A modified optimal orthogonal new additive model

ABSTRACT

In this article, a new randomized response model has been proposed. The proposed model is found to be more efficient than the randomized response models studied by Singh (2010 Singh, S. (2010). Proposed optimal orthogonal new additive model (POONAM). Statistica. Anno LXX(1):73–81. [Google Scholar]). The relative efficiency of the proposed model has been studied with respect to the Singh (2010 Singh, S. (2010). Proposed optimal orthogonal new additive model (POONAM). Statistica. Anno LXX(1):73–81. [Google Scholar]) model. Numerical illustrations are also given in support of the present study.     

Semiparametric estimator for a secondary analysis with correlated outcomes

ABSTRACT

Researchers are often required to reuse data that have been collected and analyzed for other purposes. Issues may arise if the outcome of this secondary study is related to the outcome of the first study and traditional methods may fail to deliver a consistent estimate. Here we propose a semiparametric approach that takes this correlation into account and produces asymptotically consistent and normally distributed estimates. We discuss its performance through simulations and apply the proposed method to a real dataset.     

Sequential order statistics from dependent random variables

Abstract

This paper provides an extension for “sequential order statistics” (SOS) introduced by Kamps. It is called “developed sequential order statistics” (DSOS) and is useful for describing lifetimes of engineering systems when component lifetimes are dependent. Explicit expressions for the joint density function, the marginal distributions and the means of DSOS are derived. Under the well known “conditional proportional hazard rate” (CPHR) model and the Gumbel families of copulas for dependency among component lifetimes, some findings are reported. For example, it is proved that the joint density functions of DSOS and SOS have the same structure. Various illustrative examples are also given.     

Multiple nonlinear regression of the Markovian arrival process for estimating the daily global solar radiation

Abstract

Solar radiation is a global ecological phenomenon that affects life everywhere. In this study, a new statistical method, called the Quartiles-Moment's method, is proposed to estimate the scale and shape parameters of the exponentiated Gumbel maximum distribution (EGMD). The Kolomogorov–Smirnov test and the percentiles of the dataset are thus used to fit the dataset of the daily global solar radiation and the corresponding daily maximum temperature with EGMD. Thence, multiple nonlinear regression of the daily global solar radiation and the corresponding daily maximum temperature are produced and compared with the real dataset accordingly.     

Estimation of the parameters of a regression model with a multivariate t error variable

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.     

L1 for the simple linear regression model

By modifying the direct method to solve the overdetermined linear system we are able to present an algorithm for L₁ estimation which appears to be superior computationally to any other known algorithm for the simple linear regression problem.     

A note on stratification and gain in precision in estimating diversity from large samples

Several indices of entropy have been suggested in the literature as weighted diversity measures of a population with respect to a classification process. Among them, Shannon's entropy and Havrda -Charvát's non-additive entropies of order a, have been exhaustively used.

When the population is finite but too large to be censused, the diversity with respect to a given classification process must be estimated from a sample.

In this note, on the basis of an asymptotic study of the sample indices in the stratified random sampling, we are going to confirm that when we deal with large samples one can guarantee a gain in precision from stratified random over simple random sampling. This gain becomes considerable when the ‘inaccuracy" (as intended by Kerridge and Rathie and Kannapan) between the frequency vector in each stratum and that in the whole population, varies greatly from stratum to stratum.     

Estimation of gene/haplotype frequencies in genetic marker systems based on phenotype data

Two equivalent methods (gene counting and maximum likelihood) for estimating gene frequencies in a general genetic marker system based on observed phenotype data are derived. Under the maximum likelihood approach, an expression is given for the estimated covariance matrix from which estimated standard errors of the estimators can be found. In addition, consideration is given to the problem of estimating gene frequencies when there are available several independent population data sets.