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## A Model of Aging and a Shape of the Observed Force of Mortality

### Lifetime Data Analysis (2003-03-01) 9: 93-109 , March 01, 2003

A probabilistic model of aging is considered. It is based on the assumption that a random resource, a stochastic process of aging (wear) and the corresponding anti-aging process are embedded at birth. A death occurs when the accumulated wear exceeds the initial random resource. It is assumed that the anti-aging process decreases wear in each increment. The impact of environment (lifestyle) is also taken into account. The corresponding relations for the observed and the conditional hazard rate (force of mortality) are obtained. Similar to some demographic models, the deceleration of mortality phenomenon is explained via the concept of frailty. Simple examples are considered.

## An alternative to model selection in ordinary regression

### Statistics and Computing (2003-02-01) 13: 67-80 , February 01, 2003

The weaknesses of established model selection procedures based on hypothesis testing and similar criteria are discussed and an alternative based on synthetic (composite) estimation is proposed. It is developed for the problem of prediction in ordinary regression and its properties are explored by simulations for the simple regression. Extensions to a general setting are described and an example with multiple regression is analysed. Arguments are presented against using a selected model for any inferences.

## Constructional Approaches and Methods

### Block Designs: A Randomization Approach (2003-01-01) 170: 1-62 , January 01, 2003

As already mentioned in the Preface to Volume I, and then detailed in its Section 1.5, in Volume II of this monograph constructional aspects of suitable designs are to be discussed, particularly with regard to some statistical concepts essential for planning of experiments. In the present chapter various methods of constructing designs will be described, along with some combinatorial and statistical properties of block designs, mainly those related to the efficiency factors of the design for estimating the corresponding basic contrasts in the intra-block analysis, as defined in Section 3.4. In general, the classification of block designs adopted here is based on the new terminology proposed in Section 4.4 (see, in particular, Definition 4.4.2). It may be helpful to recall it shortly.

## Perfect simulation for Reed-Frost epidemic models

### Statistics and Computing (2003-02-01) 13: 37-44 , February 01, 2003

The Reed-Frost epidemic model is a simple stochastic process with parameter *q* that describes the spread of an infectious disease among a closed population. Given data on the final outcome of an epidemic, it is possible to perform Bayesian inference for *q* using a simple Gibbs sampler algorithm. In this paper it is illustrated that by choosing latent variables appropriately, certain monotonicity properties hold which facilitate the use of a perfect simulation algorithm. The methods are applied to real data.

## Density estimation for a class of stationary nonlinear processes

### Annals of the Institute of Statistical Mathematics (2003-03-01) 55: 69-82 , March 01, 2003

Let {*X*_{t};*t*∈ℤ be a strictly stationary nonlinear process of the form*X*_{t}=ε_{t}+∑
_{r=1}^{∞}*W*_{rt}, where*W*_{rt} can be written as a function*g*_{r}(ε_{t−1},...ε_{t-r-q}), {ε_{t};*t*∈ℤ is a sequence of independent and identically distributed (*i.i.d.*) random variables with*E*|ε_{1}|^{g} < ∞ for some γ>0 and*q*≥0 is fixed integer. Under certain mild regularity conditions of*g*_{r} and {ε_{t}} we then show that*X*_{1} has a density function*f* and that the standard kernel type estimator
$$\hat f_n (x)$$
baded on a realization {*X*_{1},...,*X*_{n}} from {*X*_{t}} is, asymptotically, normal and converges a.s. to*f(x)* as*n→∞*.

## Second-Order Properties

### Resampling Methods for Dependent Data (2003-01-01): 145-173 , January 01, 2003

In this chapter, we consider second-order properties of block bootstrap estimators for estimating the sampling distribution of a statistic of interest. The basic tool for studying second-order properties of block bootstrap distribution function estimators is based on the theory of Edgeworth expansions.

## Asymptotic equivalence of the jackknife and infinitesimal jackknife variance estimators for some smooth statistics

### Annals of the Institute of Statistical Mathematics (2003-09-01) 55: 555-561 , September 01, 2003

The jackknife variance estimator and the infinitesimal jackknife variance estimator are shown to be asymptotically equivalent if the functional of interest is a smooth function of the mean or a trimmed L-statistic with Hölder continuous weight function.

## On influence diagnostic in univariate elliptical linear regression models

### Statistical Papers (2003-01-01) 44: 23-45 , January 01, 2003

We discuss in this paper the assessment of local influence in univariate elliptical linear regression models. This class includes all symmetric continuous distributions, such as normal, Student-t, Pearson VII, exponential power and logistic, among others. We derive the appropriate matrices for assessing the local influence on the parameter estimates and on predictions by considering as influence measures the likelihood displacement and a distance based on the Pearson residual. Two examples with real data are given for illustration.

## Confidence Sets

### Mathematical Statistics (2003-01-01): 471-542 , January 01, 2003

Various methods of constructing confidence sets are introduced in this chapter, along with studies of properties of confidence sets. Throughout this chapter *X* = (*X*_{1}, …,*X*_{n}) denotes a sample from a population *P* ∈ *P*; θ = θ(*P*) denotes a functional from *P* to Θ ⊂ *R*^{k} for a fixed integer *k*; and *C*(*X*) denotes a *confidence set* for θ, a set in ß_{Θ} (the class of Borel sets on Θ) depending only on *X*. We adopt the basic concepts of confidence sets introduced in §2.4.3. In particular, inf_{P∈P}*P*(θ ∈ *C*(*X*)) is the confidence coefficient of *C*(*X*) and, if the confidence coefficient of *C*(*X*) is ≥ 1- α for fixed α ∈ (0, 1), then we say that *C*(*X*) has significance level 1-α or *C*(*X*) is a level 1 - α confidence set.