1 Preliminary Notions.- 1.1 Introduction.- 1.2 Sufficiency.- 1.3 Complete Sufficient Statistics.- 1.4 Exponential Families of Distributions.- 1.5 Invariance.- 1.6 Maximum Likelihood Estimation.- 1.7 Unbiased 1.8 Least Squares 1.9 Interval Exercises.- 2 Notions in significance testing hypotheses.- 2.1 2.2 Test Statistics and Variables.- 2.3 Definition p-Value.- 2.4 Generalized Ratio Method.- 2.5 Invariance Significance Testing.- 2.6 Unbiasedness Similarity.- 2.7 Estimation Fixed-Level 3...

By taking a generalized approach to findingp values, the classical F-test of one-way ANOVA is extended case unequal error variances. The relationship this result other solutions in literature discussed. An exact test for comparing variances number populations also developed. Scheff6's procedure multiple comparison possibility and that one can take extend results simple designs involving more than factor are briefly

Abstract The definition of a confidence interval is generalized so that problems such as constructing exact regions for the difference in two normal means can be tackled without assumption equal variances. Under certain conditions, extended shown to preserve repeated sampling property practitioner expects from intervals. proposed procedure also applied problem intervals exponential and variance components mixed models. A p values given. With this characterization one carry out fixed level...

We consider the stress-strength problem in which a unit of strength X is subjected to environmental stress Y. An important reliability concerns testing hypotheses about parameter R = P[X > yl. In this article, we situations and Y are independent have normal distributions or can be transformed normality. do not require two population variances equal. Our approach leads test statistics exact p values that represented as one-dimensional integrals. On basis value, one also construct approximate...

On obtient un test exact, similaire a celui de Chow (1960), qui comporte une simple integration unidimensionnelle

SUMMARY A solution is proposed to the problem of finding ajoint decision procedure for a group n persons. It any Pareto optimal which maximizes generalized Nash product over set jointly achievable utility n-vectors. This result was originally in theory bargaining but readily adapted statistical context. The individuals involved need not have identical functions or prior (posterior) distributions. may be non-randomized rule randomized when individual opinions preferences are sufficiently...

Motivated by the serious Type-I error issues of widely used Cox-PH method in survival analysis, this article introduces an approach one can take deriving superior parametric tests based on distributions such as gamma, lognormal, and Weibull. Some data available from are allowed to be censored, usually case dealing with lifetime distributions. Since classical fails provide reasonable procedures test equality means a number Weibull populations, beyond two populations case, we will show how...

Abstract A procedure for testing one-sided hypotheses on variance components in a balanced random effects model is developed. The performed the basis of generalized p value and involves one-dimensional numerical integration. In special case which conventional methods provide an exact test, this test equivalent to usual F test. also Bayes sense that, under certain diffuse prior, numerically same as posterior probability null hypothesis.

We consider repeated observations taken over time for each of several subjects. For example, one might the growth curve a cohort babies time. assume simple linear model. Exact results based on sufficient statistics (exact tests null hypothesis that coefficient is zero, or exact confidence intervals coefficients) are not available to make inference regression coefficients when an intraclass correlation structure assumed. This paper will demonstrate such possible using generalized inference.

This work provides the elements of a framework for multi-Bayesian statistical decision theory. Solution concepts and criteria are presented. The relationship to Wald's theory is discussed. And two assessing group procedures defined. One based on idea subsampling group, it found that among proposed solution only Nash's optimal under as well. other assumes itself sample from superpopulation, this yields an analogue where elicitation priors becomes part experimental process. Results...

Motivated by poor performance of standard estimation methods in our application, the problem modeling diffusion a new service (or product) is considered without assumption homogeneous population. The model consists two-stage procedure where customers receive purchase occasions according to conventional and at each occasion they buy binary choice model. This approach permits explicit incorporation individual customer demographics product attributes, whence one can study changes as function...

Motivated by a number of drawbacks classical methods point estimation, we generalize the definitions and address such notions as unbiasedness estimation under constraints. The utility extension is shown deriving more reliable estimates for small coefficients regression models, variance components random effects mixed models. in spirit generalized confidence intervals introduced Weerahandi (1993 , S. ( 1993 ). Generalized . J. Amer. Statist. Assoc. 88 : 899 – 905 .[Taylor & Francis Online],...

In this article we derive two simple tests for two-way ANOVA under unequal variances requiring some constraints, which cannot be solved by classical regression formulas. We do so taking the generalized p-value approach and provide explicit formulas to handle constraints. The first test is an extension of fiducial one-way test, tends assure intended size but conservative, second reduces that drawback, may slightly exceed test. also a numerically equivalent parametric bootstrap (PB) contains...

Abstract We consider the problem of finding posterior probabilities ellipsoids for difference between two multivariate normal means. do not require population covariance matrices to be equal, therefore, our results pertain Behrens—Fisher problem. A Hotelling T 2-like quantity is defined, and its cdf expressed as a linear combination cdf's some F distributions. This representation enables us compute desired exactly using only one-dimensional numerical integrations. The calculation can easily...

The authors consider the diffusion of a service when customers can switch among competing offerings service. Explicit formulas for brand switching and adoption probabilities are obtained in terms customer characteristics, marketing strategies, product attributes. procedure fitting model with survey data is illustrated by telecommunications application. useful identifying target markets demand forecasting.

Inference for structural parameters that are common to several regressions is a frequent problem of statistical practice. In the unlikely case residual error variances equal all regressions, inference usually has closed–form solution within standard regression framework. unequal and unknown variances, falls into category Behrens-Fisher problems. This article describes comprehensive this using concept generalized p value introduced by Tsui Weerahandi in 1989. An example investigating effect...