Abstract:
F distribution is one of
the most frequently used distributions in statistics. For example, it is used
for testing: equality of variances of two independent normal distributions,
equality of means in the one-way ANOVA setting, overall significance of a normal
linear regression model, and so on. In this paper, a simple chi-square
approximation for the cumulative distribution of the F-distribution is obtained via an adjusted log-likelihood ratio
statistic. This new approximation exhibits remarkable accuracy even when the
degrees of freedom of the F distribution are small.

Abstract:
Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object based on a different number of replicates, the ratio of the variances of the response is then known, and is the ratio of the number of replicates going into each response. A likelihood based method is proposed. Simulation results show that the proposed method is very accurate even when the sample sizes are small. Moreover, the proposed method can be extended to the case that the ratio of the variances is unknown.

Inference for the mean of a normal distribution with known coefficient of variation is of special theoretical interest be- cause the model belongs to the curved exponential family with a scalar parameter of interest and a two-dimensional minimal sufficient statistic. Therefore, standard inferential methods cannot be directly applied to this problem. It is also of practical interest because this problem arises naturally in many environmental and agriculture studies. In this paper we proposed a modified signed log likelihood ratio method to obtain inference for the normal mean with known coeffi- cient of variation. Simulation studies show the remarkable accuracy of the proposed method even for sample size as small as 2. Moreover, a new point estimator for the mean can be derived from the proposed method. Simulation studies show that new point estimator is more efficient than most of the existing estimators.

Abstract:
We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.

Abstract:
In many areas of applied statistics, confidence intervals for the mean of the population are of interest. Confidence intervals are typically constructed as-suming normality although non-normally distributed data are a common occurrence in practice. Given a large enough sample size, confidence intervals for the mean can be constructed by applying the Central Limit Theorem or by the bootstrap method. Another commonly used method in practice is the back-transformation method, which takes on the following three steps. First, apply a transformation to the data such that the transformed data are normally distributed. Second, obtain confidence intervals for the transformed mean in the usual manner, which assumes normality. Third, apply the back- transformation to obtain confidence intervals for the mean of the original, non-transformed distribution. The parametric Wald method and a small sample likelihood-based third order method, which can address non-normality, are also reviewed in this paper. Our simulation results suggest that common approaches such as back-transformation give erroneous and misleading results even when the sample size is large. However, the likelihood-based third order method gives extremely accurate results even when the sample size is small.

Abstract:
An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar parameters of interest of the DAR(1) model. Theoretically, the proposed method has rate of convergence O(n^{-3/2}). Applying the proposed method to a real-life data set shows that the results obtained by the proposed method can be quite different from the results obtained by the existing methods. Results from Monte Carlo simulation studies illustrate the supreme accuracy of the proposed method even when the sample size is small.

Abstract:
Congenital dacryocystoceles with intranasal mucoceles are an uncommon entity. The overwhelming majority of reported cases are unilateral in nature. We present a rare case of a neonate with bilateral congenital dacryocystoceles with intranasal mucoceles. Management of dacryocystoceles includes medical and surgical treatment. Literature review revealed 186 reported cases of congenital dacryocystoceles with 82 associated with intranasal mucoceles. Prevalence rates ranged between 11% to 100%. Our case highlights the importance of nasal endoscopy in the work up and identification given the high prevalence rate of intranasal mucocele component in patients with congenital dacryocystoceles.

Abstract:
Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.

Abstract:
Background: Anaplastic thyroid cancer (ATC), while rare, carries a uniformly poor prognosis. Current treatment includes surgery when possible, radiotherapy, and chemotherapy. Multiple chemotherapeutic agents are in the process of clinical testing, and promising agents include those in the tyrosine kinase inhibitor family. Our patient represents a novel case of ATC treated with sunitinib, one such tyrosine kinase inhibitor. Methods/Results: We utilized the experimental sunitinib in conjunction with radiation therapy to treat a patient with aggressive ATC in whom curative resection was unable to be achieved due to carotid sheath and tracheal involvement. The patient had marked clinical response and sustained stable disease for 8 months, which coincides with reported data regarding sunitinib to treat other thyroid malignancies. Conclusion: Our case illustrates the efficacy of sunitinib therapy as a possible adjunct in the treatment of ATC.

Abstract:
The Sharpe ratio is the prominent risk-adjusted performance measure used by practitioners. Statistical testing of this ratio using its asymptotic distribution has lagged behind its use. In this paper, highly accurate likelihood analysis is applied for inference on the Sharpe ratio. Both the one- and two-sample problems are considered. The methodology has distributional accuracy and can be implemented using any parametric return distribution structure. Simulations are provided to demonstrate the method's superior accuracy over existing methods used for testing in the literature. 1. Introduction The measurement of fund performance is an integral part of investment analysis. Investments are often ranked and evaluated on the basis of their risk-adjusted returns. Several risk-adjusted performance measures are available to money managers of which the Sharpe ratio is the most popular. Introduced by William Sharpe in 1966 [1], this ratio provides a measure of a fund’s excess returns relative to its volatility. Expressed in its usual form, the Sharpe ratio for an asset with an expected return given by and standard deviation given by is given by the following: where is the risk-free rate of return. From this expression, it is clear to see how this ratio provides a measure of a fund’s excess return per unit of risk. The Sharpe ratio has been extensively studied in the literature. The main criticism leveled against this measure concerns its reliance on only the first two moments of the returns distribution. If investment returns are normally distributed then the Sharpe ratio can be justified. On the other hand, if returns are asymmetric then it can be argued that the measure may not accurately describe the fund’s performance as moments reflecting skewness and kurtosis are not captured by the ratio. To address this issue, several measures exist in the literature which integrate higher moments into the performance measure. The Omega measure is one such measure that uses all the available information in the returns distribution. Keating and Shadwick [2] provide an introduction to this measure. While various methods are available, they are also more complex and often very difficult to implement in practice. To gauge the trade-off between the attractiveness of such measures and their cost, Eling and Schuhmacher [3] compared the Sharpe ratio with 12 other approaches to performance measurement. Eling and Schuhmacher [3] focussed on the returns of 2,763 hedge funds. Hedge funds are known to have return distributions which differ significantly from the normal distribution