On estimating the box-cox transformation to normality

This paper studies four methods for estimating the Box-Cox parameter used to transform data to normality. Three of these are based on optimizing test statistics for standard normality tests (the Shapiro-Wilk. skewness, and kurtosis tests); the fourth uses the maximum likelihood estimator of the Box-Cox parameter. The four methods are compared and evaluated with a simulation study, where their performances under different skewness and kurtosis conditions are analyzed. The estimator based on optimizing the Shapiro-Wilk statistic generally gives rise to the best transformations, while the maximum likelihood estimator performs almost as well. Estimators based on optimizing skewness and kurtosis do not perform well in general.     

Exact tests for equality of two proportions: fisher v. bayes

Yates (1984) using theoretical and philosophical arguments claims to have proved that the Fisher exact test for comparing the proportions of two binomial experiments is the best exact test. The present article uses objective and practical arguments to confront the Fisher exact test with a Bayes exact test. Using simulated samples we claim to have proved here the inferiority of the Fisher exact test in relation to a Bayes exact test. The comparison is based on the quality concept of Dawid (1982).     

General saddlepoint approximations and normalizing transformations for multivariate statistics

The use of general saddlepoint approximations is investigated for the problem of approximating the tail probabilities of statistics in multivariate analysis. A method based on normalizing transformations is proposed to prevent po¬tential deficiencies in general saddlepoint approximations. The efficiency of the proposed method is illustrated through examples of the sample correlation     

More on the estimation of box-cox transformation

The behavior of the Box-Cox estimate of power transformation is further examined. Through the asymptotic expansions and small-σ approximations, the exact nature of dependence of transformation estimation on the model structure, the spread of the means and the error variance is revealed. The results are shown to be useful in assessing what Box and Cox called transformation potential of a particular data set.     

A Comparison of the Cost-efficiencies of the Sequential, Group-sequential, and Variable-sample-size-sequential Probability Ratio Tests

Wald and Wolfowitz (1948) have shown that the Sequential Probability Ratio Test (SPRT) for deciding between two simple hypotheses is, under very restrictive conditions, optimal in three attractive senses. First, it can be a Bayes-optimal rule. Second, of all level α tests having the same power, the test with the smallest joint-expected number of observations is the SPRT, where this expectation is taken jointly with respect to both data and prior over the two hypotheses. Third, the level α test needing the fewest conditional-expected number of observat ions is the SPRT, where this expectation is now taken with respect to the data conditional on either hypothesis being true. Principal among the strong restrictions is that sampling can proceed only in a one-at-a-time manner. In this paper, we relax some of the conditions and show that there are sequential procedures that strictly dominate the SPRT in all three senses. We conclude that the third type of optimality occurs rarely and that decision-makers are better served by looking for sequential procedures that possess the first two types of optimality. By relaxing the one-at-a-time sampling restriction, we obtain optimal (in the first two senses) variable-s ample-size- sequential probability ratio tests.     

Multivariate thin plate spline estimates for the posterior probabilities in the classification problem

A nonparametric estimate for the posterior probabilities in the classification problem using multivariate thin plate splines is proposed. This method presents a nonpararnetric alternative to logistic discrimination as well as to survival curve estimation. The degree of smoothness of the estimate is determined from the data using generalized crossvalidation.     

A ratio-of-uniforms method for generating exponential power variates

A ratio-of-uniforms method of generating exponential power variates is presented. It is compared to an established generalized rejection method developed by Tadikamalla (1980) and shown to be faster and more easily implemented.     

Error rates for poisson process discrimination

This research addresses the question of how one's ability to discriminate between two Poisson process models is affected by the relative behavior of the respective intensity functions involved. One sampling strategy studied involves observation of the process up to the k-th occurrence time, t_k. Another is to observe the process up to a fixed time T. The error probabilities for these two approaches are analyzed as k and T, respectively, tend to infinity.     

A class of simple approximate sequential tests for adaptive comparison of two treatments

We consider the problem of sequentially deciding which of two treatments is superior, A class of simple approximate sequential tests is proposed. These have the probabilities of correct selection approximately independent of the sampling rule and depending on unknown parameters only through the function of interest, such as the difference or ratio of mean responses. The tests are obtained by using a normal approximation, and this is employed to derive approximate expressions for the probabilities of correct selection and the expected sample sizes. A class of data-dependent sampling rules is proposed for minimizing any weighted average of the expected sample sizes on the two treatments, with the weights being allowed to depend on unknown parameters. The tests are studied in the particular cases of exponentially.     

A simple alternative to the likelihood ratio test in a logistic discrimination problem

We consider the problem of hypothesis-testing under a logistic model with two dichotomous independent variables. In particular, we consider the case in which the coefficients β₁, and β₂ of these variables are known on an a priori basis to not be of opposite sign. For this situation we show that there exists a simple nonparametric altenative to the likelihood ratio test for testing H₀: β₁ = β₂ = 0 VS.H₁ at least one β₁ = 0. We find the asympotic relative efficiency of this test and show that it exceeds 0.90 under a wide range of conditions. We also given an example.     

