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.     

Bayes estimation of the binomial parameter n

Bayes estimation of the binomial parameter n based on a general prior distribution for n is studied. As special cases improper prior and Poisson prior (which is a natural choice) are considered, and formulae for the marginal and posterior distributions are obtained. It is shown that the assumption of improper priors in both p and n leads to implausible results.     

Third order asymptotics: connections among test quantities

Saddlepoint methods, extended to distribution functions, can provide highly accurate tail probabilities for testing real parameters in exponential models. For extensions, asymptotic connections among various test quantities are needed. For five quantities, the maximum likelihood departure standardized by observed and expected information, the score function standardized by observed and expected information, and the signed square root of the likelihood ratio statistic, the needed connections to third order are recorded. Their use is illustrated by a simple integration proof of the Lugannani and Rice formula.     

A bayesian alternative to the analysis of matched categorical responces

This study investigates the Bayesian appeoach to the analysis of parired responess when the responses are categorical. Using resampling and analytical procedures, inferences for homogeneity and agreement are develped. The posterior analysis is based on the Dirichlet distribution from which repeated samples can be geneated with a random number generator. Resampling and analytical techniques are employed to make Bayesian inferences, and when it is not appropriate to use analytical procedures, resampling techniques are easily implemented. Bayesian methodoloogy is illustrated with several examples and the results show that they are exacr-small sample procedures that can easily solve inference problems for matched designs.     

On a pragmatic modification of survey sampling in three stages

Presented are formulae for an unbiased estimator of a finite population total and an unbiased variance estimator for it when samples are taken by usual procedures in the first two stages with varying probabilities but the third stage units are sampled for economy and convenience in a non-standard way from the pool of all sampled second stage units rather than independently from each of the latter separately containing the former.     

A Variance Estimator for Systematic Sampling from a Deliberately Ordered Population

ABSTRACT

The systematic sampling (SYS) design (Madow and Madow, 1944 Madow , L. H. , Madow , W. G. ( 1944 ). On the theory of systematic sampling . Ann. Math. Statist. 15 : 1 – 24 .[Crossref] , [Google Scholar]) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]) and usual variance estimators (Yates and Grundy, 1953 Yates , F. , Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Roy. Statist. Soc. Series B 1 : 253 – 261 . [Google Scholar]) are inadequate and can overestimate the variance significantly (Särndal et al., 1992 Särndal , C. E. , Swenson , B. , Wretman , J. H. ( 1992 ). Model Assisted Survey Sampling . New York : Springer-Verlag , Ch. 3 .[Crossref] , [Google Scholar]). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.     

Shrinkage of Variance for Minimum Distance Based Tests

This paper promotes information theoretic inference in the context of minimum distance estimation. Various score test statistics differ only through the embedded estimator of the variance of estimating functions. We resort to implied probabilities provided by the constrained maximization of generalized entropy to get a more accurate variance estimator under the null. We document, both by theoretical higher order expansions and by Monte-Carlo evidence, that our improved score tests have better finite-sample size properties. The competitiveness of our non-simulation based method with respect to bootstrap is confirmed in the example of inference on covariance structures previously studied by Horowitz (1998 Horowitz , J. ( 1998 ). Bootstrap methods for covariance structures . The Journal of Human Resources 33 : 39 – 61 .[Crossref], [Web of Science ®] , [Google Scholar]).     

The Fate Worse than Death and other Curiosities and Stupidities

The problem of finding confidence intervals for the success parameter of a binomial experiment has a long history, and a myriad of procedures have been developed. Most exploit the duality between hypothesis testing and confidence regions and are typically based on large sample approximations. We instead employ a direct approach that attempts to determine the optimal coverage probability function a binomial confidence procedure can have from the exact underlying binomial distributions, which in turn defines the associated procedure. We show that a graphical perspective provides much insight into the problem. Both procedures whose coverage never falls below the declared confidence level and those that achieve that level only approximately are analyzed. We introduce the Length/Coverage Optimal method, a variant of Sterne's procedure that minimizes average length while maximizing coverage among all length minimizing procedures, and show that it is superior in important ways to existing procedures.     

A Statistical Reanalysis of the Classical Rutherford's Experiment

Modified chi-squared and some newly developed tests for the Poisson, binomial, and an approximated Feller's distribution are discussed. A reanalysis of the classical Rutherford's experimental data on alpha decay is done. Previous analyses of the data were not correct from the point of view of the theory of statistical testing. Tests used show that the data contradict to both Poisson and binomial distribution and do not contradict to a precise “binomial” approximation of Feller's distribution that takes into account a counter's dead time. This gives a plausible statistically correct confirmation of the well-established exponential law of radioactive decay.