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Summary: This paper is concerned with the formulation of N$$ N $$‐mixture models for estimating the abundance and probability of detection of a species from binary response, count and time‐to‐detection data. A modelling framework, which encompasses time‐to‐first‐detection within the context of detection/non‐detection and time‐to‐each‐detection and time‐to‐first‐detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed‐form expressions for the likelihoods associated with time‐to‐detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times‐to‐detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times‐to‐detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times‐to‐detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice. [ABSTRACT FROM AUTHOR]

Response-adaptive randomization procedures are appropriate for clinical trials in which two or more treatments are to be compared, patients arrive sequentially and the response of each patient is recorded before the next patient arrives. However, for those procedures that involve sequential estimation of model parameters, start-up designs are commonly required in order to provide initial estimates of the parameters. In this paper, a suite of such start-up designs for two treatments and binary patient responses are considered and compared in terms of the numbers of patients required in order to give meaningful parameters estimates, the number of patients allocated to the better treatment, and the bias in the parameter estimates. It is shown that permuted block designs with blocks of size 4 are to be preferred over a wide range of parameter values. For the case of two treatments, normal responses and selected start-up procedures, a design incorporating complete randomization followed appropriately by repeats of one of the treatments yields the minimum expected number of patients and is to be preferred. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Testing for purchasing power parity (PPP) and uncovered interest parity (UIP) has been the focus of many empirically oriented studies. While these simple economic theories of exchange rate and interest rate determination are theoretically attractive, the empirical support for these equilibrium conditions is at best mixed. Many potential reasons have been cited in the literature for the failure of such studies, ranging from market imperfections to inappropriate modelling strategies. The current state-of-the-art procedure involves testing for two cointegrating vectors in a multivariate error correction model which may be economically identified as the PPP and UIP relations. However, such a procedure does not account for policy regime shifts which distort the underlying PPP and UIP relations. In this paper, a Markov-switching vector error correction model (VECM) is considered for time series data in which monetary and exchange rate regime shifts are known to be present. Weak evidence in favour of PPP and UIP is established in a standard linear VECM, although the residuals of this model indicate that it is inappropriate in terms of functional form. The Markov-switching VECM, however, provides convincing evidence in favour of both the PPP and UIP relations and a marked improvement in the residual distributions. [ABSTRACT FROM AUTHOR]

The article discusses a study which considered a problem of constructing standardized maximin D-optimal design for weighted polynomial regression models. The researchers showed that the maximum designs can be obtained as weak limits of the corresponding Bayesian designs, and that they are more broadly applicable to certain families of nonlinear models. Two specific weighted polynomial models are examined and the results are examined through weighted quadratic regression model and Bleasdale-Nelder model.

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