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## Real Data Example

### Statistical Signal Processing (2012-01-01): 91-99 , January 01, 2012

In this chapter, we analyze four data sets using multiple sinusoidal model. These data sets are namely (i) a segment of ECG signal of a healthy human being, (ii) the well-known variable star data, (iii) a short duration voiced speech signal, the “uuu” data, and (iv) the airline passenger data.

## The Borel-Cantelli Lemma

### The Borel-Cantelli Lemma (2012-01-01): 2 , January 01, 2012

## Designs in the Presence of Trends

### Topics in Optimal Design (2002-01-01) 163: 115-126 , January 01, 2002

*Model:* Fixed effects model for block designs with a first degree trend term specific to every block *Optimality criteria:* Universal optimality (UO) *Major tools:* Semi balanced arrays, Kiefer’s proposition 1 *Optimality results:* Classes of UO designs both within restricted subclasses and within the unrestricted class of designs *Thrust:* Combinatorial arrangement of treatments within each block of a BIBD so that the trend-adjusted *C*-matrix has maximal trace and completely symmetric structure

In this Chapter we consider a model for a block design where in addition to the block and treatment effect parameters, there is a linear trend term specific to every block. We first give designs which are optimal within the class of binary designs or within the class of trend free designs. We also give designs which are optimal within the unrestricted class. In all cases, we obtain trend-adjusted *C*-matrices which are completely symmetric and have maximal trace so that the designs are universally optimal. Semi balanced arrays of Rao are found very useful in this connection.

## OCDs in Balanced Treatment Incomplete Block Design Set-Up

### Optimal Covariate Designs (2015-01-01): 113-130 , January 01, 2015

In this chapter, optimum covariate designs (OCDs) have been considered for the set-up of the balanced treatment incomplete block (BTIB) designs, which form an important class of test-control designs. It is seen that the OCDs depend much on the methods of construction of the basic BTIB designs. The presentation in this chapter closely follows the work of Dutta, Das, J Stat Plan Inference 143:1203–1214, 2013, Dutta and Das (2013) who considered the problem of construction of OCDs on the series of BTIB designs mainly described in Bechhofer, Tamhane, Technometrics 23:45–57, 1981, Bechhofer and Tamhane (1981) and Das, Dey, Kageyama, Sinha, Australas J Combinatorics 32:243–252, 2005, Das et al. (2005).

## Stopping rules, permutation invariance and sufficiency principle

### Annals of the Institute of Statistical Mathematics (1989-03-01) 41: 121-138 , March 01, 1989

In the context of sequential (point as well as interval) estimation, a general formulation of permutation-invariant stopping rules is considered. These stopping rules lead to savings in the ASN at the cost of some elevation of the associated risk—a phenomenon which may be attributed to the violation of the sufficiency principle. For the (point and interval) sequential estimation of the mean of a normal distribution, it is shown that such permutation-invariant stopping rules may lead to a substantial saving in the ASN with only a small increase in the associated risk.

## Modifications of Bayes Procedures

### Topics in Survey Sampling (2001-01-01) 153: 93-129 , January 01, 2001

This chapter considers different modifications of Bayes procedures and their applications in finite population sampling. Section 4.2 reviews Bayes least squares prediction or Linear Bayes prediction. Section 4.3 addresses restricted Bayes least squares prediction. The problem of Constrained Bayes prediction and Limited Translation Bayes prediction have been considered in the next section. Applications of these procedures in finite population sampling have been illustrated in various stages. Section 4.5 considers the robustness of a Bayesian predictor derived under a working model with respect to a class of alternative models as developed by Bolfarine et al (1987). Robust Bayes estimation of a finite population mean under a class of contaminated priors as advocated by Ghosh and Kim (1993, 1997) has been addressed in the last section.

## Analysis of Categorical Data Under Logistic Regression Model

### Complex Surveys (2016-01-01): 157-177 , January 01, 2016

This chapter considers analysis of categorical data under logistic regression models when the data are generated from complex surveys. Section addresses binary logistic regression model due to Roberts et al. (Biometrika 74:1–12, 1987), and finds the pseudo ML estimators of the population parameter along with its asymptotic covariance matrix. The goodness-of-fit statistics
$$X_P^2$$
and
$$G^2$$
, and a Wald statistic have been considered and their asymptotic distributions derived. The modifications of these statistics using Rao-Scott corrections and *F* ratio have been examined. All the above problems have been considered in the light of nested models. We also considered problem of choosing appropriate cell-sample-sizes for running logistic regression program in a standard computer package. Following Morel (Surv Methodol 15:203–223, 1989) polytomous logistic regression has been considered in Sect. . Finally, using empirical logits the model has been converted into general linear model which uses generalized least square procedures for estimation. The model has been extended to accommodate cluster effects and procedures for testing of hypotheses under the extended model investigated.

## On a class of asymptotically optimal nonparametric tests for grouped data I

### Annals of the Institute of Statistical Mathematics (1973-12-01) 25: 91-108 , December 01, 1973

### Summary

Generalizing the results of Sen [8], a class of nonparametric tests for the hypothesis of no regression in the multiple linear regression model is obtained here. The asymptotic power properties of the proposed class of tests are studied, and the asymptotic optimality of the tests is established under the conditions of Wald [10]. Applications of the results are also considered.

## Estimation under two stage random permutation models

### Metrika (1985-12-01) 32: 339-349 , December 01, 1985

### Summary

Estimation of the population mean under assumptions of non-informativeness of labels in a two stage finite population of distinguishable units has been studied. Under the random permutation model, for the two stage set up, sample mean, the natural estimator, is found to be the best.

## Tests of non-monotonic stochastic aging notions in reliability theory

### Statistical Papers (2014-08-01) 55: 691-714 , August 01, 2014

Testing of various classes of life distributions has been a subject of investigation for more than four decades. In this study we restrict ourselves to the problem of testing exponentiality against *non-monotonic aging notions. *We model non-monotonic aging using the notions of *bathtub failure rate*, *increasing and then decreasing mean residual life *and *new worse then better than used in expectation* classes. The different tests of exponentiality against these alternatives are discussed in detail.