Comparison of the effectiveness of forecasts obtained by means of selected probability functions with respect to forecast error distributions

The forecasting of sales in a company is one of the crucial challenges that must be faced. Nowadays, there is a large spectrum of methods that enable making reliable forecasts. However, sometimes the nature of time series excludes many well-known and widely used forecasting methods (e.g., econometric models). Therefore, the authors decided to forecast on the basis of a seasonally adjusted median of selected probability distributions. The obtained forecasts were verified by means of distributions of the Theil U² coefficient and unbiasedness coefficient.     

The neyman accuracy and the wolfowitz accuracy of the stein type confidence interval for the disturbance variance

In this paper we consider the Neyman accuracy and the Wolfowitz accuracy of the Stein type improved confidence interval I?_S for the disturbance variance in a linear regression model. The Neyman accuracy is a measure related to the unbiasedness of a confidence interval, and the Wolfowitz accuracy is related to the closeness of the endpoints to the true parameter. We show that I?_S is not unbiased and give some numerical results for the Neyman accuracy. As for the Wolfowitz accuracy we derive the sufficient condition for I?_S to improve on the usual confidence interval under this criterion and show numerically that a large degree of improvement can be obtainted.     

COMBINING TWO UNBIASED ESTIMATORS OF A COMMON MEAN OF TWO NORMAL POPULATIONS

Consider estimating the common mean μ of two normal populations. Let () and () be the means and variances of two independent samples obtained from these populations. We give sufficient conditions for the choices of α₁ and α₂ in the unbiased estimator     

Interaction Between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach

In applied econometrics, we tend to tackle specification problems one at a time rather than considering them jointly. This has serious consequences for statistical inference. One example of this is considering autocorrelation and autoregressive conditional heteroscedasticity (ARCH) separately. In this article we consider a linear regression model with random coefficient autoregressive disturbances that provides a convenient framework to analyze autocorrelation and ARCH simultaneously. Our stationarity conditions and testing results reveal the strong interaction between ARCH and autocorrelation. An empirical example of testing the unbiasedness of experts' expectations of inflation demonstrates that neglecting conditional heteroscedasticity or misspecifying the autocorrelation structure might result in unreliable inference.     

Unbiased Estimator for a Covariance Matrix Under Two-Step Monotone Incomplete Sample

In this article, we consider an inference for a covariance matrix under two-step monotone incomplete sample. The maximum likelihood estimator of the mean vector is unbiased but that of the covariance matrix is biased. We derive an unbiased estimator for the covariance matrix using some fundamental properties of the Wishart matrix. The properties of the estimators are investigated and the accuracies are checked by a numerical simulation.     

Monotonicity and unbiasedness of tests via a. S,constructions

It is shown that the coupling of distributions by their quantile transforms leads to simple and unifying proofs of monotonicity and unbiasedness properties of tests in many nonparametric testing problems     

A new ranked set sample estimator of variance

Summary. We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.     

A Note on the Hartley-Ross Unbiased Ratio Estimator

In this article, we will construct an alternative Hartley-Ross unbiased ratio estimator for the population mean of a study variable when related auxiliary information is available. We will also present some efficiency comparisons and related results and give a numerical illustration.     

A Simulation Study of White's Test for Heteroskedasticity in Fixed and Stochastic Regression Models

We study the finite-sample properties of White's test for heteroskedasticity in fixed and stochastic regression models. We compare by simulation White and bootstrap methods when the underlying distribution is symmetric as well as asymmetric. The superior performance of the bootstrap method in small samples does not hold when the underlying distribution is asymmetric.     

Estimation of finite population parameters with several realizations

Consider a finite population of size N with T possible realizations for each population unit. In reality the realizations may represent temporal, geographic or physical variations of the population unit. The paper provides design-based unbiased estimates for several population parameters of interest. Both simple random sampling and stratified sampling are considered. Some comparisons are given. An empirical study is also included with natural population data.