Constrained Estimation Technique Research Articles

Comparing cross‐country estimates of Lorenz curves using a Dirichlet distribution across estimators and datasets

SummaryChotikapanich and Griffiths (Journal of Business and Economic Statistics, 2002, 20(2), 290–295) introduced the Dirichlet distribution to the estimation of Lorenz curves. This distribution naturally accommodates the proportional nature of income share data and the dependence structure between the shares. Chotikapanich and Griffiths fit a family of five Lorenz curves to one year of Swedish and Brazilian income share data using unconstrained maximum likelihood and unconstrained nonlinear least squares. We attempt to replicate the authors' results and extend their analyses using both constrained estimation techniques and five additional years of data. We successfully replicate a majority of the authors' results and find that some of their main qualitative conclusions also hold using our constrained estimators and additional data.

Comparing Cross-Country Estimates of Lorenz Curves Using a Dirichlet Distribution Across Estimators and Datasets

Chotikapanich and Griffiths (2002) introduced the Dirichlet distribution to the estimation of Lorenz curves. This distribution naturally accommodates the proportional nature of income share data and the dependence structure between the shares. Chotikapanich and Griffiths (2002) fit a family of five Lorenz curves to one year of Swedish and Brazilian income share data using unconstrained maximum likelihood and unconstrained non-linear least squares. We attempt to replicate the authors' results and extend their analyses using both constrained estimation techniques and five additional years of data. We successfully replicate a majority of the authors' results and find that some of their main qualitative conclusions also hold using our constrained estimators and additional data.

Ginisupport vector machines for segmental minimum Bayes risk decoding of continuous speech

We describe the use of support vector machines (SVMs) for continuous speech recognition by incorporating them in segmental minimum Bayes risk decoding. Lattice cutting is used to convert the Automatic Speech Recognition search space into sequences of smaller recognition problems. SVMs are then trained as discriminative models over each of these problems and used in a rescoring framework. We pose the estimation of a posterior distribution over hypotheses in these regions of acoustic confusion as a logistic regression problem. We also show that GiniSVMs can be used as an approximation technique to estimate the parameters of the logistic regression problem. On a small vocabulary recognition task we show that the use of GiniSVMs can improve the performance of a well trained hidden Markov model system trained under the Maximum Mutual Information criterion. We also find that it is possible to derive reliable confidence scores over the GiniSVM hypotheses and that these can be used to good effect in hypothesis combination. We discuss the problems that we expect to encounter in extending this approach to large vocabulary continuous speech recognition and describe initial investigation of constrained estimation techniques to derive feature spaces for SVMs.

Speaker adaptation using combined transformation and Bayesian methods

Adapting the parameters of a statistical speaker independent continuous-speech recognizer to the speaker and the channel can significantly improve the recognition performance and robustness of the system. In continuous mixture-density hidden Markov models the number of component densities is typically very large, and it may not be feasible to acquire a sufficient amount of adaptation data for robust maximum-likelihood estimates. To solve this problem, we have recently proposed a constrained estimation technique for Gaussian mixture densities. To improve the behavior of our adaptation scheme for large amounts of adaptation data, we combine it here with Bayesian techniques. We evaluate our algorithms on the large-vocabulary Wall Street Journal corpus for nonnative speakers of American English. The recognition error rate is approximately halved with only a small amount of adaptation data, and it approaches the speaker-independent accuracy achieved for native speakers.

Speaker adaptation using constrained estimation of Gaussian mixtures

A trend in automatic speech recognition systems is the use of continuous mixture-density hidden Markov models (HMMs). Despite the good recognition performance that these systems achieve on average in large vocabulary applications, there is a large variability in performance across speakers. Performance degrades dramatically when the user is radically different from the training population. A popular technique that can improve the performance and robustness of a speech recognition system is adapting speech models to the speaker, and more generally to the channel and the task. In continuous mixture-density HMMs the number of component densities is typically very large, and it may not be feasible to acquire a sufficient amount of adaptation data for robust maximum-likelihood estimates. To solve this problem, the authors propose a constrained estimation technique for Gaussian mixture densities. The algorithm is evaluated on the large-vocabulary Wall Street Journal corpus for both native and nonnative speakers of American English. For nonnative speakers, the recognition error rate is approximately halved with only a small amount of adaptation data, and it approaches the speaker-independent accuracy achieved for native speakers. For native speakers, the recognition performance after adaptation improves to the accuracy of speaker-dependent systems that use six times as much training data. >

Modelling disaggregated lumber demand and supply by constrained estimation techniques

Constrained estimation techniques were used to estimate a 12-equation demand and supply system for Douglas-fir and hemlock–fir (true fir) lumber by clear and common grades. Such techniques combine sample information with nonsample information and produce estimates with smaller variances than those based only on sample data. Conventional econometric estimation was compared with a quadratic programming technique with regression coefficients constrained to their a priori correct signs. A goal programming technique that minimized the sum of the absolute deviations was rejected because of its substantially different results and lack of information on the statistical properties of its estimates. The quadratic programming technique had the advantages of statistical efficiency, objectivity, and speed. The conventional estimation technique excluded fewer variables from the system and thus was less susceptible to omission of variables bias. Elasticity estimates for most key variables were similar. Quadratic programming versus conventional estimates of demand elasticity were, respectively, −0.95 and −0.88 for Douglas-fir clears, −2.83 and −2.91 for Douglas-fir commons, and −2.13 and −2.27 for all Douglas-fir; whereas supply elasticities for hemlock–fir commons were 1.35 and 1.37, and for all hemlock–fir, −1.76 and −1.42.