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Full-Text Articles in Econometrics
Optimal Nonparametric Range-Based Volatility Estimation, Tim Bollerslev, Jia Li, Qiyuan Li
Optimal Nonparametric Range-Based Volatility Estimation, Tim Bollerslev, Jia Li, Qiyuan Li
Research Collection School Of Economics
We present a general framework for optimal nonparametric spot volatility estimation based on intraday range data, comprised of the first, highest, lowest, and last price over a given time-interval. We rely on a decision-theoretic approach together with a coupling-type argument to directly tailor the form of the nonparametric estimator to the specific volatility measure of interest and relevant loss function. The resulting new optimal estimators offer substantial efficiency gains compared to existing commonly used range-based procedures.
Posterior-Based Wald-Type Statistic For Hypothesis Testing, Xiaobin Liu, Yong Li, Jun Yu, Tao Zeng
Posterior-Based Wald-Type Statistic For Hypothesis Testing, Xiaobin Liu, Yong Li, Jun Yu, Tao Zeng
Research Collection School Of Economics
A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as MCMC output) is available, …
A Posterior-Based Wald-Type Statistic For Hypothesis Testing, Yong Li, Xiaobin Liu, Tao Zeng, Jun Yu
A Posterior-Based Wald-Type Statistic For Hypothesis Testing, Yong Li, Xiaobin Liu, Tao Zeng, Jun Yu
Research Collection School Of Economics
A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a χ2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">χ2 …
A Bayesian Chi-Squared Test For Hypothesis Testing, Yong Li, Xiaobin Liu, Jun Yu
A Bayesian Chi-Squared Test For Hypothesis Testing, Yong Li, Xiaobin Liu, Jun Yu
Research Collection School Of Economics
A new Bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss. The proposed test statistic may be regarded as the Bayesian version of the Lagrange multiplier test. Its asymptotic distribution is obtained based on a set of regular conditions and follows a chi-squared distribution when the null hypothesis is correct. The new statistic has several important advantages that make it appealing in practical applications. First, it is well-defined under improper prior distributions. Second, it avoids Jeffrey-Lindley's paradox. Third, it always takes a non-negative value and is relatively easy to compute, even for models …
A New Approach To Bayesian Hypothesis Testing, Yong Li, Tao Zeng, Jun Yu
A New Approach To Bayesian Hypothesis Testing, Yong Li, Tao Zeng, Jun Yu
Research Collection School Of Economics
In this paper a new Bayesian approach is proposed to test a point null hypothesis based on the deviance in a decision-theoretical framework. The proposed test statistic may be regarded as the Bayesian version of the likelihood ratio test and appeals in practical applications with three desirable properties. First, it is immune to Jeffreys’ concern about the use of improper priors. Second, it avoids Jeffreys–Lindley’s paradox, Third, it is easy to compute and its threshold value is easily derived, facilitating the implementation in practice. The method is illustrated using some real examples in economics and finance. It is found that …
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Research Collection School Of Economics
Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on the decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function. …
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Research Collection School Of Economics
Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is easy to interpret and appropriately defined under improper priors because the method employs a …
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Research Collection School Of Economics
Hypothesis testing using Bayes factors (BFs) is known to suffer from several problems in the context of latent variable models. The first problem is computational. Another problem is that BFs are not well defined under the improper prior. In this paper, a new Bayesian method, based on decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss …
A Bayesian Decision Approach For Sample Size Determination In Phase Ii Trials, Denis H. Y. Leung, You-Gan Wang
A Bayesian Decision Approach For Sample Size Determination In Phase Ii Trials, Denis H. Y. Leung, You-Gan Wang
Research Collection School Of Economics
Stallard (1998, Biometrics54, 279–294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics50, 337–349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or …
Uncertainty And Policy Agressiveness, Douglas Steigerwald, Roger Craine
Uncertainty And Policy Agressiveness, Douglas Steigerwald, Roger Craine
Douglas G. Steigerwald
How should a decision maker proceed with uncertain knowledge of the decision outcome? We use the unknown coefficient control problem to shed light on the issue.