Query: hogg and tanis' probability and statistical inference

title: Probability and Statistical Inference
abstract: Probability and Statistical Inference. By Robert V. Hogg and Elliot A. Tanis. New York,  1977. ix, 450 p. 24 cm. PS11*25.

title: Probability and Statistical Inference

title: Probability and Statistical Inference. Ed.9

title: Probability and Statistical Inference.

title: A Brief Course in Mathematical Statistics
abstract: Preface 1. Probability 1.1 Basic Concepts 1.2 Methods of Enumeration 1.3 Conditional Probability 1.4 Independent Events 1.5 Bayes's Theorem Chapter One Comments 2. Discrete Distributions 2.1 Discrete Probability Distributions 2.2 Expectations 2.3 Special Discrete Distributions 2.4 Estimation 2.5 Linear Functions of Independent Random Variables 2.6 Multivariate Discrete Distributions Chapter Two Comments 3. Continuous Distributions 3.1 Descriptive Statistics and EDA 3.2 Continuous Probability Distributions 3.3 Special Continuous Distributions 3.4 The Normal Distribution 3.5 Estimation in the Continuous Case 3.6 The Central Limit Theorem 3.7 Approximations for Discrete Distributions Chapter Three Comemnts 4. Applications of Statistical Inference 4.1 Summary of Necessary Theoretical Results 4.2 Confidence Intervals Using X2 F,and T 4.3 Confidence Intervals and Tests of Hypotheses 4.4 Basic Tests Concerning One Parameter 4.5 Tests of the Equality of Two Parameters 4.6 Simple Linear Regression 4.7 More on Linear Regression 4.8 One Factor Analysis of Variance 4.9 Distribution Free Confidence and Tolerance Intervals 4.10 Chi Square Goodness of Fit Tests 4.11 Contingency Tables Chapter Four Comments 5. Computer Oriented Techniques 5.1 Computation of Statistics 5.2 Computer Algebra Systems 5.3 Simulation 5.4 Resampling Chapter Five Comments 6. Some Sampling Distribution Theory 6.1 Moment Generation Function Technique 6.2 M.G.F of Linear Functions 6.3 Limiting Moment Generating Functions 6.4 Use of Order Statistics in Non regular Cases Chapter Six Comments

title: Probability and statistical inference by Robert V. Hogg and Elliot A. Tanis

title: Probability and statistical inference Robert V. Hogg, Elliot A. Tanis

title: Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models
abstract: It is a well established fact that testing a null hypothesis on the boundary of the parameter space, with an unknown number of nuisance parameters at the boundary, is infeasible in practice in the sense that limiting distributions of standard test statistics are non pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly mulitiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in finite order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive finite sample properties both under the null and under the alternative hypothesis.

title: Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models
abstract: It is a well established fact that testing a null hypothesis on the boundary of the parameter space, with an unknown number of nuisance parameters at the boundary, is infeasible in practice in the sense that limiting distributions of standard test statistics are non pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly mulitiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in ?nite order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive ?nite sample properties both under the null and under the alternative hypothesis.

title: Intra and Interspecific Abundance of Birds Affects Detection of Novel Food Sources by Great Tits Parus major
abstract: Unpredictable resources in seasonal environments may favour innovative individuals that efficiently explore and exploit such resources. We tested the hypothesis that potential intraspecific abundance is a more powerful predictor of detection of a novel food source than interspecific abundance and predation risk. The hypothesis was tested using latency of Great Tits Parus major to find bird feeders in relation to the abundance of Great Tit and other birds, as well as cats recorded close to novel feeders in urban and rural habitats. Data were collected during winter 2013/2014 in eight cities and nearby rural areas across Poland. Generalized linear models, multimodel inference and hierarchical partitioning showed that the probability that Great Tits used a novel birdfeeder was positively correlated both with the number of Great Tits and all other tits combined in the vicinity of feeders. Latency in feeder usage was negatively related to the number of conspecifics, and it was less strongly negatively related to the number of other tits and the abundance of all other species. The effect of the number of other tits interacted with the environment; the number of tits positively correlated with latency in rural areas, while this relationship was negative in urban areas. Latency until arrival at a feeder was shorter for males than for females. The effect of cats at feeders on bird behaviour was statistically non significant. Thus, latency until arrival at novel birdfeeders was predicted by local population size and abundance of other bird species, but not mammalian predators, and this relationship may be altered by the environment.