The Theory and Applications of Statistical Interference Functions

1. Front Matter

   Pages i-vi

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2. Introduction

   • D. L. McLeish, Christopher G. Small

   Pages 1-12

3. The Space of Inference Functions: Ancillarity, Sufficiency and Projection

   • D. L. McLeish, Christopher G. Small

   Pages 13-36

4. Selecting an Inference Function for 1-Parameter Models

   • D. L. McLeish, Christopher G. Small

   Pages 37-56

5. Nuisance Parameters

   • D. L. McLeish, Christopher G. Small

   Pages 57-73

6. Inference under Restrictions: Least Squares, Censoring and Errors in Variables Techniques

   • D. L. McLeish, Christopher G. Small

   Pages 74-87

7. Inference for Stochastic Processes

   • D. L. McLeish, Christopher G. Small

   Pages 88-112

8. Back Matter

   Pages 113-128

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This monograph arose out of a desire to develop an approach to statistical infer­ ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com­ monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete­ ness into this setting. The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. This is in keeping with our desire to construct a theory that is rich in statistical tools for infer­ ence without the difficulties found in modern developments, such as likelihood analysis of stochastic processes or higher order methods, to name but two. The fundamental notions of orthogonality and projection are accessible to a good undergraduate or beginning graduate student. We hope that the monograph will serve the purpose of enriching the methods available to statisticians of various interests.

• Censoring
• Likelihood
• Martingale
• Median
• Stochastic processes
• stochastic process

• Department of Statistics and Actuarial Science, University of Waterloo, Canada

  D. L. McLeish, Christopher G. Small

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