Grkpack fitting smoothing spline anova models for exponential families

Wahba, Wang, Gu, Klein and Klein introduced Smoothing Spline ANalysis of VAriance (SS ANOVA) method for data from exponential families. Based on RKPACK, which fits SS ANOVA models to Gaussian data, we introduce GRKPACK a collection of Fortran subroutines for binary, binomial, Poisson and Gamma data. We also show how to calculate Bayesian confidence intervals for SS ANOVA estimates.     

Estimation for the generalized pareto distribution with censored data

We present a methodology for computing the point and interval maximum likelihood parameter estimation for the two-parameter generalized Pareto distribution (GPD) with censored data. The basic idea underlying our method is a reduction of the two-dimensional numerical search for the zeros of the GPD log-likelihood gradient vector to a one-dimensional numerical search. We describe a computationally efficient algorithm which implement this approach. Two illustrative examples are presented. Simulation results indicate that the estimates derived by maximum likelihood estimation are more reliable against those of method of moments. An evaluation of the practical sample size requirements for the asymptotic normality is also included.     

On a conjecture concerning the least favorable configuration of a two-stage selection procedure

A two-stage procedure 𝓅with screening in the first stage to find the population with the largest mean out of k ≧ 2 normal populations with unknown means and a common variance is under concern. It was proposed and previousiy studied by Cohen (1959), Alam (1970) and Tamhane and Bechhofer (1977, 1979) using the indifference-zone approach. The conjecture that the least favourable parameter configuration for the probability of a correct selection is of the slippage type remained unproved for k ≧ 3. Miescke and Sehr (1980) proved the conjecture for k=3. The problem was further discussed by Gupta and Miescke (1982). A general proof for rhe conjecture will be given in this paper.     

The essentially complete class of rules in multinomial identification

The problem of identification within two groups is considered, when the space 𝔛 of the possible values of the observed random variable X is finite. Using an essentially complete class of tests hypothesis ξ=0 (ξis real) for the multivariate exponential family, an essentially complete class of sample-based identification rules has been found. Comparison of the rules to those derived from density estimators has shown that the latter constitute a subclass of the former.     

A note on the estimation of the mixing parameter in a mixture of two distributions

Various classical methods of estimation are compared with those proposed by From (1989) for the estimation of the mixing parameter in a mixture of two distributions. Emphasis is put on the actual implementation of the estimation methods.     

Estimation of harmonic component in regression with cyclically dependent errors

This paper deals with the estimation of hidden periodicities in a non-linear regression model with stationary noise displaying cyclical dependence. Consistency and asymptotic normality are established for the least-squares estimates.     

On selecting populations better than a control: weibull populations case

Consider k( k ≥ 1) independent Weibull populations and a control population which is also Weibull. The problem of identifying which of these k populations are better than the control using shape parameter as a criterion is considered. We allow the possibility of making at most m(0 ≤ m < k) incorrect identifications of better populations. This allowance results in significant savings in sample size. Procedures based on simple linear unbiased estimators of the reciprocal of the shape parameters of these populations are proposed. These procedures can be used for both complete and Type II-censored samples. A related problem of confidence intervals for the ratio of ordered shape parameters is also considered. Monte Carlo simulations as well as both chi-square and normal approximations to the solutions are obtained.     

两类较为精确半离散非齐次核逆向的Hilbert不等式

应用权函数的方法及改进的Euler-Maclaurin求和公式,建立两个具有最佳常数因子的、较为精确的、半离散非齐次核逆向的Hilbert不等式,并考虑了它们的等价形式.     

On optimal tests for separate hypotheses and conditional probability integral transformations

Consider the problem of testing the composite null hypothesis that a random sample X₁,…,X_n is from a parent which is a member of a particular continuous parametric family of distributions against an alternative that it is from a separate family of distributions. It is shown here that in many cases a uniformly most powerful similar (UMPS) test exists for this problem, and, moreover, that this test is equivalent to a uniformly most powerful invariant (UMPI) test. It is also seen in the method of proof used that the UMPS test statistic Is a function of the statistics U₁,…,U_n?k obtained by the conditional probability integral transformations (CPIT), and thus that no Information Is lost by these transformations, It is also shown that these optimal tests have power that is a nonotone function of the null hypothesis class of distributions, so that, for example, if one additional parameter for the distribution is assumed known, then the power of the test can not lecrease. It Is shown that the statistics U₁, …, U_n?k are independent of the complete sufficient statistic, and that these statistics have important invariance properties. Two examples at given. The UMPS tests for testing the two-parameter uniform family against the two-parameter exponential family, and for testing one truncation parameter distribution against another one are derived.     

The noncentral bivariate chisquared distribution and extensions

The distribution of certain correlated noncentral chisquared variates P, Q, is termed the noncentral bivariate chisquared distribution. Moment generating functions of the distributions of (P, Q), (P+Q) and other quadratic forms have been obtained. A relationship to the linear case of the noncentral Wishart distribution is indicated. Convolution properties and applications are presented.