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Principles of Mathetmatical Analysis. 3rd. edition.
The Principles of Mathematical Analysis by Rudin, Walter [McGraw-Hill Publish...
Hardcover
Published January 1, 1976
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October 31, 2025Econometrics-Bruce Hansen
This textbook is the first in a two-part series covering the core material typically taught in a one-year Ph.D.
course in econometrics. The sequence is
1. Probability and Statistics for Economists (this volume)
2. Econometrics (the next volume).
The textbooks are written as an integrated series, but either can be used as a standalone course textbook.
This first volume covers intermediate-level mathematical statistics. It is a gentle yet a rigorous treatment
using calculus but not measure theory. The level of detail and rigor is similar to that of Casella and Berger(2002) and Hogg and Craig (1995). The material is explained using examples at the level of Hogg and Tanis(1997) and is targeted to students of economics. The goal is to be accessible to students with a variety ofbackgrounds and yet maintain full mathematical rigor.
Readers who desire a gentler treatment may try Hogg and Tanis (1997). Readers who desire more detailare urged to read Casella and Berger (2002) or Shao (2003). Readers wanting a measure-theoretic foundation in probability should read Ash (1972) or Billingsley (1995). For advanced statistical theory, see van derVaart (1998), Lehmann and Casella (1998), and Lehmann and Romano (2005), each of which has a differentemphasis. Mathematical statistics textbooks with similar goals as this textbook include Ramanathan (1993),Amemiya (1994), Gallant (1997), and Linton (2017).
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It is also highly recommended, but not necessary, to have studied mathematical analysis and/or a “prove it” mathematics course. The language of probability and statistics is mathematics. To understand the concepts,you need to derive the methods from their principles. This is different from introductory statistics, whichunfortunately often emphasizes memorization. By taking a mathematical approach, little memorization isneeded. Instead, such an approach requires a facility with detailed mathematical derivations and proofs. Thereason it is recommended to have studied mathematical analysis is not that we will be using such results. Thereason is that the method of thinking and proof structures are similar. We start with the axioms of probability
and build the structure of probability theory from these axioms. Once probability theory is built, we construct statistical theory on that base. A timeless introduction to mathematical analysis is Rudin (1976). For those wanting more, Rudin (1987) is recommended.
This textbook is the first in a two-part series covering the core material typically taught in a one-year Ph.D.
course in econometrics. The sequence is
1. Probability and Statistics for Economists (this volume)
2. Econometrics (the next volume).
The textbooks are written as an integrated series, but either can be used as a standalone course textbook.
This first volume covers intermediate-level mathematical statistics. It is a gentle yet a rigorous treatment
using calculus but not measure theory. The level of detail and rigor is similar to that of Casella and Berger(2002) and Hogg and Craig (1995). The material is explained using examples at the level of Hogg and Tanis(1997) and is targeted to students of economics. The goal is to be accessible to students with a variety ofbackgrounds and yet maintain full mathematical rigor.
Readers who desire a gentler treatment may try Hogg and Tanis (1997). Readers who desire more detailare urged to read Casella and Berger (2002) or Shao (2003). Readers wanting a measure-theoretic foundation in probability should read Ash (1972) or Billingsley (1995). For advanced statistical theory, see van derVaart (1998), Lehmann and Casella (1998), and Lehmann and Romano (2005), each of which has a differentemphasis. Mathematical statistics textbooks with similar goals as this textbook include Ramanathan (1993),Amemiya (1994), Gallant (1997), and Linton (2017).
-
It is also highly recommended, but not necessary, to have studied mathematical analysis and/or a “prove it” mathematics course. The language of probability and statistics is mathematics. To understand the concepts,you need to derive the methods from their principles. This is different from introductory statistics, whichunfortunately often emphasizes memorization. By taking a mathematical approach, little memorization isneeded. Instead, such an approach requires a facility with detailed mathematical derivations and proofs. Thereason it is recommended to have studied mathematical analysis is not that we will be using such results. Thereason is that the method of thinking and proof structures are similar. We start with the axioms of probability
and build the structure of probability theory from these axioms. Once probability theory is built, we construct statistical theory on that base. A timeless introduction to mathematical analysis is Rudin (1976). For those wanting more, Rudin (1987) is recommended.
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