Estimation Of Mixing Proportions Research Articles

On Smoothed MWSD Estimation of Mixing Proportion

The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.

A hierarchical model for compositional data analysis

This article introduces a hierarchical model for compositional analysis. Our approach models both source and mixture data simultaneously, and accounts for several different types of variation: these include measurement error on both the mixture and source data; variability in the sample from the source distributions; and variability in the mixing proportions themselves, generally of main interest. The method is an improvement on some existing methods in that estimates of mixing proportions (including their interval estimates) are sure to lie in the range [0, 1]; in addition, it is shown that our model can help in situations where identification of appropriate source data is difficult, especially when we extend our model to include a covariate. We first study the likelihood surface of a base model for a simple example, and then include prior distributions to create a Bayesian model that allows analysis of more complex situations via Markov chain Monte Carlo sampling from the likelihood. Application of the model is illustrated with two examples using real data: one concerning chemical markers in plants, and another on water chemistry.

Estimation of parameters for a mixture of normal distributions on the basis of the cressie and read divergence

The estimation of the five parameters of the mixture of two normal components is studied, with emphasis on the estimation of mixing proportion. The method proposed is based on the power-divergence introduced by Cressie and Read (1984) and Read and Cressie (1988). Computational results compare the efficiency as well as the robustness under symmetric departures from component normality of different members of the family we study. Our results indicate that the member of the family corresponding to the parameter value 2/3 is, for almost all the cases, comparable to the well-known estimators.

Estimation of mixing proportions in the presence of autoregressively correlated training data:the case of two univariate normal populations

This paper considers the estimation of mixing proportions when, in addition to the mixture sample, there are available autoregressively dependent data of known origin from each of the classes which make up the mixture population. An asymptotic variance of the usual discriminant analysis (or confusion matrix) estimator of the mixing proportion is obtained under this condition of correlated training data. The maximum likelihood estimator of the mixing proportion and the associated asymptotic variance are also obtained. A simulation experiment is used to investigate the behaviour of these estimators

Bayes estimates of mixing proportions in finite mixture distributions

With reference to the problem of estimating the mixing proportions in a finite mixture distribution with known components, employing Dirichlet prior, closed form expressions for the posterior means and variances are obtained. To avoid the difficulties in computing the estimates, an approximation procedure is introduced. Numerical studies carried out for normal mixtures indicate the closeness of the approximations and their superiority over the maximum likelihood estimates at least in the case of small samples.

Identification of Sockeye Salmon (Oncorhynehus nerka) Stocks in Mixed-stock Fisheries in British Columbia and Southeast Alaska using Biological Markers

We demonstrate the present analytical capability and the potential for coast-wide stock identification of sockeye salmon (Oncorhynchus nerka) using reference sampling data from 51 principal stocks in British Columbia and Southeast Alaska situated between the Fraser and Taku Rivers. We evaluate the relative accuracy and precision of stock composition estimates from maximum likelihood mixture analysis with four types of biological markers, either alone or in combination; these include freshwater age, six scale pattern variables, the prevalence of the brain parasite Myxobolus neurobius, and five biochemical genetic (electrophoretic) traits. Using all markers in combination, estimates of mixing proportions for all test mixtures are acceptable for most purposes (roughly ± 10% with 95% confidence) providing all samples are representative and mixture samples are large ([Formula: see text] fish). The reliability of these estimates is greatly reduced when reference samples are corrupted to simulate observed annual variation in scale pattern markers. Annual variation may preclude the use of scale pattern markers for complicated stock identification problems where representative reference samples cannot be obtained annually, or until after the fishing period. In contrast, no significant annual variation is detectable for biochemical genetic and brain parasite markers in stocks that have been sampled repeatedly. Using only these stable markers, contributions from about 15 different groups of the 51 stocks can be estimated with acceptable precision, but in general, estimates for individual stocks are unreliable.

A Comparison of Minimum Distance and Maximum Likelihood Estimation of a Mixture Proportion

Abstract The estimation of mixing proportions in the mixture model is discussed, with emphasis on the mixture of two normal components with all five parameters unknown. Simulations are presented that compare minimum distance (MD) and maximum likelihood (ML) estimation of the parameters of this mixture-of-normals model. Some practical issues of implementation of these results are also discussed. Simulation results indicate that ML techniques are superior to MD when component distributions actually are normal, but MD techniques provide better estimates than ML under symmetric departures from component normality. Interestingly, an ad hoc starting value for the iterative procedures occasionally outperformed both the ML and MD techniques. Results are presented that establish strong consistency and asymptotic normality of the MD estimator under conditions that include the mixture-of-normals model. Asymptotic variances and relative efficiencies are obtained for further comparison of the MD and ML estimators.

A Comparison of Minimum Distance and Maximum Likelihood Estimation of a Mixture Proportion

Abstract The estimation of mixing proportions in the mixture model is discussed, with emphasis on the mixture of two normal components with all five parameters unknown. Simulations are presented that compare minimum distance (MD) and maximum likelihood (ML) estimation of the parameters of this mixture-of-normals model. Some practical issues of implementation of these results are also discussed. Simulation results indicate that ML techniques are superior to MD when component distributions actually are normal, but MD techniques provide better estimates than ML under symmetric departures from component normality. Interestingly, an ad hoc starting value for the iterative procedures occasionally outperformed both the ML and MD techniques. Results are presented that establish strong consistency and asymptotic normality of the MD estimator under conditions that include the mixture-of-normals model. Asymptotic variances and relative efficiencies are obtained for further comparison of the MD and ML estimators.

Estimation of Mixing Proportions: A Case Study

Observations are taken from a mixture of several populations and the problem is to estimate the unknown mixing proportions on the basis of this sample which is unclassified; that is, it is not known to which population an observation belongs. There are reference data of known origin available separately from each of the populations for the purposes of estimation of the unknown population parameters. Two approaches to this problem are illustrated by the presentation of a case study involving an unclassified sample of n = 1107 four-dimensional observations taken from a mixture of seven populations. The usefulness of atypicality indices for assessing whether an unclassified observation comes from one of the specified populations is exhibited.

Estimation of mixing proportions via distance between characteristic functions

The weighted and integrated squared error between the sample characteristic function and the assumed characteristic function is shown to be an effective procedure for estimation of mixing proportions. For a particular form of the weighting, this procedure is equivalent to that of minimization with respect to the mixing proportions of the integrated squared error between a density and its kernel estimate. The efficiency, mean squared error, and ease of computation properties of this procedure are compared against those of several competitors.

The Estimation of Mixing Proportions by Double Sample Using Bulk Measurement

The Estimation of Mixing Proportions by Double Sample Using Bulk Measurement

The Estimation of Mixing Proportions by Double Sample Using Bulk Measurement

The estimation of category proportions in a population consistSing of a mixtrne of categories is considered by double sampling. Large sample formulae are developed for the combination of information from one sample consisting of items for which a brrlk measurement only is available and the other which has individual items measured and categorized. It is shown, both by making simplifying assumptions, and by computer simulation that the asymptotic formulae are applicable over a wide range of parameter values.