Detection and correction of artificial shifts in climate series

Summary.  Many long instrumental climate records are available and might provide useful information in climate research. These series are usually affected by artificial shifts, due to changes in the conditions of measurement and various kinds of spurious data. A comparison with surrounding weather-stations by means of a suitable two-factor model allows us to check the reliability of the series. An adapted penalized log-likelihood procedure is used to detect an unknown number of breaks and outliers. An example concerning temperature series from France confirms that a systematic comparison of the series together is valuable and allows us to correct the data even when no reliable series can be taken as a reference.     

Interpreting DNA Mixtures with Related Contributors in Subdivided Populations

Abstract.  In this paper, we study the statistical interpretation of forensic DNA mixtures with related contributors in subdivided populations. Compact general formulae for match probabilities are obtained for two situations: a relative of one tested person is an unknown contributor of a DNA mixture; and two related unknowns are contributors. The effect of kinship and population structure is illustrated using a real case example.     

Estimating the First- and Second-Order Parameters of a Heavy-Tailed Distribution

This paper suggests censored maximum likelihood estimators for the first‐ and second‐order parameters of a heavy‐tailed distribution by incorporating the second‐order regular variation into the censored likelihood function. This approach is different from the bias‐reduced maximum likelihood method proposed by Feuerverger and Hall in 1999. The paper derives the joint asymptotic limit for the first‐ and second‐order parameters under a weaker assumption. The paper also demonstrates through a simulation study that the suggested estimator for the first‐order parameter is better than the estimator proposed by Feuerverger and Hall although these two estimators have the same asymptotic variances.     

Interval estimation for log-linear models with one variable subject to non-ignorable non-response

Summary.  Log-linear models for multiway contingency tables where one variable is subject to non-ignorable non-response will often yield boundary solutions, with the probability of non-respondents being classified in some cells of the table estimated as 0. The paper considers the effect of this non-standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator. The first method relies on the estimator being approximately normally distributed with variance equal to the inverse of the information matrix. It is shown that the information matrix is singular for boundary solutions, but intervals can be calculated after a simple transformation. For the second method, based on the bootstrap, asymptotic results suggest that the coverage properties may be poor for boundary solutions. Both methods are compared with profile likelihood intervals in a simulation study based on data from the British General Election Panel Study. The results of this study indicate that all three methods perform poorly for a parameter of the non-response model, whereas they all perform well for a parameter of the margin model, irrespective of whether or not there is a boundary solution.     

Adjusted empirical likelihood models with estimating equations for accelerated life tests

This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.     

Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference

In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a logistic distribution. The use of these relations in a systematic manner allows us to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R₁,…,R_m). The results established here generalize the corresponding results for the usual order statistics due to [Shah, 1966] and [Shah, 1970]. These moments are then utilized to derive best linear unbiased estimators of the location and scale parameters of the logistic distribution. A comparison of these estimators with the maximum likelihood estimations is then made. The best linear unbiased predictors of censored failure times are briefly discussed. Finally, an illustrative example is presented.     

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented.     

Exponential tilt models for two-group comparison with censored data

We study application of the Exponential Tilt Model (ETM) to compare survival distributions in two groups. The ETM assumes a parametric form for the density ratio of the two distributions. It accommodates a broad array of parametric models such as the log-normal and gamma models and can be sufficiently flexible to allow for crossing hazard and crossing survival functions. We develop a nonparametric likelihood approach to estimate ETM parameters in the presence of censoring and establish related asymptotic results. We compare the ETM to the Proportional Hazards Model (PHM) in simulation studies. When the proportional hazards assumption is not satisfied but the ETM assumption is, the ETM has better power for testing the hypothesis of no difference between the two groups. And, importantly, when the ETM relation is not satisfied but the PHM assumption is, the ETM can still have power reasonably close to that of the PHM. Application of the ETM is illustrated by a gastrointestinal tumor study.     

Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

On some mixture models based on the Birnbaum-Saunders distribution and associated inference

In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) distribution, viz., (1) mixture of two different BS distributions, (2) mixture of a BS distribution and a length-biased version of another BS distribution, and (3) mixture of a BS distribution and its length-biased version. For all these models, we study their characteristics including the shape of their density and hazard rate functions. For the maximum likelihood estimation of the model parameters, we use the EM algorithm. For the purpose of illustration, we analyze two data sets related to enzyme and depressive condition problems. In the case of the enzyme data, it is shown that Model 1 provides the best fit, while for the depressive condition data, it is shown all three models fit well with Model 3 providing the best fit.