Measure of Asymmetry for Square Contingency Tables Having Ordered Categories

For the analysis of square contingency tables with nominal categories, Tomizawa and coworkers have considered measures that represent the degree of departure from symmetry. This paper proposes a measure that represents the degree of asymmetry for square contingency tables with ordered categories (instead of those with nominal categories). The measure proposed is expressed using the Cressie–Read power-divergence or Patil–Taillie diversity index, defined for the cumulative probabilities that an observation falls in row (column) category i or below and column (row) category j (> i ) or above. The measure depends on the order of listing the categories. It should be useful for comparing the degree of asymmetry in several tables with ordered categories. The relationship between the measure and the normal distribution is shown.     

An alternative local polynomial estimator for the error-in-variables problem

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle et al. [(2009), ‘A Design-adaptive Local Polynomial Estimator for the Errors-in-variables Problem’, Journal of the American Statistical Association, 104, 348–359] as a benchmark, we propose an alternative way of solving the problem without transforming the kernel function. The asymptotic properties of the alternative estimator are rigorously studied. A detailed implementing algorithm and a computationally efficient bandwidth selection procedure are also provided. The proposed estimator is compared with the existing local polynomial estimator via extensive simulations and an application to the motorcycle crash data. The results show that the new estimator can be less biased than the existing estimator and is numerically more stable.     

Unified Conditional Frequentist and Bayesian Testing of Composite Hypotheses

Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data. The resulting tests are also seen to be Bayesian tests, in the strong sense that the reported frequentist error probabilities are also the posterior probabilities of the hypotheses under default choices of the prior distribution. The new procedures are illustrated in a variety of applications to model selection and multivariate hypothesis testing.     

Bootstrap for finite populations

The bootstrap method is compared with the classical (linearization) and jackknife procedures for estimating the mean square errors (MSEs) of the ratio estimator and the combined ratio estimator. The initial samples are considered to be selected without replacement, and different procedures for selecting the bootstrap samples with or without replacement from them are examined. The biases, stabilities, coverage probabilities and confidence widths of all the procedures are compared.     

Estimation of error rate in multiple group logistic discrimination. the approximate leaving-one-out method

We present an approximate leaving-one-out technique for estimating the error rate in logistic discrimination. The new measure is based on the one-step approximation of a(i), the maximum likelihood estimate of the parameter vector based on the sample without the ith case. Some inequalities between the resubstitution error rate, the approximate and exact leaving-one-out error rates for the multiple group logistic model are investigated. Monte-Carlo simulations assess the adequacy of the approximate leaving-one-out method as an estimate of the actual error rate. The usefulness of this approach is demonstrated by means of two medical examples.     

On the connection between orthant probabilities and the first passage time problem

This article describes a new Monte Carlo method for the evaluation of the orthant probabilities by sampling first passage times of a non-singular Gaussian discrete time-series across an absorbing boundary. This procedure makes use of a simulation of several time-series sample paths, aiming to record their first crossing instants. Thus, the computation of the orthant probabilities is traced back to the accurate simulation of a non-singular Gaussian discrete-time series. Moreover, if the simulation is also efficient, this method is shown to be speedier than the others proposed in the literature. As example, we make use of the Davies–Harte algorithm in the evaluation of the orthant probabilities associated to the ARFIMA(0, d, 0) model. Test results are presented that compare this method with currently available software.     

Local Weighted Average Estimation of the Regression Operator for Functional Data

We are concerned with the problem of local weighted average estimation of the regression operator when the responses are real-valued random variables, the explanatory data are of functional fixed-design type, and the errors consist of an independent and identically distributed variables. In this article, our main contributions on the local linear functional estimation concern from one part, the situation when the data are of functional fixed-design kind, and from the other part, in deriving uniform asymptotic results on the behavior of this estimator with respect to the topological properties of the space data (normed or semi-metric).     

Effect of dimensionality on discrimination

Discrimination problems in a high-dimensional setting is considered. New results are concerned with the role of the dimensionality in the performance of the discrimination procedure. Assuming that data consist of a block structure two different asymptotic approaches are presented. These approaches are characterized by different types of relations between the dimensionality and the size of the training samples. Asymptotic expressions for the error probabilities are obtained and a consistent approximation of the discriminant function is proposed. Throughout the paper the importance of the dimensionality in the asymptotic analysis is stressed.     

On discrimination procedure with mixtures of continuous and categorical variables

A discrimination procedure, based on the location model is described and suggested for use in situation where the discriminating variables are mixtures of continuous and binary variables. Some procedures that have been previously employed, in a similar situation, like Fisher's linear discriminant function and the logistic regression were compared with this method using error rate (ER). Optimal ERs for these procedures are reported using real and simulated data for the case of varying sample size and number of continuous and binary variables and were used as a measure for assessing the performance of the various procedures. The suggested procedure performed considerably better in the cases considered and never did produce a result that is poor when compared with other procedures. Hence, the suggested procedure might be considered for such situations.     

An empirical investigation of the box-cox model and a nonlinear least squares alternative

In this paper we present a generalized functional form estimator, recently developed by jeffrey Wooldridge; and then we compare it empirically to the popular Box-Cox (BC) estimator using three data sets. We begin by briefly reviewing the drawbacks of the BC estimator. We Then introduce the nonlinear lest squares (NLS) alternative of Wooldridge which retains the desirable qualities of the BC estimator without the associated theoretical problems. We continue by applying both the BC and the NLS models to data from three classic hedonic regression studies and then compare the estimation resuts-point estimates, inferences and fitted values. The estimations include a wage rate equation, and two computer hedonic regression equations, one using data from a classic study by Gregory Chow and the other using an IBM data set that formed the basis of the new official BLS computer price index.