Richard (Dick) Dykstra in 2011
Professor Emeritus Richard (Dick) Lynn Dykstra passed away peacefully on September 19, 2025. Dick received his PhD in 1968 from the University of Iowa, where his doctoral work on characterizing a conditional expectation with respect to a sigma-lattice was advised by Tim Robertson and Jon Cryer. Dick then worked at University of Missouri, Columbia, first as an assistant professor and became a full professor there in 1981. In 1982, he returned to the University of Iowa as a full professor in the Department of Statistics and Actuarial Science until his retirement in 2012.
Dick made significant contributions to several areas, including probability, mathematical statistics, nonparametric inference, multivariate theory, and constrained optimization. Of particular note are his deep and fundamental contributions to order restricted inference. Many interesting problems in order restricted inference can be posed as constrained optimization problems subject to convex cone constraints. These problems often do not have closed-form solutions. Dick developed several useful and efficient algorithms for solving such constrained optimization problems. Dykstra’s algorithm, with variants for other settings including Hilbert space, is now a classic optimization technique. Dick invented it for solving the general problem of least squares regression subject to finitely many closed convex-cone constraints. Dykstra’s algorithm assumes that the problem has a tractable solution if it were subject to only one (any one) of the convex-cone constraints – the solution is then simply obtained by projecting the response vector into the convex cone under consideration. The solution to the easier problem subject to one constraint can be expressed as the sum of the response plus an increment vector specific to that convex cone. Dykstra’s algorithm alternately updates the increment vectors one constraint at a time, until convergence. Dick’s proof of the validity of the algorithm is a tour de force. Dick co-wrote a monograph on order restricted inference and co-edited conference proceedings, with Tim Robertson and Farroll T. Wright.
He and Robertson ran a seminar on order restricted inference almost every semester until their retirement, which covered hot research topics at the time. The seminars were always well attended by graduate students and faculty members. They also organized at least three conferences on order restricted inference. Because of Dick Dykstra and Tim Robertson and the strong faculty interest in order restricted inference, the department enjoyed the presence of many visiting scholars as they came to Iowa City to collaborate with Dick and Tim.
Dick was the department chair from 1989-92. As department chair, he hired several faculty members – including Martin Appel, Kung-Sik Chan, Elias Shiu, Bruce Jones, Joseph Lang, and Jens Praestgaard — some of whom have played leadership roles in the department. Even though it was a short three years, his steady leadership and vision during those years cemented the strength of the department to this day.
Dick was an outstanding teacher. He put in extra efforts teaching students. Besides regular class meeting times, he held a weekly problem session for many of his classes, in which he worked lots of problems for the students, and sometimes discussed relevant topics not covered in class; he referred to the latter as “and sometimes digress to statistical topics not covered in class,” in his understated mannerism. The extra problem sessions were not required but almost the whole class would show up. He undertook these extra works willingly because he loved teaching and because he wanted to help students realize “that knowledge and understanding usually only come with lots of hard work and perseverance.”
Dick was born on October 19, 1942. He grew up on a farm in Runnels, Iowa. Dick is survived by his wife Patricia Dykstra. Pat and Dick were high-school sweethearts. They married in 1964, and raised four children and fostered many others, creating a home filled with love and laughter.
Dick was athletic. He played football at Central College, during his undergraduate studies. He was selected as an All-State running back/defensive back three times. He was a co-captain of the football team in his senior year that went on to capture the league title. He was also an all-league selection in baseball. Dick was inducted into Central College’s Athletics Hall of Honor in 2003.
We’ll always remember Dick as a kind person, generous with his time and freely sharing his insights with students and colleagues, a penetrating yet humble thinker. His legacy will live on through the many lives he touched.
Written by Kung-Sik Chan