directly observed but are measured with multiplicative measurement errors. Under the logarithmic calibration, the direct-plug-in estimators of parameters and empirical likelihood based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.     

Heterogeneous component multiplicative error models for forecasting trading volumes

We propose a novel approach to the modelling and forecasting of high-frequency trading volumes. The new model extends the component multiplicative error model of Brownlees et al. (2011) by introducing a more flexible specification of the long-run component. This uses an additive cascade of MIDAS polynomial filters, moving at different frequencies, to reproduce the changing long-run level and the persistent autocorrelation structure of high-frequency trading volumes. After investigating the statistical properties of the proposed approach, we illustrate its merits by means of an application to six stocks that are traded on the XETRA market in the German Stock Exchange.     

Minimum variance unbiased estimation of the parameters of the Pareto distribution

Summary This paper presents a simpler proof of some results concerning estimation of the Pareto distribution due toLike [1969].     

Risk-parameter estimation in volatility models

This paper introduces the concept of risk parameter in conditional volatility models of the form _?t=_σt(_θ0)_ηt${?}_t={\sigma }_t\left({\theta }_0\right){\eta }_t$ and develops statistical procedures to estimate this parameter. For a given risk measure r$r$, the risk parameter is expressed as a function of the volatility coefficients _θ0${\theta }_0$ and the risk, r(_ηt)$r\left({\eta }_t\right)$, of the innovation process. A two-step method is proposed to successively estimate these quantities. An alternative one-step approach, relying on a reparameterization of the model and the use of a non Gaussian QML, is proposed. Asymptotic results are established for smooth risk measures, as well as for the Value-at-Risk (VaR). Asymptotic comparisons of the two approaches for VaR estimation suggest a superiority of the one-step method when the innovations are heavy-tailed. For standard GARCH models, the comparison only depends on characteristics of the innovations distribution, not on the volatility parameters. Monte-Carlo experiments and an empirical study illustrate the superiority of the one-step approach for financial series.     

Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator

The goal of this paper is to investigate the repeated substitution method (seeSrivastava, 1967) estimating population variance in finite population sample surveys. We propose an almost unbiased multivariate ratio estimator that has a smaller mean squared error than the conventional biased multivariate ratio estimator (established byIsaki (1983)) and with the same precision as the multivariate regression estimator. Furthermore, it is a computationally much more interesting estimator since to compute it we only need to have knowledge of correlation among available variables, which it is common to have in several practical situations. A comparison of the multivariate ratio estimator proposed and the multivariate regression estimator is given.     

On uniformly minimum variance unbiased estimation when no complete sufficient statistics exist

Summary A simple generalization of the Lehmann-Scheffé theorem is given. It is used to find cases when UMVUE's exist but complete sufficient statistics do not. Another method to find such cases is also presented.